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oliveirabruno01

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intersection-count-pixmap-CoT

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Here's an image. My task is to find intersections or areas where lines come close together. These zones are intriguing. I bet there's something interesting happening within them. <!-- image --> ```palette Key,Color ,#fefefeff a,#b7d24bff b,#318b2eff c,#b1d7b1ff d,#62a660ff e,#e2edcfff f,#cbdf87ff g,#94c794ff ``` ```image cg gbbd bbbb cbbbb bbbbbe ebbbbbd bbbbbbb bbbdbbb dbbb bbbe bbbd bbbg gbbb bbbb bbbb gbbb cbbbe bbb bbbb bbbg ebbbc bbbb bbbb gbbb cggggggggggggggggggggggbbbg ebbb gcccccccccccccccccccccbbbb bbbc gccccccccccccccccccccbbbbd bbbd gcccccccccccccccccccbbbbd dbbb gccccccccccccccccccbbbbb cbbb gcccccccccccccccccbbbbbg bbbe gccccccccccccccccbbbbbcg bbbd gcccccccccccccccbbbbbccg bbbbb eaaafgccccccccccccccbbbbbcccg ebbbbbe eaaaaaaafcccccccccccbbbbbccccg ebbbbbd eaaaaaaaaaaaacccccccbbbbbcccccg bbbbbb faaaaaaaaaaaaaaaacccbbbbbccccccg cbbbbbg aaaaae gaaaaaaaaaabbbbbcccccccg bbbbbb aaaaae gcccaaaaaabbbbbfcccccccg gbbbbb aaaaa gccccccaabbbbbaaaafccccg bbb eaaaaa gcccccccbbbbbaaaaaaaafcg de faaaaa gccccccbbbbbcfaaaaaaaaaaf faaaaf gcccccbbbbbcccccfaaaaaaaaaafe aaaaae gccccbbbbbcccccccccfaaaaaaaaaaae aaaaa gcccbbbbbccccccccccccccaaaaaaaaaaae aaaaa gccbbbbbcccccccccccccccg faaaaaaaaaae eaaaaa gcbbbbbccccccccccccccccg faaaaaaaaaaf faaaaa gbbbbbcccccccccccccccccg faaaaaaaaaa faaaaf bbbbbccccccccccccccccccg eaaaaaaaf aaaaae bbbbbcccccccccccccccccccg eaaaaf aaaaa bbbbbccccccccccccccccccccg aaaa aaaaa bbbbbcccccccccccccccccccccg faaa eaaaaa bbbbbccccccccccccccccccccccg faaa faaaaf bbbbb faaa faaaaf dbbbb eaaa aaaaae dbbbb eaaa aaaaa dbbbb aaa aaaaa dbbbb aaa eaaaaa dbbbb aaa faaaaf dbbbb aaa faaaaf dbbbb aaae faaaae dbbbb aaae aaa dbbbb aaaf a dbbbb aaaf dbbbb aaaf dbbbb aaaa dbbbb faaa dbbbb faaa dbbbb faaa gbbbbe eaaa gbbbbe eaaa gbbbbe aaa gbbbbe aaa gbbbbe aaa gbbbbe aaa gbbbbe aaae gbbbbe aaae cbbbbe aaaf cbbbbe aaaf cbbbbe aaaf cbbbbe aaaa cbbbbc faaa cbbbbc faaa cbbbbc faaa cbbbbc eaaa ebbbbc eaaa bbbc aaa bc aaa aaa aaa aaae ``` <!-- end of image --> Let's see if area A yields any clues. <!-- image --> ```palette Key,Color ,#fefefeff a,#b7d24bff b,#328b2fff c,#b5d5b4ff d,#8bba42ff e,#e1edd2ff f,#d3e392ff g,#8cbe8aff ``` ```image b gb gbb gbbb gbbbb gbbbbb gbbbbbb gbbbbbbb gbbbbbbbb gbbbbbbbbb gbbbbbbbbbe gbbbbbbbbbe gbbbbbbbbbe gbbbbbbbbbe gbbbbbbbbbe gbbbbbbbbbe e gbbbbbbbbbe aafe gbbbbbbbbbe aaaaafe gbbbbbbbbbe aaaaaaaafe gbbbbbbbbbe aaaaaaaaaaafe gbbbbbbbbbe aaaaaaaaaaaaaaff cbbbbbbbbbe aaaaaaaaaaaaaaaaaafe cbbbbbbbbbe aaaaaaaaaaaaaaaaaaaaafecbbbbbbbbbe efaaaaaaaaaaaaaaaaaaadbbbbbbbbbe efaaaaaaaaaaaaaaadbbbbbbbbbe effaaaaaaaaaadbbbbbbbbbae efaaaaaadbbbbbbbbbdaaaff efaadbbbbbbbbbdaaaaaaaafe gbbbbbbbbbdaaaaaaaaaaaafe cbbbbbbbbbdaaaaaaaaaaaaaaaafe cbbbbbbbbbdaaaaaaaaaaaaaaaaaaaaf cbbbbbbbbbc efaaaaaaaaaaaaaaaaaaa cbbbbbbbbbc ffaaaaaaaaaaaaaaa cbbbbbbbbbc efaaaaaaaaaaaa cbbbbbbbbbc efaaaaaaaaa cbbbbbbbbbc efaaaaaa cbbbbbbbbbc efaaa cbbbbbbbbbc ef cbbbbbbbbbc ebbbbbbbbbc ebbbbbbbbbc ebbbbbbbbbc ebbbbbbbbbc ebbbbbbbbbc ebbbbbbbbbc ebbbbbbbbbc bbbbbbbbbc bbbbbbbbc bbbbbbbg bbbbbbg bbbbbg bbbbg bbbg bbg ``` <!-- end of image --> I observe 1 intersection inside area A. Answer: A: 1; 1 = 1 The image features one single intersection point.

<!-- image --> ```palette Key,Color ,#fefefeff a,#b7d24aff b,#318b2eff c,#c9dfb1ff d,#5aa258ff e,#e6f0d3ff f,#cade7cff g,#8ebf8dff ``` ```image cg gbbd bbbb cbbbb bbbbbc ebbbbbd bbbbbbb bbbdbbb dbbb bbbe bbbd bbbg gbbb bbbb bbbb gbbb cbbbe bbb bbbb bbbg ebbbc bbbb bbbb gbbb bbbg ebbb bbbb bbbc bbbbg bbbd bbbbd dbbb bbbbd cbbb bbbbd bbbe bbbbd bbbd bbbbd dbbbb eaaac bbbbb ebbbbbe eaaaaaaaf bbbbb ebbbbbd caaaaaaaaaaaf bbbbb dbbbbb faaaaaaaaaaaaaaafe bbbbb cbbbbbg aaaaae eaaaaaaaaaabbbbb bbbbbb aaaaae efaaaaabbbbbe gbbbbb aaaaa fabbbbbaaaac bbb eaaaaa bbbbbaaaaaaaaf dc caaaaf bbbbb caaaaaaaaaaf faaaaf bbbbb eaaaaaaaaaafe aaaaae bbbbb eaaaaaaaaaaae aaaaae bbbbb efaaaaaaaaaae aaaaa bbbbb faaaaaaaaaac eaaaaa bbbbb faaaaaaaaaac caaaaf bbbbb caaaaaaaaaa faaaaf bbbbb caaaaaaaf aaaaae bbbbb eaaaaf aaaaa bbbbb aaaa aaaaa bbbbb faaa eaaaaa bbbbb faaa caaaaf dbbbb caaa faaaaf dbbbb eaaa aaaaae dbbbb eaaa aaaaa dbbbb aaa aaaaa dbbbb aaa eaaaaa dbbbb aaa caaaaf dbbbb aaae faaaac dbbbb aaae faaaae dbbbb aaac aaa dbbbb aaac a dbbbb aaaf dbbbb aaaf dbbbb aaaa dbbbb faaa gbbbb faaa gbbbbe caaa gbbbbe eaaa gbbbbe eaaa gbbbbe aaa gbbbbe aaa gbbbbe aaa gbbbbe aaa gbbbbe aaae gbbbbe aaae gbbbbe aaac cbbbbe aaaf cbbbbc aaaf cbbbbc aaaa cbbbbc faaa cbbbbc faaa cbbbbc caaa cbbbbc eaaa cbbbbc eaaa bbbc aaa bc aaa aaa aaa aaae ``` <!-- end of image -->

This is the image I'm working with. The goal is to count the intersections. I wonder what's going on inside those areas? Perhaps intersections are hiding there. <!-- image --> ```palette Key,Color ,#fefefeff a,#6dd2d1ff b,#b8da68ff c,#1ebec7ff d,#a9d225ff e,#b2d8b1ff f,#e3f4e8ff g,#96ca96ff ``` ```image fccf fcc ae aca fa aca fa ccf c ggggggggggggggggggggggggggggggggge fccf c feeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeg fcc c feeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeg aca c feeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeg aca c feeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeg cce c feeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeegfccf c feeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeecc c feeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeacg c feeeeeeeeeeeeeeeeeeeebeeeeeeeeecceg af feeeeeeeeeeeeeeeeeeeddbeeeeeeaceeeg af feeeeeeeeeeeeeeeeeedbedeeeeecaeeeeg fa feeeeeeeeeeeeeeeeedbeedeeecceeeeeeg fa feeeeeeeeeeeeeeeedeeeedegcaeeeeeeeg c feeeeeeeeeeeeeebdeeeeedcceeeeeeeeeg c feeeeeeeeeeeeeddeeeeeacgeeeeeeeeeeg c feeeeeeeeeeeedbeeeeeccdeeeeeeeeeeeg c feeeeeeeeeeedbeeeeaceebbeeeeeeeeeeg c feeeeeeeeeedeeeeecaeeegbeeeeeeeeeeg c feeeeeeeebdeeeecceeeeeedeeeeeeeeeeg c feeeeeeebdeeeecaeeeeeeedeeeeeeeeeeg c feeeeeeddeeecceeeeeeeeedeeeeeeeeeeg c feeeeedbeeacaeeeeeeeeeedeeeeeeeeeeg af feeeedeeecceeeeeeeeeeeedeeeeeeeeeeg af feebdeeaceeeeeeeeeeeeeedeeeeeeeeeeg ea febdeecceeeeeeeeeeeeeeebbeeeeeeeeeg fa fddeaceeeeeeeeeeeeeeeeegbeeeeeeeeeg a dbecaeeeeeeeeeeeeeeeeeeedeeeeeeeeeg c fcceeeeeeeeeeeeeeeeeeeeedeeeeeeeeeg c caggggggggggggggggggggggdggggggggge c d c d c bf c ee c fb c d af d af d aa d fa d fa bf c egggggggggggggggggg ee cfgeeeeeeeeeeeeeeeeee fb aaccccccccccccccceeee d geeeeeeeeeeeeeeeeee d geeeeeeeeeeeeeeeeee d geeeeeeeeeeeeeeeeee d geeeeeeeeeeeeeeeeee d geeeeeeeeeeeeedeeee bf geeeeeeeeeeegdgeeee ee geeeeeeeeeeddeeeeee fb geeeeeeeeedbeeeeeee d geeeeeeebdeeeeeeeee d geeeeeeddeeeeeeeeee d geeeegdgeeeeeeeeeee d geeeddeeeeeeeeeeeee d geedbeeeeeeeeeeeeee bf gbdeeeeeeeeeeeeeeee ee dbeeeeeeeeeeeeeeeee fb edgeeeeeeeeeeeeeeeeee d dd egggggggggggggggggg d fdf d bd d db d bd bf db eb fdf fb dd d fde d bd d db de edf eddb dd eddbf fdf fdddf bd fbdb ``` <!-- end of image --> Let's see if area A yields any clues. <!-- image --> ```palette Key,Color ,#fefefeff a,#55ced2ff b,#c1df61ff c,#1bbec8ff d,#aad323ff e,#daeba0ff f,#e5f5e3ff g,#9de3e7ff ``` ```image g fac gcca faccg edf gccaf bdde gcccg fbdddb acca fddbfdb gcccg eddb db faccg edde dd gccaf bdde bd faccg bddf bdf gccaf fddbf ede faccg fddb ede accaf edde edbcccg bdde facca bddf gcccf fddbf faccad fddb gccafbdf edde faccg bdf edde gccaf ede bddf gcccg ede fbdbf accaf fdb fddb gcccg fdb edde facca dd edde gccaf dd bddf faccg bdf fbddf gccaf bdf fddb faccg ede eddb gccaf ede edde gcccg fdb bdde acca fdb fbddf gcccg dd fddb faccg dd eddb gccaf bdf edde faccg bdf bdde gccaf ede bddf faccg ede fddbf accaf fdb fddb gcccg fdb dde facca dd ee gcccf dd faccg bdf gccaf bdf ``` <!-- end of image --> Case closed! This is definitely 1 intersection point in area A. Alright, let's concentrate on the next area. Let's take a closer look at area B. <!-- image --> ```palette Key,Color ,#fefefeff a,#62d2d9ff b,#bedd58ff c,#1bbec8ff d,#aad322ff e,#d3e88fff f,#e9f3c6ff g,#aae6eaff ``` ```image ccccccccccaaaaaaaaaaaggggggggg aaaccccccccccccccccccccccccccca ggggggggggggaaag fde edde fbddf eddb bdde fddbf bdde fdddf eddb fbddf eddb bdde fddbf edde fbddf eddb bdde fddbf bdde fdddf eddb ddf b ``` <!-- end of image --> Area B is clear of intersections, but the search continues. Answer: A: 1; B: 0; 1 + 0 = 1 I have found one intersection!

<!-- image --> ```palette Key,Color ,#fefefeff a,#54ced5ff b,#c1de5eff c,#19bec8ff d,#aad322ff e,#dbeca2ff f,#e5f5e6ff g,#9ae2e6ff ``` ```image fccf gcc gg gca gg acg fa acg a fccf c gcc c gca c acg c acg c fccf c cc c gcf a ef ca af bdb ac gg db b fcg gg de d ac fa fdf d fcg a ed dcc c bd gcf c db cabf c de gcf ee c fdf ca eb c ed ac d c bd fcg d c db ac d a de gcg d af fdf cc d gg ed gcf bf gg bd ca ee fa db acf fb a defca d c ac d c cg d c d c d c bf c ee c fb c d af d gg d gg d fa d fa bf c ee cf fb aaaaccccccccccccc d d d d d d bf fde ee bd fb de d ed d db d edf d bd d fde bf bd ee db fb edf d db d fde d bd d de d ed bf db ee edf fb bd d fde d bd d db de edf eddb db eddbf fde fddbf bd fbde ``` <!-- end of image -->

I'm optimistic that I'll find some intersections in this image. These zones are intriguing. I bet there's something interesting happening within them. <!-- image --> ```palette Key,Color ,#fefefeff a,#7cec39ff b,#7d9f65ff c,#b1d7b1ff d,#eef6ecff e,#d6edc8ff f,#98c593ff g,#a1ec78ff ``` ```image fbb bbb bbf bbc bbe dbb ebb fbb bbb bbf bbc bbe dbb cbb fbb bbb bbf bbbc bbbf dbbbc dbbbe ebbbe cbbbd cbbbd fbbb bbbb bbbb bbbb gaa bbbf aaa bbbf aag cfffffffffffffffffffffffffffffffbbbc aad fcccccccccccccccccccccccccccccfbbbe eaa fccccccccccccccccccccccccccccfbbbd aaa fcccccccccccccccccccccccccccfbbbd aag fccccccccccccccccccccccccccfbbbcd aae fcccccccccccccccccccccccccbbbbccd eaa fccccccccccccccccccccccccbbbbcccd gaa fcccccccccccccccccccccccbbbbccccd aaa fccccccccccccccccccccccbbbbcccccd aac fcccccccccccccccccccccbbbbccccccd egaaaaa fccccccccccccccccccccbbbfcccccccd caaaaaaaaaa fcccccccccccccccccccbbbfccccccccdegaaaaaaaaaagd fcccccccccccccccccfbbbfccccccgaaaaaaaaaage fccccccccccccccccfbbbcccgaaaaaaaaaaagd fcccccccccccccccfbbbgaaaaaaaaaaae fccccccccccccccbaaaaaaaaaaagccccd fcccccccccgaaaaaaaaaaagcccccccccd fcccccgaaaaaaaaaaagcccccccccccccd fgaaaaaaaaaaaabbccccccccccccccccd egaaaaaaaaaagfcbbbbcccccccccccccccccd caaaaaaaaaaagcccccbbbfccccccccccccccccccd egaaaaaaaaaagfccccccccbbbfcccccccccccccccccccd dgaaaaaaaaaage fccccccfbbbfccccccccccccccccccccd egaaaaaaaaaagd fcccccfbbbfcccccccccccccccccccccd egaaaaaaaaaage fccccfbbbcccccccccccccccccccccccd aaaaaaaaaaac fcccfbbbccccccccccccccccccccccccd gaaaaagd fccbbbbcccccccccccccccccccccccccd dge fcbbbbccccccccccccccccccccccccccd fbbbbcccccccccccccccccccccccccccd bbbbccccccccccccccccccccccccccccd bbbbcccccccccccccccccccccccccccccd dbbbfccccccccccccccccccccccccccccccd dbbbfcccccccccccccccccccccccccccccccd ebbbecfffffffffffffffffffffffffffffffd ebbbd cbbbd fbbb fbbb bbbb bbbb bbbf bbbf dbbbc dbbbe ebbbe cbbbd fbbb fbbb fbbbbbbbbbbbb fbbbbbbbbbbb cbbffccedd ``` <!-- end of image --> Let's put area A under the microscope. <!-- image --> ```palette Key,Color ,#fefefeff a,#7cec38ff b,#7ea066ff c,#b5f38fff d,#cce3beff e,#e7f2dfff f,#a4bc94ff g,#97ed63ff ``` ```image e eb ebb dbbb dbbbb dbbbbb fbbbbbb fbbbbbbf fbbbbbbf fbbbbbbf ebbbbbbbd ebbbbbbbd ebbbbbbbd dbbbbbbbe dbbbbbbbe dbbbbbbbe fbbbbbbf fbbbbbbf fbbbbbbf fbbbbbbf efbbbbbbd ebbbbbbbd ebbbbbbbd e ebbbbbbbe edcgaa dbbbbbbbe ecgaaaaaaa dbbbbbbbe edcgaaaaaaaaaaa dbbbbbbfe dcgaaaaaaaaaaaaaaaa fbbbbbbgcgaaaaaaaaaaaaaaaaaaaa fbbbaaaaaaaaaaaaaaaaaaaaaagcde dgaaaaaaaaaaaaaaaaaaaaagcce edcgaaaaaaaaaaaaaaaaaaaagcde dcgaaaaaaaaaaaaaaaaaaaagcde edcgaaaaaaaaaaaaaaaaaaaagce edcgaaaaaaaaaaaaaaaaaaaagcde ecgaaaaaaaaaaaaaaaaaaaaaabd edcgaaaaaaaaaaaaaaaaaaaaaabbbbe aaaaaaaaaaaaaaaaaaaagccbbbbbbbe aaaaaaaaaaaaaaaagce fbbbbbbf aaaaaaaaaaagcde fbbbbbbf aaaaaagcce fbbbbbbf aagcde fbbbbbbf e efbbbbbbd ebbbbbbbd ebbbbbbbd ebbbbbbbe dbbbbbbbe dbbbbbbbe dbbbbbbfe fbbbbbbf fbbbbbbf fbbbbbbf fbbbbbbf ebbbbbbbd ebbbbbbbd ebbbbbbbd dbbbbbbbe dbbbbbbbe bbbbbbbe bbbbbf bbbbf bbbf bbf bd d ``` <!-- end of image --> Gotcha! I've found 1 intersection hiding in area A! Answer: A: 1; 1 = 1 My investigation reveals that there is exactly one intersection in this image.

<!-- image --> ```palette Key,Color ,#fefefeff a,#7cec39ff b,#7d9f65ff c,#c4f6a6ff d,#bfd0b4ff e,#e1efd8ff f,#9eb78cff g,#a1f071ff ``` ```image fbb bbb bbf bbd bbe bb dbb fbb bbb bbf bbd bbe ebb dbb fbb bbb bbf bbbd bbbf bbbd ebbbd ebbbe dbbbe dbbb fbbb fbbb bbbb bbbb caa bbbf aaa bbbf aag bbbd aae ebbbe caa ebbbe aaa dbbb aag fbbb aac fbbb eaa bbbb gaa bbbb aaa bbbf aac bbbf egaaaaa bbbd caaaaaaaaaa ebbbd egaaaaaaaaaage ebbbe ecaaaaaaaaaagc dbbbe cgaaaaaaaaaac dbbbgaaaaaaaaaage gaaaaaaaaaaac egaaaaaaaaaage ecaaaaaaaaaagc cgaaaaaaaaaaabb egaaaaaaaaaage bbbf caaaaaaaaaaac bbbf egaaaaaaaaaage bbbd ecaaaaaaaaaagc ebbbe cgaaaaaaaaaac ebbbe egaaaaaaaaaage dbbb aaaaaaaaaaac fbbb gaaaaage fbbb egc bbbb bbbb bbbf bbbf bbbd ebbbd ebbbe dbbbe dbbb fbbb fbbb bbbb bbbb bbbf bbbf bbbd ebbbd ebbbe dbbbe fbbb fbbb fbbbbbbbbbbbb fbbbbbbbbbbb dbbffddee ``` <!-- end of image -->

Let's examine this image for potential line intersections. It's crucial to examine these regions more closely. <!-- image --> ```palette Key,Color ,#fefefeff a,#328d2cff b,#98c890ff c,#339401ff d,#79b66bff e,#b1d7b0ff f,#ebf4eaff g,#56a43eff ``` ```image b daaa faaaaaf gaaaaaag eaaaaaaaaa aaaaaaf aaaf daaaaab aaad faaaaaa baaa gaaaaae aaa eaaaaag aaad aaaaaaf daaa daaaaab aaa fcd faaaaaa aaab ccccf gaaaaae daaa cccccb eaaaaag faaa ccccccg aaaaaaf aaae ccccccccf aaaab gaaa ccc cccccb baa faaa ccc gccccc e aaae ccc ecccccf gaaa ccc cccccd eaaa ccc dccccc aaaf fccc fccccc aaag fccc ccccg eaaa eccc gcccd aaaf eccc cccce aaad bccc ccccf baaa bccc fcccc aaa dccc fcccc aaad dccg bcccc daaa gccg gcccg aaa gccd ccccb aaab cccd ccccf daaa cccb cccc faaa cccb fcccc aaae ccce ecccc gaaa ccce dcccg faaa cccf acccd aaae cccf cccce gaaa ccc ccccf eaaa ccc fcccc aaaf ccc ecccc aaag ccc bcg eaaa ccc b aaaf ccc aaad fccc baaa eccc aaa eccc aaad eccc daaa bccc bbbbbaaabbbbbbbbgcccbbb feeeeeaaadeeeeeeegccceeef feeeeegaaaeeeeeeegccgeeef feeeeeeaaaeeeeeeeaccgeeef feeeeeeaaadeeeeeecccgeeef feeeeeegaaaeeeeeecccdeeef feeeeeebaaaeeeeeecccdeeef fcf feeeeeeeaaabeeeeecccdeeef cccg feeeeeeeaaaaeeeeecccbeeef eccccce feeeeeeebaaaeeeeecccbeeef fcccccc feeeeeeeeaaabeeeeccceeeef dcccccb feeeeeeeeaaageeeeccceeeef ccccccf feeeeeeeedaaaeeeeccceeeef bcccccd feeeeeeeeeaaaeeebccceeeef ccccccf ffeddggccccccccccccccceeeef ecccccgebdggcccccccccccccccccccccccccccccccceeeef gccccccccccccccccccccccccccccccccccccccccdeeeef fccccccccccccccccccccccccgggddbbaaadeeeeeeeeef dccccggdbeef feeeeeeeeeedaaaeeeeeeeeef feeeeeeeeeeeaaaeeeeeeeeef feeeeeeeeeeeaaadeeeeeeeef feeeeeeeeeeegaaaeeeeeeeef feeeeeeeeeeeeaaaeeeeeeeef feeeeeeeeeeeeaaadeeeeeeef feeeeeeeeeeeegaaaeeeeeeef edaa feeeeeeeeeeeebaaaeeeeeeef fbgaaaaaaa feeeeeeeeeeeeeaaabeeeeeef edaaaaaaaaaaaaae feeeeeeeeeeeeeaaaaeeeeeef fbgaaaaaaaaaaaaaaaade feeeeeeeeeeeeebaaaeeeeebedaaaaaaaaaaaaaaaagbf feeeeeeeeeeeeeeaaaddaaaaaaaaaaaaaaaaade fbeeeeeeeeeeeeeaaaaaaaaaaaaaaaade ffffffffffffffeaaaaaaaaagbf aaaade ``` <!-- end of image --> I'm now examining the contents of area A in detail. <!-- image --> ```palette Key,Color ,#fefefeff a,#338d2cff b,#9fcb93ff c,#339401ff d,#7eb96eff e,#bfdcb7ff f,#dfeddbff g,#5ca645ff ``` ```image aaaaaag dcccccc daaaaaaf dcccccc eaaaaaab dccccca aaaaaag gcccccg daaaaaaf gcccccg eaaaaaab gcccccg faaaaaag gcccccg gaaaaaaf acccccd baaaaaab ccccccd faaaaaad ccccccd gaaaaaa ccccccb baaaaaae ccccccb faaaaaad fccccccb gaaaaaa fccccccb baaaaaae fcccccce faaaaaad ecccccce aaaaaaa ecccccce daaaaaae eccccccf eaaaaaad bccccccf aaaaaag bccccccf daaaaaaf bcccccc eaaaaaab dcccccc aaaaaag dcccccc daaaaaaf dcccccc eaaaaaab dccccca faaaaaag gcccccg gaaaaaaf fccccccg fffeedacccccagaccccccccccg eebbdddgggaccccccccccccccccccccccccccccg cccccccccccccccccccccccccccccccccccccccd cccccccccccccccccccccccccccccccccccccccb cccccccccccccccccccccccccccccccccccccccf cccccccccccccccccccccccccccccccccccccae ccccccccccccccccccccccccccccgddbbeeef ccccccagggdddbbbeefffeaaaaaad eff aaaaaaa daaaaaae eaaaaaad aaaaaag daaaaaaf eaaaaaab aaaaaag daaaaaaf eaaaaaab faaaaaag gaaaaaaf baaaaaab faaaaaad gaaaaaa baaaaaae faaaaaad gaaaaaa baaaaaae faaaaaad aaaaaaa daaaaaae eaaaaaad aaaaaag febdga daaaaaabbdgaaaaaaa eaaaaaaaaaaaaaaaaa aaaaaaaaaaaaaaaaa ``` <!-- end of image --> Wow! I can see 1 intersection so clearly in area A! Answer: A: 1; 1 = 1 After careful examination, I conclude that there is one intersection.

<!-- image --> ```palette Key,Color ,#fefefeff a,#328d2cff b,#9fcb91ff c,#339401ff d,#7bb76bff e,#bfdcb8ff f,#e2efdfff g,#56a33dff ``` ```image b daaa faaaaaf gaaaaaag eaaaaaaaaa aaaaaaf aaaf daaaaad aaad faaaaaa baaa gaaaaae aaa eaaaaag aaad aaaaaaf daaa daaaaad aaa cd faaaaaa aaab cccc gaaaaae daaa cccccb eaaaaag faaa ccccccg aaaaaaf aaab ccccccccf aaaab gaaa ccc cccccb baa faaa ccc gccccc e aaae ccc ecccccf gaaa ccc cccccd eaaa ccc dccccc aaaf ccc fccccc aaag fccc ccccg eaaa eccc gcccd aaaf eccc cccce aaad bccc ccccf baaa bccc cccc aaa dccc fcccc aaad dccg bcccc daaa gccg gcccg aaa gccd ccccb aaab cccd ccccf daaa cccb cccc faaa cccb fcccc aaab ccce ecccc gaaa ccce dcccg faaa cccf gcccd aaae ccc cccce gaaa ccc ccccf eaaa ccc cccc aaaf ccc ecccc aaag ccc bcg eaaa ccc b aaaf ccc aaad fccc baaa eccc aaa eccc aaad bccc daaa bccc aaa dccc aaab dccg daaa gccg faaa gccd aaab cccd gaaa cccb faaa cccb cf aaae ccce cccg gaaa ccce bccccce eaaa cccf fcccccc aaaf ccc dcccccb aaag ccc cccccc eaaa ccc bcccccd aaaf fccc ccccccf ffebddggcccccccccccccc ecccccgbbdggcccccccccccccccccccccccccccccccc gcccccccccccccccccccccccccccccccccccccccce fcccccccccccccccccccccccagddbeefaaad dccccggdbbef daaa aaa aaab daaa faaa aaab gaaa edaa faaa fbgaaaaaaa aaae edaaaaaaaaaaaaae gaaa fbgaaaaaaaaaaaaaaaade eaaa edaaaaaaaaaaaaaaaagbf aaabdaaaaaaaaaaaaaaaaade aaaaaaaaaaaaaaaade eaaaaaaaaagbf aaaade ``` <!-- end of image -->

This image might have some surprises. Let's look for intersections carefully. These spots mark what I'd call 'danger zones' - areas where intersections are more likely. <!-- image --> ```palette Key,Color ,#fefefeff a,#728d9aff b,#c9b3a4ff c,#2f5472ff d,#dad0ccff e,#a2cda4ff f,#eef1edff g,#b2d7b2ff ``` ```image ggggggggggggggggef ggggggggggggggggef ggggggggggggggggef ggggggggggggggggef gggbggggggggggggef ggggggggggggggggef ggggbgggggggggggef ggggbgggggggggggef ggggbgggggggggggef gggcagggggggggggef ggggacggggggggggef gggggacgggggggggef gggggbgcggggggggef gggggbggceggggggef gggggggggcagggggef ggggggbgggacggggef ggggggbggggecgggef ggggggbggggggcggef ggggggggggggggceef gggggggbgggggggcaf gggggggbggggggggac gggggggbggggggggedc gggggggbggggggggef cf ggggggggggggggggef cd eeeeeeeebeeeeeeeef aa ffffffffbffffffff ec b fc ff cf d cd b aa b gc b fc b cf d cd d aa ff gc ff fc d cf d cg b aa b dc b fc b cf b cg b aa d dc d fc ff cf ff cg d aa d dc b fc b cf fdgeaaccccccc b acaaagdff a b a b c b fa d c d ed ff c ff a d c d c b fa b c b gd b c b ffddbf af b fdddbbbbbbddff b c d ffddbbbbbbbddff b c d ffdddbbbbbbddff df fa ddddbbbbbbdddf beeeeeeeeeeeceeeee f febggggggggggaagggg febgggggggggggcgggg fegbggggggggggegggg feggbgggggggggggggg feggbgggggggggggggg fegggbggggggggggggg feggggbgggggggggggg feggggbgggggggbgggg fegggggbggggbbggggg feggggggbgbbggggggg feggggggbbggggggggg feggggggggggggggggg feggggggggggggggggg feggggggggggggggggg ``` <!-- end of image --> I'm eager to see what's happening in this magnified view of area A. <!-- image --> ```palette Key,Color ,#fefefeff a,#4b6a83ff b,#cbb2a4ff c,#274d6dff d,#d4c9c5ff e,#99a7b5ff f,#e6e3e2ff g,#748a9eff ``` ```image bd db fb fbf bd bd db fbf bf bd eddb aceb gcaf gca gcaf deccd fbface bf gcg bd ecaf db ecaf fb fccd fbf face bd gcg dd ecaf db dcaf fbf fccd bf face bd gcg db ecaf fb dcaf fbf facd bd face db gc db e fbf bf bd db fb bf bd db ``` <!-- end of image --> The lines cross each other within area A, forming 1 intersection. Now, let's scrutinize the next spot. I wonder what we'll find inside area B? <!-- image --> ```palette Key,Color ,#fefefeff a,#627d95ff b,#cbb1a3ff c,#2c5170ff d,#d5c5bcff e,#97a9b9ff f,#f3efedff g,#e4d9d4ff ``` ```image db acf fbd gce gbf ac bb dcd fbd ca gbf ecg bb fce fbg f dbf bd fbg dbf bd gbg dbf fbd gbg dbf gbg fbd gbbdf gbg gbbdf dbf gbbdf fbd gbbdf gbdbbdf dbdf f ``` <!-- end of image --> I had hoped to find an intersection in area B, but there isn't one. Answer: A: 1; B: 0; 1 + 0 = 1 I have found one intersection!

<!-- image --> ```palette Key,Color ,#fefefeff a,#52708aff b,#ccb2a5ff c,#284e6eff d,#dbcdc6ff e,#869aaaff f,#ebe7e6ff g,#b3c0cbff ``` ```image d ff d b b ae ea ec b c d cf ff ae b ea b dc b c f cf d ae b ea b fc d c ff cd b ae b ga b fc ff c d cd b ae b ga b fc b cf d cg d ae ff ga ff fc d cf d cg b ee b gc b fc b cf b ag b ea d gc d fc ff cf ff ag d ea d dc b c b cf fdgeeaacccccc b aaaeeggf a b a b c b fe d c d gd ff c ff a d a d c b fe b c b gg b c b ffddbf e b ffddbbbbbbddff b a d ffddbbbbbbddff b c d ffddbbbbbbddff df fe ffddbbbbbbddff b c f b gg df c b f b df b d d b b bd fd bd bd ``` <!-- end of image -->

This image looks interesting. I wonder if there are any intersections hidden in there? I'm going to focus my attention on these specific areas. <!-- image --> ```palette Key,Color ,#fefefeff a,#ed8eb0ff b,#d25fe9ff c,#f3c2e1ff d,#c3a3bbff e,#ce26eeff f,#b1d7b1ff g,#96c996ff ``` ```image cac aaaa aaac caaa aaaa aaac caaa aaaa aa aaac aac caaa aaaa aaaa aaaa aaac b caaaa caaa bee aacaac aaaa eee caa caa aaac eee aac aa caaa eee aa aa aaaa eee aaa aac aaac eee aa caa caaa eeec caa aa aaaa eeec aac aa aaac eeecgggggggggggggggdaagggggfaac caaa eeedffffffffffffffaadfffffgcaa aaaa eeedfffffffffffffaaffffffg aa aaac beebfffffffffffaaaffffffg aa caaa beebffffffffffaafffffffg aaa aaaa fbeebffffffffdaafffffffg caa aaac ffbeebfffffffaadfffffffg aa caaa fffdeeeffffffaaffffffffg aac aaaa ffffdeeeffffaaaffffffffg aaaaaac b fffffdeeefffaafffffffffg caaaa ceee ffffffdeeefdaafffffffffg aaa eeeec fffffffdeeeaadfffffffffg cc beeeb fffffffffeeaaffffffffffg ceeee ffffffffffaaaffffffffffg eeeec ffffffffffaabefffffffffg beeeb ffffffffffaaeeeffffffffg ceeee fffffffffaaafeeefffffffg eeeec fffffffffaafffeeeffffffg beeeb ffffffffdaaffffeeedffffg ceeee ffffffffaadfffffeeedfffg eeeec ffffffffaafffffffeeedffg beeeb fffffffaaaffffffffeeedfg ceeee fffffffaaffffffffffeeedg eeeec ffffffdaafffffffffffbeeb beeeb ffffffaadffffffffffffbeeb ceeee ffffffaaffffffffffffffbeeb eeeec fffffaaafffffffffffffffbeeb beeeb gggggaaggggggggggggggggfceee ceeee caa ceee eeeec aac ceee beeeb aa ceeeceeee aaa ceeeeec aa eeb caa aac aa aaa aa caa aac aa aaa aac caa aac aa aaa aac caa aaa aaa aaa aaa caac aac aaa aaa aaa aaa a ``` <!-- end of image --> Let's take a closer look at area A. <!-- image --> ```palette Key,Color ,#fefefeff a,#ed8dafff b,#d64beeff c,#f2afc7ff d,#e075f2ff e,#ce26efff f,#ebabf7ff g,#f8daeeff ``` ```image aaaaa gaaaag f caaaa ef gaaaac eef caaaag eeef aaaac eeeed gaaaag eeeeed caaaa beeeeed gaaaac beeeeed caaaag deeeeed aaaac deeeeeb gaaaag deeeeeb caaaa deeeeeb gaaaac deeeeebg caaaag feeeeebg aaaac feeeeebg gaaaag feeeeeeg caaaa feeeeeeg gaaaac feeeeeeg caaaag feeeeeef aaaac geeeeeef gaaaag geeeeeef caaaa geeeeeefaaaac gbeeeebaaaag gbeeeaaaaa gbebaaaac baaaaad gaaaaaed caaaabeed aaaaaeeeed gaaaadeeeeeb caaaagdeeeeeb aaaac deeeeeb gaaaag deeeeebg aaaaa feeeeebg gaaaac feeeeebg caaaag feeeeeeg aaaac feeeeeeg gaaaag feeeeeeg caaaa feeeeeef gaaaac geeeeeef caaaag geeeeeef aaaac geeeeeef gaaaag gbeeeeef caaaa gbeeeeef gaaaac gbeeeee caaaag beeee aaaac beee gaaaag bee caaaa de gaaaac d caaaag aaaac ``` <!-- end of image --> Aha! I've found 1 intersection inside area A! Answer: A: 1; 1 = 1 One intersection, that's it, but I found it.

<!-- image --> ```palette Key,Color ,#fefefeff a,#ee8eb0ff b,#d74ff0ff c,#f4bfd1ff d,#e079f4ff e,#ce26efff f,#eeb8f9ff g,#fae6f2ff ``` ```image cac aaaa aaac caaag aaaa aaac caaag aaaa aa aaac gaac caaag aaaa aaaa aaaa aaac d caaaa caaag dee aagaac aaaa geee caa caa gaaac eee aac aa caaag eee gaa aag aaaa eeeg aaa aac gaaac eeeg aa caa caaag eeeg caa aa aaaa eeef aag aag gaaac eeef caa aac caaag eeef aac caa aaaa beed aa aa gaaac beed aaa aag caaag beed aag aac aaaa deeb caa caa gaaac deeb aac aa caaag deeb aa aag aaaa feee aaa aaaaaac bg feee aag gaaaa feee feee gaa aaa geeeeg geeeaac cg beeed geeaa feeee gaaa geeeef aabe beeed gaaeee feeee aac eeeg eeeef aa eeeg beeed caa eeeg feeee aag eeef eeeef gaa eeef deeed aaa eeef feeee aa beed eeeef caa beed deeeb aac beed feeee gaa deeb eeeef aaa deeb deeeb aa deeb feeeeg caa feee eeeef aac feee deeeb gaa feeegeeeeg aaa geeeeef aag geeb caa aac aa aaa aag caa aac aa aaa aag gaa aac aa caa aag gaa aac aaa aaa caag caac gaac aaa aaa aaa aaa ag ``` <!-- end of image -->

I have an image in front of me. I need to determine if there are any intersection segments. I have a hunch that these areas might contain the intersections we're looking for. <!-- image --> ```palette Key,Color ,#fefefeff a,#0c9fabff b,#d20ee0ff c,#b1d7b1ff d,#cd7ad5ff e,#ebf2f0ff f,#93c99aff g,#52b1b9ff ``` ```image e aaa gaae aaa gaa aag aaa eaag aaa caac aaa gaae aaa gaae aaa aaa eaag aaa eaac aaa caae aaa d gaae dbb aaa bbbb aaa bbbb eaag bbbbeeeeeaaaeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee d bbbbccccfaagccccccccccccccccccccccccccccccccccccccccccccccccfe dbb bbbbccccaaaccccccccccccccccccccccccccccccccccccccccccccccccce dbbb fbbbbcccgaafcccccccccccccccccccccccccccccccccccccccccccccccce dbbb fcbbbbcccaaacccccccccccccccccccccccccccccccccccccccccccccccce dbbb fccbbbbccgaafccccccccccccccccccccccccccccccccccccccccccccccce dbbb fcccbbbbccaaaccccccccccccccccccccccccccccccccccccccccccccccce dbbbe fccccbbbbcaaaccccccccccccccccccccccccccccccccccccccccccccccce ebbbe fcccccbbbdcaaacccccccccccccccccccccccccccccccccccccccccccccce ebbbe fccccccbbbdaaacccccccccccccccccccccccccccccccccccccccccccccce ebbbe fcccccccbbbdaagccccccccccccccccccccccccccccccccccccccccccccce ebbbe fccccccccbbbaaaccccccccccccccccccccccccccccccccccccccccccccce bbbd fcccccccccbbbaagcccccccccccccccccccccccccccccccccccccccccccce bbbd fccccccccccbbaaacccccccccccccccccccccccccccccccccccccccccccce bbbd fcccccccccccbgaafccccccccccccccccccccccccccccccccccccccccccce bbbd fccccccccccccbaaaccccccccccccccccccccccccccccccccccccccccccce bbbd fcccccccccccccgaadccccccccccccccccccccccccccccccccccccccccccebbbb fccccccccccccccaaadcccccccccccccccccccccccccccccccccccccccccbbbb fccccccccccccccaaabdcccccccccccccccccccccccccccccccccccccccbbbb fcccccccccccccccaagbdcccccccccccccccccccccccccccccccccccccbbbb fcccccccccccccccaaabbccccccccccccccccccccccccccccccccccccbbbb fcccccccccccccccfaagbbccccccccccccccccccccccccccccccccccbbbbe fccccccccccccccccaaabbbccccccccccccccccccccccccccccccccbbbbce fccccccccccccccccgaagbbbccccccccccccccccccccccccccccccbbbbcce fcccccccccccccccccaaadbbbccccccccccccccccccccccccccccdbbbccce fcccccccccccccccccgaacdbbbdcccccccccccccccccccccccccdbbbcccce fccccccccccccccccccaaacdbbbbcccccccccccccccccccccccdbbbccccce fccccccccccccccccccaaacccbbbbcccccccccccccccccccccdbbbccccfaae fcccccccccccccccccccaaacccbbbbcccccccccccccccccccdbbbccccfaaaae fcccccccccccccccccccaaaccccbbbbcccccccccccccccccdbbbccccfaaaaaac fcccccccccccccccccccfaagccccbbbbdcccccccccccccccbbbccccfaaafcaaac fccccccccccccccccccccaaacccccdbbbbcccccccccccccbbbccccfaaafceeaaag fccccccccccccccccccccfaagccccccbbbbcccccccccccbbbdcccfaaafcce eaaag fcccccccccccccccccccccaaacccccccbbbbcccccccccbbbdcccgaaafccce eaaag fcccccccccccccccccccccgaafcccccccbbbbcccccccbbbdcccgaaafcccce aaag fccccccccccccccccccccccaaaccccccccbbbbdccccbbbdcccgaaacccccce aaaa fccccccccccccccccccccccgaacccccccccdbbbbccbbbdcccgaaaccccccce aaaa fcccccccccccccccccccccccaaaccccccccccbbbbbbbdcccgaaacccccccce aaaa fcccccccccccccccccccccccaaacccccccccccbbbbbbcccgaaaccccccccce aaaa cffffffffffffffffffffffffaagfffffffffffbbbbfffgaaaffffffffff aaaa aaa dd gaaa gaaa eaac gaaa gaaae aaa gaaa gaaae caae gaaa caaae aaa gaaa cag gaae aaaa e aaa aaaa aaa aaaa eaag aaaa aaa aaaa eaag aaaa aaa aaaa caaaaaa aaaaa gaaa ag ``` <!-- end of image --> This is a magnified view of the region A. <!-- image --> ```palette Key,Color ,#fefefeff a,#0d9fabff b,#d30ce1ff c,#5ebec7ff d,#efadf4ff e,#b4e0e5ff f,#df55e9ff g,#7253c6ff ``` ```image bbbb aaaaac bbbbb caaaaa bbbbbb eaaaaac bbbbbbb caaaaa dbbbbbb eaaaaa dbbbbbb aaaaa dbbbbbf eaaaae dbbbbbf caaaae dbbbbbf aaaac dbbbbbf caaaae bbbbbbf eaaaac fbbbbbbf caaaa fbbbbbbf eaaaac fbbbbbbf caaaa fbbbbbbf eaaaae fbbbbbbf aaaaa fbbbbbbf aaaaae fbbbbbbfaaaaac fbbbbbbcaaaaae fbbbbbfaaaaac fbbbbbcaaaaa fbbbbbaaaaac fbbbgaaaaae fbbbaaaaaa bbbgaaaaae fbbbaaaaac fbbgaaaaae fbbaaaaac bbgaaaaa bbaaaaac bgaaaaad gaaaaagd aaaaaab eaaaaagd d aaaaaabd db eaaaaabbd dbb caaaabbbbd dbbbb aaaagbbbbd bbbbb caaaabbbbbd bbbbbb eaaaagbbbbbd bbbbbbb caaaabbbbbbd bbbbbbd eaaaagbbbbbbd fbbbbbd aaaaabbbbbbb fbbbbbd eaaaaebbbbbbb fbbbbbd aaaacdbbbbbbb fbbbbbd caaaaedbbbbbbb fbbbbbf aaaac dbbbbbbb fbbbbbf aaaaa dbbbbbbd fbbbbbb aaaaac dbbbbbbf fbbbbbbf caaaaa dbbbbbbf fbbbbbbf eaaaaae dbbbbbbb dbbbbbbf c eaaaaae fbbbbbbd dbbbbbbf eaaa aaaaac bbbbbbbf dbbbbbbf eaaaa caaaaae dbbbbbbbf dbbbbbbb eaaaaa aaaaac dbbbbbbbb bbbbbbb eaaaaaa caaaaae bbbbbbbbd dbbbbbb aaaaaaa eaaaaac fbbbbbbbd dbbbbbb eaaaaaae caaaaa fbbbbbbbf dbbbbbbd eaaaaaae eaaaaac dbbbbbbb dbbbbbbd eaaaaaae caaaaa dbbbbbbb bbbbbbd eaaaaaae eaaaaae bbbbbbbd bbbbbbd eaaaaaae aaaaaa fbbbbbbd bbbbbbd eaaaaaae eaaaaae fbbbbbbf fbbbbbb eaaaaaae aaaaac dbbbbbbf fbbbbbbd eaaaaaaa caaaaae dbbbbbbb fbbbbbbd eaaaaaaae aaaaac bbbbbbbbd fbbbbbbd caaaaaaa eaaaaa fbbbbbbbf fbbbbbbf caaaaaaa caaaa dbbbbbbbf fbbbbbbf caaaaaaa eaaaae dbbbbbbbb fbbbbbbf caaaaaaa aaaaa bbbbbbbbbbbbbbf aaaaaac eaaaae fbbbbbbbbbbbf caaaaac aaaac fbbbbbbbbbf caaaaac caaaae dbbbbbbbf caaaaac ``` <!-- end of image --> The close-up clearly shows 1 intersection point in area A. Answer: A: 1; 1 = 1 My investigation reveals that there is exactly one intersection in this image.

<!-- image --> ```palette Key,Color ,#fefefeff a,#0c9fabff b,#d20be1ff c,#87ced5ff d,#eea8f3ff e,#c7e8ebff f,#de51e9ff g,#4aadbfff ``` ```image e aaa gaae aaa gaa aag aaa eaac aaa eaac aaa caae aaa gaa aaa aaa aag aaa eaac aaa caae aaa d gaa dbb aaa bbbb aaa bbbb aag bbbb aaa f bbbb eaac fbb bbbb aaa fbbb bbbf caae fbbb bbbf aaa dbbb bbbf caae dbbb bbbf aaa dbbb bbbf gaa dbbb bbbf aag dbbbd bbbfaaa bbbd bbbfaag bbbd bbbaaa bbbd bbbaac bbbd bbaaa bbbf bgaae bbbf baaa bbbf gaad bbbf aaad bbbf aaabd bbbb aagbd bbbb aaabbd bbbb eaagbbd bbbb aaabbb fbbb caacbbb fbbb aaadbbb fbbb gaaedbbbd fbbb aaa dbbbf fbbb gaa bbbb dbbb eaae aag bbbb dbbb eaaaae aaa bbbb dbbb eaaaaaae eaac fbbbd dbbb eaaaeeaaac aaa dbbbf bbbd eaaae eaaac eaac bbbb bbbd caaae eaaag aaa bbbb bbbd caaae aaag caae bbbb bbbd caaae aaag aaa fbbbd bbbd caaae aaaa gaa dbbbf bbbf caaa aaaa aaa bbbbbbbf caaa aaaa aaa bbbbbf gaaa aaaa aag bbbf gaaa aaaa aaa df gaaa gaaa eaac gaaa gaaa aaa gaaa gaaae caae gaaa caaae aaa gaaa cag gaa aaaa e aaa aaaa aaa aaaa aag aaaa aaa aaaa eaac aaaa aaa aaaa caaaaaa aaaaa caaa ag ``` <!-- end of image -->

Based on a first glance, I suspect there could be intersection regions here. I wonder what's going on inside those areas? Perhaps intersections are hiding there. <!-- image --> ```palette Key,Color ,#fefefeff a,#3883a3ff b,#e08864ff c,#9cc2cdff d,#659eb0ff e,#e8b79fff f,#e8ebe9ff g,#afd6afff ``` ```image c aaa faaac daaaa aaaaaa faaaaaac daadcaaa aaaf aaaa faaa faaac daad daaa aaaf aaaa aaa faaaf daad daaa aaaf aaad aaa faaaf daad daaa aaaf aaad aaa faaaf caaa aaaa aaaf aaad aaa caaaf caaa aaaa daa aaaf aaac aaaaf aaa caaa faaaaac caaa aaaa caaaaaad aaac aaac daaaacaaa aaa caaa aaaaa aaa fd aaaa ffaaaadfffaaaffffffff aaac fdaaaadggggaaagggggggg daaa daaaaggggggaaagggggggg aaaa aaaaagggggggaaagggggggg faaac faaaadggggggggaaacggggggg daaa caaaadgggggggggdaadggggggg aaaa daaaafggggggggggdaadggggggg faaaf aaaaa fggggggggggcaaaggggggg daaa faaaad fgggggggggggaaaggggggg aaad caaaac fgggggggggggaaaggggggg faaaf daaaaf fgggggggggggaaagbbbggg daaa aaaaa fgggggggggggaaabbbbegg aaad faaaad fgggggggggggaaabbbbggg faaaf caaaac fgggggggggggaaabbegggg aaaa daaaaf fgggggggggebdaadgggggg aaad aaaaa fggggggggbbbdaadgggggg caaaf faaaad fgggggggbbbbbaaagggggg aaaa caaaac fgggggbbbbbbgaaagggggg aaaddaaaaaaaf fggggbbbbbgggaaagggggg caaaaaaaaaa fggbbbbbbggggaaagggggg aaaaaaaad fgbbbbbggggggaaagggggg adcf ebbbbbgggggggaaagggggg bbbbbeggggggggaaacggggg fbbbbbggggggggggdaadggggg bbbbbbgggggggggggdaadggggg fbbbbbfggggggggggggcaaaggggg ebbbbb fgggggggggggggaaaggggg bbbbbf gggggggggggggaaaggggg ebbbbb aaa fbb bbbbbe aaa fbbbe ebbbbb aaa bbbbf bbbbbe aaaf bbbb fbbbbb daac bbbb bbbbbe caad bbbb fbbbbbf faaa fbbbe ebbbbb aaa ebbbf bbbbbf aaa bbbb ebbbbb aaa bbbb bbbbbe aaa bbbb fbbbbb aaa fbbbe bbbbbe aaaf ebbbe fbbbbbf daac bbbbf ebbbbb caad bbbb bbbbbf faaa bbbb ebbbbb aaa fbbbb bbbbbe aaa ebbbe fbbbbb aaa ebbbf bbbbbe aaa bbbb fbbbbb aaaf bbbb ebbbbe bbbb bbbbbf fbbbbbbbbb ebbbbbbe bbbbb bbe ``` <!-- end of image --> Could this be where the intersection is hiding, in area A? <!-- image --> ```palette Key,Color ,#fefefeff a,#3883a3ff b,#e18864ff c,#a4c6d4ff d,#6fa4bbff e,#edbeabff f,#e1e3e4ff g,#98847dff ``` ```image faaaaaaaaad daaaaac caaaaaaaaac daaaaad daaaaaaaaaf caaaaad daaaaaaaadf caaaaad aaaaaaaad faaaaaa aaaaaaac faaaaaa aaaaaaf aaaaaaf aaaadf aaaaaaf aaad daaaaac aac daaaaac af daaaaad f caaaaad caaaaad faaaaaa faaaaaa aaaaaaf aaaaaaf daaaaac fe daaaaac ebbe daaaaad fbbbbbf caaaaadebbbbbbb caaaaaabbbbbbbbe faaaaaabbbbbbbbe faaaaaabbbbbbbf aaaaaabbbbbe eaaaaaagbbbe fbbaaaaaagbe ebbbaaaaaage ebbbbgaaaaad ebbbbbbgaaaaad ebbbbbbbgaaaaad fbbbbbbbbbgaaaaaa ebbbbbbbbbbeaaaaaa fbbbbbbbbbbe aaaaaaf ebbbbbbbbbbe aaaaaaf fbbbbbbbbbbbf daaaaac ebbbbbbbbbbe daaaaac ebbbbbbbbbbf daaaaad fbbbbbbbbbbe caaaaad ebbbbbbbbbbf caaaaad fbbbbbbbbbbe faaaaaa ebbbbbbbbbbe faaaaaa bbbbbbbbbb aaaaaaf bbbbbbbbe aaaaaaf bbbbbbbf daaaaac bbbbbe daaaaac bbbbf daaaaad bbe caaaaad bf caaaaad faaaaaa faaaaaa aaaaaaf ``` <!-- end of image --> I observe 1 intersection inside area A. Answer: A: 1; 1 = 1 My investigation reveals that there is exactly one intersection in this image.

<!-- image --> ```palette Key,Color ,#fefefeff a,#3883a3ff b,#e08863ff c,#9cc1d1ff d,#679db5ff e,#eaae96ff f,#f5d9ceff g,#d3e3eaff ``` ```image g aaa gaaac daaaa aaaaaa gaaaaaac daadcaaa aaa aaaa aaa aaac daad daaa aaag aaaa aaa gaaag daad daaa aaag aaad aaa gaaag daad daaa aaag aaad aaa gaaag caaa aaaa aaag aaad aaa caaa caaa aaaa daa aaag aaad aaaag aaa caaa gaaaaac caaa aaaa caaaaaad aaag aaac daaaacaaa aaa caaa aaaaa aaa gd aaaa gaaaad aaa aaac caaaac aaa daaa daaaag aaa aaaa aaaaa aaa aaac gaaaad aaag daaa caaaac daac aaaa daaaag caad gaaag aaaaa gaaa daaa gaaaad aaa aaad caaaac aaa f gaaag daaaag aaa ebb daaa aaaaa aaabbbbe aaad gaaaad aaabbbb gaaag caaaac aaabbf aaaa daaaa fbdaad aaad aaaaa bbbdaad caaa gaaaad fbbbbbaaa aaaa caaaac bbbbbe aaa aaaddaaaaaaa bbbbb aaa caaaaaaaaaa ebbbbb aaa aaaaaaaad bbbbbf aaa adcg ebbbbb aaa bbbbbf aaag fbbbbb daac bbbbbe caad fbbbbb gaaa ebbbbe aaa bbbbbf aaa ebbbbb aaa bb bbbbbf aaa fbbbe fbbbbb aaa ebbbf bbbbbe aaag bbbb fbbbbb daac bbbb ebbbbe caad bbbb bbbbbf gaaa fbbbe ebbbbb aaa ebbbf bbbbbf aaa bbbb fbbbbb aaa bbbb bbbbbe aaa bbbb fbbbbb aaa fbbbe bbbbbe aaag ebbbf bbbbb daac bbbb ebbbbb caad bbbb bbbbbf gaaa bbbb ebbbbb aaa bbbb bbbbbf aaa fbbbe fbbbbb aaa ebbbf bbbbbe aaa bbbb fbbbbb aaa bbbb ebbbbe bbbb bbbbbf fbbbbbbbbb ebbbbbbf bbbbb bbe ``` <!-- end of image -->

I'm curious to see if this image contains any intersection points. These areas seem to enclose narrow spaces where lines might be close. <!-- image --> ```palette Key,Color ,#fefefeff a,#277664ff b,#d48065ff c,#dcaf9bff d,#94c798ff e,#b1d7b1ff f,#539283ff g,#e8ded8ff ``` ```image bbg gbbb cbbbg cbbbb bbbbbg bbbbbb bbbbbb bbbcbbb bbb bbb bbb cbbb bbb bbb bbb cbbb gbbc bbb gbbc cbbc cbbg bbb cbbg bbbc bbb bbb ag bbb bbbc aaa bbb bbb aaaa bbb bbbg aaaa bbb c aaaf bbb gaaad bbb eaaae bbb daaag gbbc faaa gbbc aaaa cbbg aaaa cbbg aaaf bbb gaaae bbb daaag bbb faaa bbb aaaa bbb aaaa bbb aaaf bbb gaaad bbb daaag gbbc faaa gbbc aaaa cbbg aaaa cbbg aaaf bbb gaaad bbb eaaag bbb faaa bbb aaaa bbb aaaa bbb aaaf bbb gaaad bbb eaaae gbbc faaa gbbc faaa cbbg aaaa cbbg aaaa bbb aaaf eddddddddddbbbddddddddde gaaae deeeeeeeeeebbbeeeeeeeeed daaag deeeeeeeeeebbbeeeeeeeeed faaa deeeeeeeeeebbbeeeeeeeeed aaaa deeeeeeeeeebbbeeeeeeeeed aaaa deeeeeeeeeebbbeeeeeeeeed aaaf deeeeeeeeeebbbeeeeeeeeed gaaae deeeeeeeeeebbceeeeeeeeed daaag deeeeeeeeecbbceeeeeeeeed faaa deeeeeeeeecbbceeeeeeeeed aaaa deeeeeeeeebbbeeeeeeeeeed aaaa deeeeeeeeebbbeeeeeeeeeed aaafffffffffaaaaaaaaaaaaaabbbaaaaaaaafed gaaaaaaaaaaaaaaaaaaaaaaaaabbbaaaaaaaaaaafg eaaaaaaaaaaaaaaaaaaaaaaaabbbaaaaaaaaaaaaaag ggg deeeeeeeeebbbeeeeeeeefaaaaa deeeeeeeeebbbeeeeeeeeeedgfa deeeeeeeeebbbeeeeeeeeeed deeeeeeeeebbbeeeeeeeeeed deeeeeeeeebbceeeeeeeeeed bbbbbbbbccgg deeeeeeeecbbceeeeeeeeeed bbbbbbbbbbbbbbbbbbbbcccgg deeeeeeeecbbceeeeeeeeeed cbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbccgg deeeeeeeebbbeeeeeeeeeeed ggccbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbccgg deeeeeeeebbbeeeeeeeeeeed ggccbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbcceeeebbbeeeeeeeeeeed ggccbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbeeeeeeeeeeed ggccbbbbbbbbbbbbbbbbbbeeeeeeeeeeed ggccbbbbbc ``` <!-- end of image --> I'm eager to see what's happening in this magnified view of area A. <!-- image --> ```palette Key,Color ,#fefefeff a,#277664ff b,#d37f64ff c,#e9c0b3ff d,#dca18dff e,#a2c4bcff f,#67998bff g,#e8e3deff ``` ```image bbbbbd gbbbbbd gbbbbbd gbbbbbc cbbbbbc cbbbbbc cbbbbbg dbbbbbg dbbbbbg dbbbbb bbbbbb bbbbbb bbbbbd gbbbbbd gbbbbbd gbbbbbc cbbbbbc cbbbbbc cbbbbbg dbbbbbg dbbbbbg dbbbbb bbbbbb gggggggggggggggbbbbbbeeeeeeeeeeeeeeg aaaaaaaaaaaaaaaaaaaaabbbbbbaaaaaaaaaaaaaaaafe aaaaaaaaaaaaaaaaaaaaabbbbbbaaaaaaaaaaaaaaaaaaa aaaaaaaaaaaaaaaaaaaaabbbbbbaaaaaaaaaaaaaaaaaaa aaaaaaaaaaaaaaaaaaaaabbbbbfaaaaaaaaaaaaaaaaaaa aaaaaaaaaaaaaaaaaaaafbbbbbfaaaaaaaaaaaaaaaaaaa ffffffffffffffffffffdbbbbbdeeeeeeeeeeeeeefaaaa cbbbbbg gefa dbbbbbg dbbbbbg dbbbbb bbbbbb bbbbbb bbbbbd gbbbbbd gbbbbbd gbbbbbc cbbbbbc cbbbbbc cbbbbbg dbbbbbg dbbbbbg dbbbbb bbbbbb g bbbbbb bbbbdddcccggg bbbbbd bbbbbbbbbbbbbbbbdddbbbbbd bbbbbbbbbbbbbbbbbbbbbbbbd bbbbbbbbbbbbbbbbbbbbbbbbc ``` <!-- end of image --> Eureka! There's definitely 1 intersection in area A! Answer: A: 1; 1 = 1 There's only one, but is an intersection after all.

<!-- image --> ```palette Key,Color ,#fefefeff a,#277664ff b,#d47f64ff c,#eac1b5ff d,#de9e8aff e,#a1c3bbff f,#589587ff g,#e9e2ddff ``` ```image bbg gbbb cbbbg dbbbb dbbbbg bbbbbb bbbbbb bbbcbbb bbb bbb bbb cbbb bbb bbb bbb dbbd gbbd bbb gbbc dbbd cbbc bbb dbbg dbbd dbb bbb ag bbb bbbc aaa bbb bbb aaaa bbb bbbc aaaa bbb d aaaf bbb gaaaf bbb eaaae bbd faaag gbbd faaa gbbc aaaa cbbc aaaa dbbg aaaf dbb gaaae bbb eaaag bbb faaa bbb aaaa bbb aaaa bbb aaaf bbb gaaae bbd eaaag gbbd faaa cbbc aaaa cbbc aaaa dbbg aaaf dbb gaaae bbb eaaag bbb faaa bbb aaaa bbb aaaa bbb aaaf bbb gaaaf bbd eaaae gbbd faaag cbbc aaaa cbbg aaaa dbbg aaaa dbb aaaf bbb gaaae bbb eaaag bbb faaa bbb aaaa bbb aaaa bbb aaaf bbd gaaae gbbd eaaag cbbc faaa cbbg aaaa dbbg aaaa bbb aaaffffffffaaaaaaaaaaaaaaabbbaaaaaaaaf gaaaaaaaaaaaaaaaaaaaaaaaaabbbaaaaaaaaaaafg eaaaaaaaaaaaaaaaaaaaaaaaabbbaaaaaaaaaaaaaag ggg bbb eaaaaa bbb gfa bbb bbd gbbd bbbbbbbbdccg cbbc bbbbbbbbbbbbbbbbbbbbddcgg cbbg dbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbddcgg dbbg gccdbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbddccg bbb gccdbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbdccg bbb gccddbbbbbbbbbbbbbbbbbbbbbbbbbbbbb ggcddbbbbbbbbbbbbbbbbb ggcddbbbbc ``` <!-- end of image -->

This image seems promising for intersection detection. My next step is to analyze the details within each area. <!-- image --> ```palette Key,Color ,#fefefeff a,#8253b6ff b,#48d833ff c,#c7b2dfff d,#6bd75eff e,#9989baff f,#b1d7b1ff g,#96cd94ff ``` ```image b gggggggggggggggggggggggggggggggggggggggggggggggggggbbbdgggggggggg fffffffffffffffffffffffffffffffffffffffffffffffffgbbgbbbfffffffff ffffffffffffffffffffffffffffffffffffffffffffffffgbbgffbbbffffffff fffffffffffffffffffffffffffffffffffffffffffffffgbbgffffdbbgffffff ffffffffffffffffffffffffffffffffffffffffffffffgbbgffffffgbbdfffff fffffffffffffffffffffffffffffffffffffffffffffgbbgfffffffffbbbffff ffffffffffffffffffffffffffffffffffffffffffffgbbgfffffffffffdbbgff fffffffffffffffffffffffffffffffffffffffffffgbbffffffffffffffgbbdf ffffffffffffffffffffffffffffffffffffffffffgbbffffffffaafffffffbbb fffffffffffffffffffffffffffffffffffffffffgbbffffffffaaaafffffffbbb ffffffffffffffffffffffffffffffffffffffffgbbffffffffaaeaaffffffffdbbf fffffffffffffffffffffffffffffffffffffffgbbffffffffaaeffaaffffffff bbd ffffffffffffffffffffffffffffffffffffffgbbffffffffaaafffaaffffffff bbb fffffffffffffffffffffffffffffffffffffgbbffffffffaaafffffaafffffff gbbf ffffffffffffffffffffffffffffffffffffgbbffffffffaaaffffffaafffffff bbd fffffffffffffffffffffffffffffffffffgbbffffffffaaaffffffffaaffffff bbb ffffffffffffffffffffffffffffffffffgbbffffffffaaafffffffffaaffffff dbb fffffffffffffffffffffffffffffffffgbbffffffffaaafffffffffffaafffff fbbg ffffffffffffffffffffffffffffffffgbbffffffffaaaffffffffffffaafffff bbb fffffffffffffffffffffffffffffffgbbffffffffaaaffffffffffffffaaffff dbb ffffffffffffffffffffffffffffffdbbffffffffaaafffffffffffffffaaffff fbbg fffffffffffffffffffffffffffffdbbffffffffaaafffffffffffffffffaafff bbb ffffffffffffffffffffffffffffdbbffffffffeaaffffffffffffffffffaafff bbb fffffffffffffffffffffffffffdbbffffffffeaaffffffffffffffffffffaeff gbg ffffffffffffffffffffffffffdbbffffffffeaafffffffffffffffffffffaaff fffffffffffffffffffffffffdbbffffffffeaaffffffffffffffffffffffeaef ffffffffffffffffffffffffdbbffffffffeaaffffffffffffffffffffffffaaf fffffffffffffffffffffffdbbffffffffeaafffffffffffffffffffffffffeae ffffffffffffffffffffffdbbffffffffeaafffffffffffffffffffffffffffaa fffffffffffffffffffffdbbffffffffeaaffffffffffffffffffffffffffffeac ffffffffffffffffffffdbbffffffffeaaffffffffffffffffffffffffffffffaa fffffffffffffffffffdbbfffffffffaafffffffffffffffffffffffffffffffeac ffffffffffffffffffdbbffffffffffaaffffffffffffffffffffffffffffffffaa fffffffffffffffffdbbfffffffffffaeffffffffffffffffffffffffffffffffeac ffffffffffffffffdbbfffffffffffeafffffffffffffffffffffffffffffffff aa fffffffffffffffdbbffffffffffffaafffffffffffffffffffffffffffffffff eac ffffffffffffffdbbfffffffffffffaafffffffffffffffffffffffffffffffff aa fffffffffffffdbbffffffffffffffaafffffffffffffffffffffffffffffffff eac ffffffffffffdbbffffffffffffffeaefffffffffffffffffffffffffffffffff aa fffffffffffdbbfffffffffffffffaaffffffffffffffffffffffffffffffffff ea fffaefffffdbbffffffffffffffffaaffffffffffffffffffffffffffffffffff aa fffaaffffbbbfffffffffffffffffaaffffffffffffffffffffffffffffffffff aa fffeaeffbbbfffffffffffffffffeaeffffffffffffffffffffffffffffffffff aa ffffaafbbbffffffffffffffffffaafffffffffffffffffffffffffffffffffff aa ffffeadbbfffffffffffffffffffaafffffffffffffffffffffffffffffffffff aa fffffaabffffffffffffffffffffaafffffffffffffffffffffffffffffffffff aa ffffbaaffffffffffffffffffffeaefffffffffffffffffffffffffffffffffff aa fffbbdaefffffffffffffffffffaaffffffffffffffffffffffffffffffffffff aa ffgbbfaafffffffffffffffffffaaffffffffffffffffffffffffffffffffffff aa fffgffeaeffffffffffffffffffaaffffffffffffffffffffffffffffffffffff aa fffffffaaffffffffffffffffffaeffffffffffffffffffffffffffffffffffff ae fffffffeafffffffffffffffffeafffffffffffffffffffffffffffffffffffff aa ffffffffaaffffffffffffffffaafffffffffffffffffffffffffffffffffffff cae ffffffffaaffffffffffffffffaafffffffffffffffffffffffffffffffffffff aa fffffffffaefffffffffffffffaefffffffffffffffffffffffffffffffffffff cae fffffffffaaffffffffffffffeaffffffffffffffffffffffffffffffffffffff aa fffffffffeaefffffffffffffaaffffffffffffffffffffffffffffffffffffff cae ffffffffffaafffffffffffffaaffffffffffffffffffffffffffffffffffffff aa ffffffffffeafffffffffffffaeffffffffffffffffffffffffffffffffffffff cac fffffffffffaafffffffffffeafffffffffffffffffffffffffffffffffffffff aa fffffffffffaafffffffffffaafffffffffffffffffffffffffffffffffffffff cac ffffffffffffaeffffffffffaafffffffffffffffffffffffffffffffffffffff aa ffffffffffffaaffffffffffaefffffffffffffffffffffffffffffffffffffff cac ffffffffffffeaeffffffffeaffffffffffffffffffffffffffffffffffffffff aa fffffffffffffaaffffffffaaffffffffffffffffffffffffffffffffffffffff eac gggggggggggggaaggggggggaagggggggggggggggggggggggggggggggggggggggg aa aa ae eac aa ca ac ae aa aa aa cac ae aa ca ea aa aa aa aa ea aeaa aaae caa aa ``` <!-- end of image --> Let's see if area A yields any clues. <!-- image --> ```palette Key,Color ,#fefefeff a,#8253b7ff b,#49d934ff c,#ccbae2ff d,#79e06bff e,#a482cbff f,#b5efadff g,#e6ece9ff ``` ```image gbbbbg bbbbbbf gbbbbfbbbbg gbbbbg dbbbbf gbbbbg fbbbbf bbbbg gbbbbd gbbbbg fbbbbf gbbbbg gbbbbd gbbbbg gdbbbb bbbbg bbbbf gbbbbg gdbbbdg gbbbbg dbbbb gbbbbg gg bbbbd bbbbg caae gdbbbd gbbbdg caaaa fbb gbbbdg caaaaag bb gbbbdg caaaeaae gd bbbbg caaae eaag fbbbdg caaae eaag fbbbd gaaae caae fbbbd gaaae aaag bbbb gaaae aaae fbbbd gaaae caaa fbbbd gaaaeg aaag fbbbd gaaaeg caac bbbb gaaaag aaa fbbbd gaaaa aaa fbbbd gaaaag caac fbbbd gaaaag aaa bbbb gaaaag aaac fbbbd gaaaa eaaa fbbbd geaaag gaaa fbbbd eaaag eaac bbbb eaaag gaae fbbbd aaaa gaae fbbbd eaaag eaac fbbbd eaaac gaae bbbb eaaac aaac fbbbd aaaa eaaa fbbbd eaaac caaa fbbbd eaaac eaag bbbb eaaac caae dbbbf aaaa caae dbbbf eaaac aaa dbbbf eaaac caa bbbb eaaac aa dbbbf aaaa aa dbbbf caaac ca dbbbf caaac a bbbb caaac c dbbbf aaa dbbbf gaaa dbbbf caaa bbbb eaaa dbbbf aaae dbbbf aaag dbbbf aaa bbbb aae dbbbf gaac dbbbf eaa dbbbf aae bbbb gaac dbbbf caac gc dbbbf aae gaac dbbbf gaae gaae gbbbb caac aaag gdbbbf eaa aaaa gdbbbg gaaa caaa dbbbg caaa aaa gbbbb eaaa eaac gdbbbg eaaa eaadbbbg aaac caaabbg aaag aaabb aaa gdaadg aae gbbbaaac eaag bbbbaaae eaa gbbbbeaaa aae fbbbgcaaa caac fg caac eaa aaa aae eaac caac gaae caag caae aaa aaa gaaa aaac caaa aaaa eaaa gaaa aaac eaag aaag caae aaa aaa aae aaa caag eaac eaa gaae aae aaag gaac aaaa eaa caaa aae aaa gaac eaac caac eaag aaa caae gaaa aaa caaa caac eaaa aaac aaae aaae aaac ``` <!-- end of image --> The close-up clearly shows 1 intersection point in area A. Answer: A: 1; 1 = 1 My investigation reveals that there is exactly one intersection in this image.

<!-- image --> ```palette Key,Color ,#fefefeff a,#8252b7ff b,#49d934ff c,#c6b0deff d,#7ee370ff e,#a17dc9ff f,#baf0b2ff g,#e5eae9ff ``` ```image gb gbbbf gbbfbbd gbbg bbb gbbg dbbf gbbg gbbd gbbg bbb gbbg dbbg gbbg g fbbd gbbg aag bbb gbbg aaaa bbbg fbbg aaeeag fbbf fbbg aae aa gbbb fbb aae eag bbb fbb aae aa dbbf fbb aae aag gbbd fbb aae aa bbb fbb aaa aa dbbg fbb aaa aa fbbd fbb eaa aa bbb fbb eaa gaa bbbg fbb eaa aa fbbf fbb eaa gae gbbb fbb eaa aa bbb fbb eaa gae dbd fbb eaa aa g dbb eaa cae dbb eaa aa dbb eaa cae dbb caa aa dbb caa cac dbb caa aa dbb aa cac dbb aa aa dbb ae cac dbb cag aa dbb aa eac dbb aa aa dbb ae eag dbb cac aa g dbb aa eag gae dbb aa aa aa dbb ae eag cac dbb cac aa aa bbb ea aag eadbb aa aa aab aa aa baa cac aa bbbae ea aa fbb aa aa gaa f cac aa aa aa gac gae eag ea aa aa aa gae aa aa aa gae gac cae aa ea aa cac aa cae aa aa aa eag gac cac aa ea aa aa aa cac gae aa aa aa gac cac cac ea aa aa aa eac eag aa aa aa gae eag aa cag ac gae aa aa aa cac ae aa cag eag aa aa aa aa eag gaeaa aaae caa aa ``` <!-- end of image -->

I'm on the case! Let's uncover any intersections hidden in this image. I've noticed 1 areas of interest. These could be potential intersection zones. <!-- image --> ```palette Key,Color ,#fefefeff a,#52cfd2ff b,#6c4ceeff c,#a999f2ff d,#3f0ef5ff e,#a7e3eaff f,#b1d7b1ff g,#95c998ff ``` ```image cb dc d cb gffffffffffffffffffffffg cbddbc gffffffffffffffffffffffg cbddbc gffffffffffffffffffffffg cbddbc gffffffffffffffffffffffg cbddbc gffffffffffffffffffffffg cbddbc gffffffffffffffffffffffg cbddbc gffffffffffffffffffcbddbc gfffffffffffffffffbcfffg ee gffffffffffffffffgbffffg a ae gffffffffffffffffdfffffg a aafffffffffffffffdffffffg e gaaffffffffffffdfffffffg e gffaafffffffffbffffffffg a gffffaaffffffbcffffffffg a gffffffaaffffbfffffffffg e gffffffffaafdffffffffffg e gffffffffffdaffffffffffg a gfffffffffdffgaffffffffg a gffffffffbgffffgagfffffg e gfffffffcbffffffffagfffg e gfffffffdfffffffffffaafg a gffffffbffffffffffffffaa a gffffffdfffffffffffffffgae e gffffffdfffffffffffffffg aa e gffffffdfffffffffffffffg aa a gffffffdfffffffffffffffg aa a gffffffbfffffffffffffffg aa a gffffffbfffffffffffffffg ea e gffffffcfffffffffffffffg ea a gfffffcffffffffffffffffg ea a gfffffbffffffffffffffffg eae a gfffffbffffffffffffffffg eae e fgggggdggggggggggggggggf eae a d ae a d ae a d ae e b aa e c aa a ec aa a c aa e b ea e b ea e d ea d cc d b d d b d cc d b b d c d ce d b b d ec d c d b b d cc d b d d ``` <!-- end of image --> Here's a close-up of the area A. <!-- image --> ```palette Key,Color ,#fefefeff a,#89dee2ff b,#6442f6ff c,#b4a2faff d,#410ff6ff e,#8d6ff9ff f,#d1e3f6ff g,#4bced3ff ``` ```image fce cebddddd bddbecf edc cde fde fdb bdf f bdf gaf edc fggaf cde fgggf fdb fgggf fdb fgggf bdf faggf edf fagga cdc fagga cde fagga fdb agga db aggafbdf agbdc cdbgaf cde aggaf fdb fggaf bdf fgggf bdf fgggf edc fgggf cde faggf fde fagga fdb fagga edf fagga bb agg be a de dc fdc fdf cdf cd ed eb bb be de dc fdc fdf cdf cd ed eb bb be ``` <!-- end of image --> My analysis confirms the presence of 1 intersection in area A. Answer: A: 1; 1 = 1 The final count is: one intersection.

<!-- image --> ```palette Key,Color ,#fefefeff a,#74d9ddff b,#704af8ff c,#ad98faff d,#400df6ff e,#a5e6e9ff f,#dfe7f9ff g,#47cdd2ff ``` ```image f cb dc fd fcb fcbddbc fcbddbc fcbddbc fcbddbc fcbddbc fcbddbc cbddbc cc ee fb g ga d g ga d e ga d e ag bf g ag cc g ag fb e egfd e dgf g d egf g bf ege e cc fge e fb fge g b fge g d ga a d ga ef d ga a d ag g b ag a c ag ff fc egf a cf egf g c egf a b ege ff d fge a d fge g d fge a d ga fe b ga a c aa g ff ag g c ag e b agf e b egf f d eg d cc d bf d d fb d cc d b b d fc d cf d b b d fc d cf d b fb d cc d bf d d ``` <!-- end of image -->

This image looks interesting. I wonder if there are any intersections hidden in there? My next step is to analyze the details within each area. <!-- image --> ```palette Key,Color ,#fefefeff a,#1c09f4ff b,#8b85f3ff c,#e7e2f1ff d,#564bf2ff e,#c0bafbff f,#b1d7b1ff g,#95c898ff ``` ```image e a a a c a cccc cd c cc eb c ccc be c ccc dc c cc a c ccc a c ccc a c ccc a c ccc a c cc a c ccc cd c ccc eb c cc be c ccc d c ccc a c ccc a c ccc a c cc a c ccc a c c d c c ed c c bb c c de c c d c c a c c a c c a cc a c c a c c d c c eb c be c dc c a d c a aac fgggcggggggggggagggggggg abeb gfffcffffffffffaffffffff ae a gffffcfffffffffaffffffff ac a gffffcfffffffffaffffffff ca a gfffffcffffffffdffffffff ea de gfffffcfffffffbdffffffff ea ed gffffffcffffffdbffffffff ba a gffffffcffffffdfffffffff dd a gfffffffcfffffafffffffff ad a gffffffffcffffafffffffff ab be gffffffffcffffafffffffff ae cd gfffffffffcfffafffffffff ac a gfffffffffcfffafffffffff cac a gffffffffffcffafffffffff ea dc gffffffffffcdaffffffffff ea eb gfffffffffgacfffffffffff ba a gffffffffaafcfffffffffff dd a gffffffbagfffcffffffffff ad a gfffffadfffffcffffffffff ab de gfffdaffffffffcfffffffff ae ed gfgabfffffffffcfffffffff ac a gaaffffffffffffcffffffff a bagfffffffffffffcffffffff a adgfffffffffffffffcfffffff be da gfffffffffffffffcfffffff cd eab gffffffffffffffffcffffff a aa gfffffffffffffffffcfffff a bae gfffffffffffffffffcfffff dc ad gffffffffffffffffffcffff eb da gffffffffffffffffffcffff a eab fggggggggggggggggggggggg a aa a bae de ad ed da a eab a aa a bae bbad ca ``` <!-- end of image --> Here's a close-up of the area A. <!-- image --> ```palette Key,Color ,#fefefeff a,#3928f5ff b,#958cf9ff c,#e7e0f1ff d,#695df7ff e,#c0bbfbff f,#1703f5ff g,#f3f0f8ff ``` ```image gcg cfd cc efb gcg bfb cc bfe gcg dfe cc dfc gcg af cc aa gcc fa ccg cfd gcc efd ccg efb cc bfb gcg bfe cc dfe gcg dfc cc af gcg fa cc gfa gcg cfd cc efd gcg efb cc bfb gcc dfe ccg dfc gcc afg ccg af gcc gfa ccg eafd ccdffdg ecdae eaacc gdffdccg eafae cc cdffdg gcg bffae cc eaffb gcg gdffdc cc eafae gcg cdffdg cc bffae gcc eaffb ccg gdffdc gcc eafae ccg dffdg gcc fae ccg b cc gcg cc gcg cc gcg cc gcg cc gcg cc gcc ccg gcc g ``` <!-- end of image --> Aha! I've found 1 intersection inside area A! Answer: A: 1; 1 = 1 My investigation reveals that there is exactly one intersection in this image.

<!-- image --> ```palette Key,Color ,#fefefeff a,#301ef5ff b,#8e85f9ff c,#ebe6f4ff d,#5d4ff7ff e,#cfcbfbff f,#1602f4ff g,#b0a9fbff ``` ```image e f f f c a cccc cd c ccc gb c ccc bg c ccc dc c cc a c ccc f c ccc f c ccc f c ccc f c ccc a c ccc ed c ccc gb c cc be c ccc dc c ccc f c ccc f c ccc f c ccc f c ccc f c c a c c ed c c bb c c de c c a c c f c cc f c c f cc cc f c c f c cc cd c c eb c bg c de c a d c f afc c f fbgb c f fg a c f fe f c a cfc f c cd ef de c gb gf ed c bg ba f cc dc da f c a ad a cc f fb bg c f fg ca c f fe f c f cfc f c ca ef dc cdfc gf gb eae ba a aa c da f bfe c ad f cfd c fb de dfc c fg ed efb c fe f aa c f bfe c a cfd c bg dfc cc ca efb c f aa cc f bfe c dc cfd c gb dfc c a efb f aa f bfe de cfd ed dfc f efb f aa a bfe bbfd cfc ``` <!-- end of image -->

This image looks interesting. I wonder if there are any intersections hidden in there? There are 2 regions I'd like to highlight in the image. <!-- image --> ```palette Key,Color ,#fefefeff a,#56aa62ff b,#b24c49ff c,#b1d7b1ff d,#1e8f2fff e,#bb7c72ff f,#d7d3c7ff g,#93c794ff ``` ```image g ad ddd ddfd cd da da fd gd da dg cd ad da df gd dd dg fd gd da dg gd ad dg dc ad ad dc df dd ad fd df dd dd cd d da dd ad fd dc ggddgggggggggggggggggggc ad ccgdcccccccccccccccccccg df cccdaccccccccccccccccccg dd cccgdccccccccccccccccccg fd ccccdacccccccccccccccccg da ccccadcccccccccccccccccg fb gd cccccdaccccccccccccccccg ebbe dg cccccadccccccccccccccccg fbbbf ad ccccccdacccccccccccccccg ebbe df ccccccadcccccccccccccccg fbbbf dd cccccccdgccccccccccccccg ebbe fd cccccccadccccccccccccccg fbbbf da ccccccccdgcccccccccccccgebbb gggggggggggadc ccccccccddcccccccccccgbbbf cccccccccccdag cccccccccdgccccccccebbbg ccccccccccadcg cccccccccddcccccgbbbeccg ccccccccccdgcg ccccccccccdcccebbbcccccg cccccccccddccg ccccccccccddbbbecccccccg ccccccccgdgccg cccccccccebbbgcccccccccg ccccccccddcccg cccccccbbbeddccccccccccg cccccccgdccccg ccccebbbgccgdccccccccccg cccccccdaccccg ccbbbeccccccdacccccccccg ccccccadcccccg fbbbgccccccccgdcccccccccg ccccccdacccccg ebbeccccccccccccdaccccccccg cccccddccccccg fbbbf cccccccccccccadccccccccg cccccdgccccccg ebbe ccccccccccccccdacccccccg ccccddcccccccg fbbbf ccccccccccccccadcccccccg cccgdccccccccg ebbe cccccccccccccccdaccccccg cccdaccccccccg fbbbf cccccccccccccccadccccccg cccgcccccccccg ebbe ccccccccccccccccdgcccccg cccccccccccccg fbbbf ccccccccccccccccadcccccg cccccccccccccg febbbe cccccccccccccccccdgccccg cccccccccccebbbbbef cccccccccccccccccddccccg ccccccebbbbbbe ccccccccccccccccccdgcccg cccbbbbbeccccg ccccccccccccccccccddcccg cccecccccccccg cccccccccccccccccccdcccg cccccccccccccg gccccccccccccccccccddccg gggggggggggggc fd da fd da cd da a gd adf dg adf gd adf dg adf ad adf dc adf ad adc df adc ad gdc df gdc dd gdc d gdc dddc fdc ``` <!-- end of image --> Let's see what secrets area A holds. <!-- image --> ```palette Key,Color ,#fefefeff a,#4ca559ff b,#b44e4bff c,#a4d1abff d,#1e8e2eff e,#d09290ff f,#deddd3ff g,#7abc84ff ``` ```image cdda dddf gddg fddd addc fdda addc cdda dddf gddg fdddf gddg fddd addc cdda addf cdda dddf gddg fddd addc cdda addc cdda dddf gddg fddd addc fdda addc cdda addf cg f feebb feebbbbbbb feebbbbbbbbbbbe feebbbbbbbbbbbeef ebbbbbbbbbeeff ebbbbeeff feff ``` <!-- end of image --> The evidence suggests that this is not an intersection point in area A. Moving on to the next area. Let's see what secrets area B holds. <!-- image --> ```palette Key,Color ,#fefefeff a,#50a85dff b,#b44f4bff c,#b8dabcff d,#1e8e2fff e,#d09290ff f,#e5ddd7ff g,#87c18eff ``` ```image fdda addc cdda addc cdda addc cdda addf cdda dddf gddg dddf gddg ddd gddg fddd gddg fddd addc fdda addc cdda addc cdda addc cdda addf feb cdda ebbbb dddf febbbbbb gddg ebbbbbbef dddf febbbbbbef gddg fbbbbbbef ddd febbbbbbef gddg febbbbbef fdddebbbbbbef gbbbbbbbf febbbbbbef febbbbbbdc febbbbbbecdda febbbbbbe addc febbbbbbef cdda febbbbbbe addc ebbbbbbef cdda febbbbbbe addc bbbbbbef cdda bbbbe addf bef cdda f dddf gddg dddf gddg ddd gddg fddd gddg fddd addc fdda addc cdda addc cdda addc cdda addf cdda dddf gddg dddf gddg ddd gddg ``` <!-- end of image --> I am surprised, so clear, 1 intersection has appeared in area B. Answer: A: 0; B: 1; 0 + 1 = 1 My investigation reveals that there is exactly one intersection in this image.

<!-- image --> ```palette Key,Color ,#fefefeff a,#44a152ff b,#b5504dff c,#a5d2acff d,#1d8e2eff e,#d59c9bff f,#d8e0d2ff g,#70b87bff ``` ```image c ad ddd ddfd fd da da fd gd da dc cd ad dg df cd dd dg fd gd da dc cd gd dg dc gd ad dc df dd ad fdf df da dd cd d dg dd gd fd dc da ad fd df da dd cd fd dg da cd eb gd dg bbbb dc gd fbbbe ad dc ebbb df gd fbbbe dd dc ebbb fd ad fbbbe da df ebbb cd ad fbbbe dg df ebbb gd dd fbbbe dc d ebbbf dd dabbbe fdf ebbbf da fbbbeda cd ebbbf fd dg bbbe da gd ebbbf cd dc bbbe dg ad ebbbf cd df bbbe dg dd ebbbf gd fd bbbb dc da fbbbe gd c ebbb dc fbbbe ad febbbb df ebbbbbbe ad ebbbbbbe df bbbbbe dd ef d dd fd da fd da cd dg g cd gdf dg gdf gd gdf dc gdf gd gdf dc gdf ad gdf df gdf ad gdc df gdc dd gdc d gdc dddc fdc ``` <!-- end of image -->

I have an image in front of me. I need to determine if there are any intersection segments. My next step is to analyze the details within each area. <!-- image --> ```palette Key,Color ,#fefefeff a,#a6192cff b,#5f08b1ff c,#c68488ff d,#925fc5ff e,#dabbd8ff f,#b34653ff g,#aed5adff ``` ```image dbbd dbbbbbbb dbbbbbbbbd edbbbbbbbbd gggggggggggggggggggggggg edbbbbbbbbe gggggggggggggggggggggggg edbbbbbbbbe ggggggggggggggggggggggggedbbbbbbbbe ggggggcfggggggggggggdbbbbbbbbde gggggfaacgggggggdbbbbbbbbde ggggaaaaaggggbbbbbbbbdgg eaa gggaaacaaaggbbbbbdgggggg aaf ggaaagggaaggbbgggggggggg aa gaaaggggfaagbbgggggggggg caa eaaaggggggaafbbgggggggggg aae caaagggggggcaabdgggggggggg eaa faafgggggggggaaaggggggggggg aaf aaacgggggggggggaacgggggggggg aa aaae gggggggggggaaagggggggggg caa aaae ggggggggggdbaafggggggggg aac eaaa ggggggggggbbdaaggggggggg aa eaaa ggggggggggbbgaaagggggggg faf caaa ggggggggggbbggaacggggggg aa faaf ggggggggggbbggcaaggggggg caa aaac gggggggggdbbgggaaagggggg aac aaae gggggggggbbdggggaagggggg aa aaa gggggggggbbgggggfaaggggg faa eaaa gggggggggbbggggggaafgggg aae eaaa ggggggggdbbggggggcaagggg eaa caaa ggggggggbbdgggggggaaaggg aac faaf bbe aac aa aaac bb caa faa aaae bb aaf aae aaa dbb aae eaa eaaa bbd faa aaf eaaa bb aac aa caaf bb eaa caa faaf ebb aaa aae aaac dbb aae eaa faae bbe caa faf a bb aaf aae bb eaa aa ebb aaa caa dbd aac aac bbe caa aa bb aaf eaa bb aae faf dbb faa aae bbd aac aa bbe eaa caa bb aaa aae ebb aae aa dbb caacaa bbd aaaac bb eaaa bb faa ebb ac dbd bbe bb bb ebb bbd bbe bb ebb dbb bbd bb bb ebb dbd bbe bb de bb ebbbbbde ebb ebbbbbbbbbbde bbd ebbbbbbbbbbbde bbe edbbbbbbbbbbde bb edbbbbbbbbbbbb dbbbbbbb ed ``` <!-- end of image --> I'm now examining the contents of area A in detail. <!-- image --> ```palette Key,Color ,#fefefeff a,#a6192dff b,#6008b0ff c,#da9fa7ff d,#9459caff e,#c19fe0ff f,#bd5665ff g,#ebd8e6ff ``` ```image ged cffg gedbbbb faaaf gedbbbbbbbb faaaaac gedbbbbbbbbbbbb gfaaaaaaag gedbbbbbbbbbbbbbbbb gaaaaaaaaaf gdbbbbbbbbbbbbbbbbdeg caaaaaaaaaaac dbbbbbbbbbbbbbdeg caaaaaaccaaaaa gbbbbbbbbbbdeg caaaaaag faaaac ebbbbbbdeg faaaaaag gaaaaag dbbbbg faaaaafg caaaaf dbbbd gfaaaaaf faaaac bbbbe aaaaaaf gaaaaaebbbbe aaaaac faaaafbbbb aaaac aaaaabbbb aaag caaaaabbd aag faaaabbe fg gaaaaabg caaaaa aaaaac baaaaa gbaaaaac ebbaaaaag dbbbaaaaf dbbbaaaaac bbbbdaaaaag gbbbbecaaaaf ebbbbg aaaaag dbbbb caaaaf bbbbd faaaac bbbbe gaaaaag ebbbbg caaaaf ebbbb faaaac dbbbd gaaaaa bbbbd faaaaf gbbbbe aaaaag ebbbbg caaaaf dbbbb faaaac dbbbd gaaaaag bbbbd caaaaf gbbbbe faaaac ebbbbg gaaaaa dbbbb faaaac ``` <!-- end of image --> There's no doubt about it - I see 1 intersection in area A. Answer: A: 1; 1 = 1 One intersection, that's it, but I found it.

<!-- image --> ```palette Key,Color ,#fefefeff a,#a6192cff b,#5f07b1ff c,#ce828cff d,#9256c9ff e,#d0aad0ff f,#b84959ff g,#ebdae8ff ``` ```image dbbd gdbbbbbbb gdbbbbbbbbd gdbbbbbbbbe gdbbbbbbbbe edbbbbbbbbe edbbbbbbbde ec ebbbbbbbbde faac ebbbbbbbbdg aaaaa gbbbbbbbbdg gaa aaaeaaf bbbbbdg aaf aaag gaag bbg aa gaaa faa bb caa eaaa aafbb aae caaa eaabd gaa faaf aaag aaf aaac aae aa aaae gaaa caa aaag dbaaf aac gaaa bbdaag gaa eaaa bbgfaa faf caaa bb aac aag faaf ebb caa caa aaac dbd aaa aac aaae bbe aag aa aaag bb faa faa gaaa bb aaf aag eaaa ebb eaa eaa caaa dbd aaa aac faaf bbe aae aa aaac bb caa faa aaae gbb aaf aae aaag dbb gaag eaa gaaa bbd faa aaf eaaa bbg aac aa caaa bb eaa caa faaf gbb aaa aae aaac dbb aae gaa aaae bbe faa faf ag bb aaf aae bb gaag aa ebb aaa caa dbd aac aac bbe caa aa bb aaa eaa bb gaag faf ebb faa aag bbd aac aa bbg eaa caa bb aaa aae gbb aae aa dbb caacaa bbe aaaac bb gaaa bb faa ebb ac dbd bbe bb bb ebb bbd bbg bb gbb dbb bbd bbg bb ebb dbd bbe bb dg bb ebbbbbde ebb ebbbbbbbbbbde dbd edbbbbbbbbbbdg bbe edbbbbbbbbbbde bb gdbbbbbbbbbbbb gebbbbbbb ed ``` <!-- end of image -->

I'm on the case! Let's uncover any intersections hidden in this image. I'd describe these as 'hotspots' for potential intersections. <!-- image --> ```palette Key,Color ,#fefefeff a,#66d64cff b,#a9c6bfff c,#97d093ff d,#eff6efff e,#d0ebd0ff f,#82d96eff g,#b1d7b1ff ``` ```image ddeeeeggggccfc eaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa aaaffffcccgggeeeeddd ad ad ae ca ag af af ad aa ca fa ae bd af ca da dccccccccccbbcccccccccacccccccd ea ga dgggggggggbbbggggggggfagggggggd da fa dgggggggggbbbbgggggggafgggggggd a af dgggggggggbbbbgggggggaggggggggd ae ag dgggggggggbggbbgggggfaggggggggd ag a dgggggggggbggbbgggggafggggggggd ac ea dgggggggggbgggbgggggagggggggggd af ca dggggggggbbgggbbgggaagggggggggd fa aa dggggggggbbggggbgggafgggggggggd ca ac dggggggggbbggggbbgcaggggggggggd ga ae dggggggggbggggggbgaaggggggggggd ea da dggggggggbggggggbbafggggggggggd a ga dgggggggbbggggggbbagggggggggggd ad aa dgggggggbbgggggggbcgggggggggggd ae ac dgggggggbbgggggggcbgggggggggggd ag ae dgggggggbgggggggcabgggggggggggd af ea dgggggggbgggggggaabbggggggggggd aa ca dgggggggbgggggggacgbggggggggggd fa aa dggggggbbggggggcaggbbgggggggggd ga ag dggggggbbggggggaagggbbggggggggd ea ad dggggggbbggggggacggggbbbbgggggd da ea dggggggbggggggcagggggggbbbbgggd a fa dggggggbggggggaaggggggggggbbggd ae af dggggggbggggggacgggggggggggbbgd ag ae dgggggbbgggggfagggggggggggggbbe ac da dgggggbbgggggaaggggggggggggggbbe af ga dgggggbbgggggacgggggggggggggggebb fa aa dgggggbgggggfaggggggggggggggggddbb ca ac dgggggbgggggaaggggggggggggggggd dbb ga ad dggggbbgggggagggggggggggggggggd bb ea ea dggggbbggggfagggggggggggggggggd bb a ca dggggbbggggafgggggggggggggggggd bb ad af dggggbgggggaggggggggggggggggggd bbd ae ag dggggbggggfaggggggggggggggggggd bbd ag a dggggbggggafggggggggggggggggggd bbd af ga dgggbbggggagggggggggggggggggggd bbe aa fa dgggbbgggfagggggggggggggggggggd ebe fa af dgggbbgggafgggggggggggggggggggd ebb ga ae dgggbggggaggggggggggggggggggggd dbb ea da dgggbgggfaggggggggggggggggggggd dbb da ga dgggbgggafggggggggggggggggggggd dbb a aa dggbbggcagggggggggggggggggggggd bb ae ac dggbbggaagggggggggggggggggggggd bb gcccccafccacccccd dggbbggafgggggggggggggggggggggd bbd cgggggafgcagggggd dggbggcaggggggggggggggggggggggd bbd cgggggaagfagggggd dggbggaaggggggggggggggggggggggd bbd cgggggaagaagggggd dgbbggafggggggggggggggggggggggd bbe cgggggfagacgggggd dgbbgcagggggggggggggggggggggggd ebe cgggggcagaggggggd dgbbgaagggggggggggggggggggggggd ebb cgggggcacaggggggd dgbggacgggggggggggggggggggggggd dbb cggggggaaaggggggd dgbgcaggggggggggggggggggggggggd dbb cggggggaafggggggd dgbgaaggggggggggggggggggggggggd dbbcggggggaacggggggd dbbgacggggggggggggggggggggggggd bbggggggaagggggggd dbbcagggggggggggggggggggggggggd bbgggggaagggggggd dbbaagggggggggggggggggggggggggd cbbggggaagggggggd dbgacgggggggggggggggggggggggggd cgbbggggggggggggd dbcaggggggggggggggggggggggggggd cggbbgggggggggggd ebaaggggggggggggggggggggggggggd cgggbbbgggggggggd bbacggggggggggggggggggggggggggd cggggbbbggggggggd bbagggggggggggggggggggggggggggd cgggggbbbgggggggd bcagggggggggggggggggggggggggggd gcccccccbbccccccd bacgggggggggggggggggggggggggggd dbb caggggggggggggggggggggggggggggd dbb aaggggggggggggggggggggggggggggd bb acccccccccccccccccccccccccccccd bb bbd bbd bbd bbe ebe ebe d ``` <!-- end of image --> Let's take a closer look at area A. <!-- image --> ```palette Key,Color ,#fefefeff a,#67d64cff b,#a9c5c0ff c,#a7e699ff d,#e2efe7ff e,#c9f0bfff f,#87dd74ff g,#c4d8d4ff ``` ```image bbbg fae bbbb aa bbbbg eaa bbbbb faa bbdbbb eaaf dbg bbbd faae dbg dbbg daaa gbd bbbd eaac gbd gbbg faae bb bbb daaa bb gbb caac dbg gbd daaa gbd dbg caac gbd bbd faad bb gbg aaa bb bb aac dbb bbg aad dbb bbb daf bbb dbbb aad bbb bbbddaf dbbg dbbgcac dbbg bbbfad gbbd gbbca gbbd bbba bbb gbbf dbbg cbbb dbbg afbb gbbd eaabbd gbbd faabbg bbb aaadbbd bbb eaaf gbg dbbg aaa bbg gbbd eaaf bbb bbb faae gbbg bbb aaa dbbbbgd dbbg aaf gbbbbbgd dbbg aae dgbbbbbgd gbbd daa dbbbbbbgd bbb fae dgbbbbd bbb daa dbbbd bbg cac dbbbd bbg fae bbbb bbd daa gbb bbd caa gb bb faa g dbg caac dbg faad gbd daaf bb caac bb aaad dbg eaaf dbg caac gbd eaaf bb caac bb aaad dbb eaaf dbb caae gbb aaad gbb aaf bbb aad dbbg eaf dbbg fae gbbd aa gbb eaf bbb fae dbbg daa gbbd faa gbbd daaa bbb eaac bbb faae dbbg daaa dbbg caac gbbd faae bbb caac bbb faad dbbg daaa dbbg caac gbbd aaad gbb aaf bbb aac bbg aad bbd cac bbd aad bb eaf bb cac dbg aad dbg eaa gbd caa bb eaaf bb faae dbg aaad dbg eaaf gbd faae gb aaa bb eaaf dbbdaaa gbbeaaf gbbfaae bbbaaa bbbaac dbbgaae dbbgaa gbbfae bbbaa bbbac bbcad bbfa bbfa gbaa caac aaad aaf ``` <!-- end of image --> Oh my, look at that! It's 1 intersection in area A! Alright, let's concentrate on the next area. This close-up might reveal an intersection in area B. <!-- image --> ```palette Key,Color ,#fefefeff a,#66d64cff b,#a9c5c0ff c,#a7e797ff d,#e2f1e4ff e,#c7efbeff f,#85de70ff g,#c4d7d4ff ``` ```image caae caae caae faad eaac aaa eaac eaaf daaf caac aaf faae aaa aaa faa daaf faad eaac caae caae caae faad eaac aaa eaacdaaf daafeaac daafcaae aaafaad aaaaaa faaaaf faaaac caaaae g caaaa bg eaaaf bbg eaaac bbbg daaae dbbbg aaad dbbbb aaa dbbbb efe dbbbbd dbbbbd bbbbd gbbbd gbbbg gbbbg gbbbg gbbbg dbbbg dbbbb ``` <!-- end of image --> Based on this close-up, I can conclude that there's no intersection in area B. Answer: A: 1; B: 0; 1 + 0 = 1 I've found a single intersection point in the image.

<!-- image --> ```palette Key,Color ,#fefefeff a,#66d64bff b,#a9c5c0ff c,#a3e693ff d,#e4f1e5ff e,#c6efbcff f,#83dc6eff g,#c6d8d5ff ``` ```image ddddeeeeccccfc eaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa aaaffffccccceeeedddd ad ad ae ca ac af af ad aa ca fa ad bd af ca da dbb a ea ca gbb fa da fa bbbb ac a af bggb da ad ae bd bg fa ae a b gb ac ac ea db bd da af ca gb bb fa fa aa bb b ac ca ac bg bb da ea ad b db fa da da db bgac a ca gb gba ad aa bb bf ae ac bg bb ac ad bd eabd af da b aabb aa ca db ae b fa aa gb ea bb ca ac bb aa dbbd ea a bg ae dbbbg da ea bd ea gbbb a fa b aa bbd ad af db ae bbd ae ae gb ca gbg ac da bb af gbg af ca bg ad dbg fa aa b ca dbb ca ac db af dbb ea ad gb ad bb da da bb ca bb a ca bg af bb ad af bd ad bb ae ae b ca bbd ac a db af bbd af ea gb a gbg aa fa bb fa gbg fa af bg ac dbg ca ae bd da dbb ea da b fa dbb da ca db ac bb a aa gb da bb ad ac bb fa bb ae ad bg ac bb ac ea b da bbd af fa db fa bbd fa af gb ac gbg ca ae bb ea gbg ea a bg aa dbg daea bd ae dbb afa b ea dbb aaf db aa bb aae gb ae bb aa bbea bb aa bgaa bb aa bdae bbd bea bbd dbaa gbg gbae gbg bba dbg bff dbb gad dbb ca bb af bb ad bb bb bbd bbd gbg gbg gbg d ``` <!-- end of image -->

I'm approaching this image with caution. Intersections might be tricky to spot. I'm going to focus my attention on these specific areas. <!-- image --> ```palette Key,Color ,#fefffeff a,#90c968ff b,#a8d3a5ff c,#96ca96ff d,#8dd665ff e,#99d17dff f,#b1d7b1ff g,#a2d392ff ``` ```image bfffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffc bfffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffc bfffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffefffc bffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffeddffc bfffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffbdddffc bfffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffdddfffc bffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffdddgfffc bfffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffeddeffffc bffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffbdddfffffc bffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffdddffffffc bfffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffdddbffffffc bffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffeddefffffffc bfffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffgdddffffffffc bfffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffdddfffffffffc bffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffdddbfffffffffc bfffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffdddeffffffffffc bffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffgdddfffffffffffc bfffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffbdddffffffffffffc bfffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffdddbffffffbaafffc bffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffdddgfffffffaaafffc bfffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffedddfffffffaaaafffc bffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffbdddfffffffgaaaafffc bffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffdddfffffffbaaaaafffc bfffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffdddgfffffffaaagaafffc bffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffeddefffffffaaagbaafffc bfffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffbdddfffffffgaaafbaafffc bfffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffdddffffffffaaaffbaafffc bffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffdddbfffffffaaabffbaafffc bfffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffeddefffffffeaaefffbaafffc bffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffgdddfffffffgaaaffffbaafffc bffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffdddffffffffaaaffffffaabffc bfffffffffffffffffffffffffffffffffffffffffffffffffffffffffffdddbfffffffaaabffffffaabffc bffffffffffffffffffffffffffffffffffffffffffffffffffffffffffdddefffffffeaaefffffffaabffc bfffffffffffffffffffffffffffffffffffffffffffffffffffffffffgdddfffffffbaaaffffffffaabffc bfffffffffffffffffffffffffffffffffffffffffffffffffffffffffdddffffffffaaafffffffffaabffc bffffffffffffffffffffffffffffffffffffffffffffffffffffffffdddbfffffffaaabfffffffffaabffc bfffffffffffffffffffffffffffffffffffffffffffffffffffffffdddgfffffffeaaeffffffffffaabffc bffffffffffffffffffffffffffffffffffffffffffffffffffffffgdddfffffffbaaafffffffffffaagffc bfffffffffffffffffffffffffffffffffffffffffffffffffffffbdddffffffffaaaffffffffffffaagffc bfffffffffffffffffffffffffffffffffffffffffffffffffffffdddffffffffaaagffffffffffffaagffc bffffffffffffffffffffffffffffffffffffffffffffffffffffdddgfffffffeaaefffffffffffffaagffc bfffffffffffffffffffffffffffffffffffffffffffffffffffedddfffffffbaaaffffffffffffffaagffc bffffffffffffffffffffffffffffffffffffffffffffffffffbdddffffffffaaafffffffffffffffaagffc bffffffffffffffffffffffffffffffffffffffffffffffffffdddffffffffaaagfffffffffffffffaagffc bfffffffffffffffffffffffffffffffffffffffffffffffffdddgfffffffgaaaffffffffffffffffaagffc bffffffffffffffffffffffffffffffffffffffffffffffffeddeffffffffaaafffffffffffffffffaaeffc bfffffffffffffffffffffffffffffffffffffffffffffffbdddffffffffaaaffffffffffffffffffaaeffc bfffffffffffffffffffffffffffffffffffffffffffffffdddffffffffaaagffffffffffffffffffaaeffc bffffffffffffffffffffffffffffffffffffffffffffffdddbfffffffgaaafffffffffffffffffffaaeffc bfffffffffffffffffffffffffffffffffffffffffffffeddeffffffffaaaffffffffffffffffffffaaeffc bffffffffffffffffffffffffffffffffffffffffffffgdddffffffffaaabffffffffffffffffffffaaeffc bffffffffffffffffffffffffffffffffffffffffffffdddffffffffeaaefffffffffffffffffffffaaeffc bfffffffffffffffffffffffffffffffffffffffffffdddbfffffffgaaaffffffffffffffffffffffaaeffc bffffffffffffffffffffffffffffffffffffffffffdddeffffffffaaafffffffffffffffffffffffaaeffc bfffffffffffffffffffffffffffffffffffffffffgdddffffffffaaabfffffffffffffffffffffffaaaffc bffffffffffffffffffffffffffffffffffffffffbdddffffffffeaaeffffffffffffffffffffffffaaaffc bffffffffffffffffffffffffffffffffffffffffdddffffffffbaaafffffffffffffffffffffffffaaaffc bfffffffffffffffffffffffffffffffffffffffdddgffffffffaaaffffffffffffffffffffffffffaaaffc bffffffffffffffffffffffffffffffffffffffdddeffffffffaaabffffffffffffffffffffffffffaaaffc bfffffffffffffffffffffffffffffffffffffedddffffffffeaaefffffffffffffffffffffffffffaaaffc bffffffffffffffffffffffffffffffffffffbdddffffffffbaaaffffffffffffffffffffffffffffaaaffc bffffffffffffffffffffffffffffffffffffdddfffffffffaaafffffffffffffffffffffffffffffaaaffc bffagfffffffffffffffffffffffffffffffdddbffffffffaaagfffffffffffffffffffffffffffffaaaffc bfaaaabffffffffffffffffffffffffffffdddeffffffffeaaeffffffffffffffffffffffffffffffaaaffc bfbaaaaaffffffffffffffffffffffffffedddffffffffbaaafffffffffffffffffffffffffffffffaaaffc bfffgaaaagfffffffffffffffffffffffgdddfffffffffaaaffffffffffffffffffffffffffffffffaaaffc bfffffaaaaabfffffffffffffffffffffdddfffffffffaaagffffffffffffffffffffffffffffffffaaaffc bffffffbaaaaefffffffffffffffffffdddbffffffffgaaafffffffffffffffffffffffffffffffffaaaffc bffffffffeaaaagffffffffffffffffdddgfffffffffaaaffffffffffffffffffffffffffffffffffaaaffc bffffffffffaaaaaffffffffffffffedddfffffffffaaafffffffffffffffffffffffffffffffffffaaaffc bfbdefffffffbaaaaefffffffffffgdddfffffffffaaagfffffffffffffffffffffffffffffffffffbbbffc bfddddbfffffffeaaaagffffffffbdddfffffffffgaaafffffffffffffffffffffffffffffffffffffffffc bffdddddffffffffaaaaafffffffdddbfffffffffaaaffffffffffffffffffffffffffffffffffffffffffc bfffgddddgfffffffbaaaaeffffdddgfffffffffaaabffffffffffffffffffffffffffffffffffffffffffc bfffffdddddffffffffeaaaabfdddefffffffffeaaefffffffffffffffffffffffffffffffffffffffffffc bffffffbddddeffffffffaaaaadddfffffffffgaaaffffffffffffffffffffffffffffffffffffffffffffc bffffffffeddddbfffffffgaaaaaffffffffffaaafffffffffffffffffffffffffffffffffffffffffffffc bffffffffffdddddffffffffaaaaabfffffffaaabfffffffffffffffffffffffffffffffffffffffffffffc bfffffffffffgddddgfffffdddaaaaafffffeaaeffffffffffffffffffffffffffffffffffffffffffffffc bfffffffffffffdddddfffdddefgaaaaeffbaaafffffffffffffffffffffffffffffffffffffffffffffffc bffffffffffffffbddddeedddffffeaaaabaaaffffffffffffffffffffffffffffffffffffffffffffffffc bffffffffffffffffeddddddffffffbaaaaaabffffffffffffffffffffffffffffffffffffffffffffffffc bffffffffffffffffffddddfffffffffgaaaefffffffffffffffffffffffffffffffffffffffffffffffffc bfffffffffffffffffffgdbfffffffffffeaffffffffffffffffffffffffffffffffffffffffffffffffffc bfffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffc bfffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffc ``` <!-- end of image --> Here's a close-up of the area A. <!-- image --> ```palette Key,Color ,#fefefeff a,#90c968ff b,#b3de98ff c,#dbefceff d,#8dd765ff e,#a0d57eff f,#c8e7b5ff g,#eff7e9ff ``` ```image g ddf gdddc ddde dddd gdddf dddd dddf fdde gddd ddd gdddc eddd fdddg gdddf dddd eddf fdde gaac dddc eaab eddb caaae dddd aaaae eddd aaaaae cdddg baaeaae dddb caaacaae bdde eaafcaae gddd faae caaa ddd aaa gaaa cdddc caaag gaaa dddb aaaf gaaa dddd aaaa gaaa gdddf gaaac gaaa ddde aaae aaa dddc aaaf aaa bdde faae aaa gddd gaaa aaa bddd faaag aaa cdddc gaaaf eaa eddd baaa eaa fdddg gaaac eaa gdddf aaae eaa dddg aaac eaa dddf baae eaa bdde gaaa baa dddg eaab baa eddb aaaa baa dddd baaa baa eddd caaag baa fdddg aaab baa gdddf aaac faa eddb aaa faa cddd aaag faa ddd eaaf faa cdddg aaaa faa dddb eaaa faa dddd caaag caa gdddc aaaa caa ddde faae caa dddc gaaa caa eddb aaa caa fddd eaaf caa dddd faae gaa gdddb gaaac gaa dddd aaab gaa dddd aaaa gaa edde baaa gaa ea fddd gaaac gaag gaaaag gddd aaa aag baaaae bdddg aaac aag eaaaab dddd aaa aag gbaaaac dddd caaag aag aaaaaf bddd aaab aac caaaaag cdddc aaaa aac eaaaae gddd baaa aac cc gbaaaac dddg gaaac aac ddg eaaaae fddd eaaf gg cddddg gaaaaac gddd caaa fdddde faaaaa bdddg aaa dddddf caaaabg cdddc caaag eddddg baaaae dddb aaab gdddddg aaaaadddd aaaa cddddd gaaaaaddc gaaac eddddb aaaaaf aaae gbddddg ddaaaaag eaaf gdddddc gdddfeaaaae faae fddddd ddde gbaaaac gaaa edddddddd aaaaaaaag bddddddf gaaaaaaa dddde faaaa cdg eag ``` <!-- end of image --> Success! This area contains 1 intersection point! Answer: A: 1; 1 = 1 There's only one, but is an intersection after all.

<!-- image --> ```palette Key,Color ,#fefefeff a,#90c968ff b,#b6e09cff c,#def1d3ff d,#8dd765ff e,#a1d680ff f,#cbe8b8ff g,#f0f8eaff ``` ```image b bdd gddd ddd dddc bdde cddd ddd dddc eddb cddd ddd dddg eddb fddd gddd dddg gaa dddf aaa bdde aaaa gddd faaaa ddd gaaaaa dddc aaacaa bdde eaafcaa cddd faaa caa ddd aaa gaa dddc aaag gaa eddb eaab gaa cddd caaa gaag ddd aaa gaag dddg aaag aag eddb eaab aag fddd caaa aag gddd aaa aac dddg aaac aac eddf baae aac fdde gaaa aac gddd aaa aac dddg aaac aaf dddf baae aaf bdde gaaa aaf gddd aaa aaf ddd aaaf aaf dddc faae aaf bdde gaaa aab cddd aaag aab ddd eaaf aab dddc faaa aab eddb aaa aab cddd aaag aab ddd eaab aae dddg caaa aae eddb aaa aae fddd aaag aae gddd eaab aae dddg caaa aae dddc aaa aaa eddb aaac aaa bddd baae aaa cddd gaaa aaa ddd aaa aaa af dddc aaac aaa aaaag dddb baae aaa gaaaae bdde gaaa aaa faaaaf cddd aaa aaa eaaaag gddd aaaf aaa gaaaae dddg faae aaa baaaaf dddf gaaa eaa aaaaag edde aaag eaa gdb caaaae fddd eaaf ggg ddddc baaaac gddd faaa dddde aaaaa dddg aaa fddddf caaaab dddf aaag eddddg baaaac edde eaab gddddb aaaaaddd caaa bddddc caaaaa aaa ddddd aaaaac aaag cddddf dddaaaaa baab eddddg eddb faaaab caaa gddddebddd eaaaagaaa bdddddd gaaaaaac dddd faaae cdg ee ``` <!-- end of image -->

I have an image in front of me. I need to determine if there are any intersection segments. The image has some tight areas where segments are too close. I should investigate those closely. <!-- image --> ```palette Key,Color ,#fefefeff a,#de2db5ff b,#8690f5ff c,#f2afe2ff d,#b0d6b1ff e,#bbc0f9ff f,#f0f0f3ff g,#dc70c3ff ``` ```image aa aaac faaaaa caaa aa gaaa aac aaac gaa faaaf faa caaa aaf gaaa aag aaag caa faaac aa caaa aac gaaa caa aaag aa aaac aac caaaf gaa gaaa aa aaag aaf aaac gag faaaf faa caaa aa aaag aag aaac caa faaaf aa caaa fffffaacfffffffffffff gaaa fdddddgaaddddddddddddd aaag fddddddaaddddddddddddd faaaf fddddddaaddddddddddddd caaa fddddddgaadddddddddddd gaaa fdddddddaadddddddbbddd aaag fdddddddaaddddddbbdddd aaac fdddddddaagdddddbbdddd caaa fddddddddaaddddbbbdddd gaaa fddddddddaaddddbgaaddd aaag fddddddddaagddbbaagddd aaac fddddddddgaaddbbaadddd faaaf fdddddddddaadbbbaadddd caaa fdddddddddaagbbdaadddd aaag fdddddddddgaabbdaadddd aaac fddddddddddaabbgaadddd faaaf fddddddddddaabdaagdddd caaa fddddddddddaaadaaddddd gaaa fddddddddddbaadaaddddd aaag fdddddddddbbaadaaddddd faaaf fdddddddddbbaaaaaddddd caaa fdddddddddbbgaaaaddddd gaaa fddddddddbbbdaaagddddd aaag fddddddddbbddaaadddddd aaac fdddddddbbbddgaadddddd caaa fdddddddbbddddaadddddd gaaa fddddddbbbdddddddddddd ag fddddddbbddddddddddddd f fddddbbbbddddddddddddd fddbbbbbdddddddddddddd ebbbbbdddddddddddddddd fbbbbbbdddddddddddddddddd bbbbbbddddddddddddddddddddd ebbbbbe fddddddddddddddddddddd fbbbbbbf fffffffffffffffffffff ebbbbbe fbbbbbb ebbbbbf ebbbbbe fbbbbbbf ebbbbbe fbbbbbbf ebbbbbe ebbbbbe bbbbbbf ebbbbbe fbbbbbbf ebbbbbe fbbbbbe ebbbbbf ebbbbbe fbbbbbbf ebbbbbe fbbbbbb ebbbbbe ebbbe bf ``` <!-- end of image --> I'm now examining the contents of area A in detail. <!-- image --> ```palette Key,Color ,#fefefeff a,#de2cb5ff b,#858ef6ff c,#e7ddf8ff d,#f0a7e0ff e,#a964dbff f,#b2b6f8ff g,#e765c9ff ``` ```image caaaad gaaag daaaa caaaad aaaag gaaaa daaaac aaaad gaaaa ff daaaac bbbfc aaaad fbbbbc gaaag bbbbb daaaa cbbbbf caaaad fbbbb aaaag cbbbbf daaaa fbbbbc caaaad bbbef aaaag fbbeaaagc gaaaa bbbeaaaa daaaac cbbbeaaag aaaad fbbbaaaag gaaag cbbbbaaaad daaaac fbbbbaaaad caaaad bbbbfaaaac gaaag fbbbbdaaaa daaaa bbbbfgaaag caaaadcbbbbcgaaag aaaagbbbbb aaaad gaaaabbbbfcaaaad daaaaebbb daaaa aaaaebbf daaaa gaaaabbc gaaag daaaabf gaaag aaaaec aaaad aaaaa caaaac ceaaaa daaaa fbaaaad daaaa cbbaaaag gaaag fbbeaaaa aaaad bbbeaaaadaaaad fbbbbaaaagaaaac bbbbbgaaaaaaaa cbbbbcdaaaaaaag fbbbb aaaaaaag cbbbbf gaaaaaad fbbbb daaaaaad bbbbf caaaaaac fbbbbc gaaaaa bbbbf daaaag cbbbbc caaaag bbbbb aaaad cbbbbf daaa fbbbb cd cbbbbf fbbbbc cbbbbf cfbbbbbbc cfbbbbbbbb cfbbbbbbbbbbc cfbbbbbbbbbbfc bbbbbbbbbbfc bbbbbbbbfc bbbbbfc bbbf fc ``` <!-- end of image --> Incredible, there's actually 1 intersection in area A! Answer: A: 1; 1 = 1 The final count is: one intersection.

<!-- image --> ```palette Key,Color ,#fefefeff a,#df2bb5ff b,#858ef6ff c,#f6cbecff d,#ee92d8ff e,#cfd3fbff f,#a9aef8ff g,#e356c4ff ``` ```image ga aaad caaaaa daaa aa gaag aac aaad gag aaac aa daaa aa gaag gag aaad caa aaac aa caaa aad gaaa daa aaag aa aaac aac caaa daa daaa aa gaag aac aaad gag caaa caa daaa aa gaag aad aaad caa aaac aa daaa aad gaag daa aaad aa aaac aac caaa gag e gaaa aa ebb aaag aa bbe aaac gag ebb caaa caa bbf daaa aa bbaa aaag aad fbgag aaac daa bbaac caaa aa ebbaa daaa aacbbeaa gaag daabbcaa aaad aabfdaa caaac aab gad daaa gag aac gaag baa aa aaad fbaa aa aaac bbaagaa caaa ebbcaaag gaaa bbe aaad aaad bb aaac aaac bbf daa caaa bb aa daaa fbb c ag bb ebbb bbbbbe fbbbbbe ebbbbbf fbbbbbe ebbbbbf bbbbbb fbbbbbe ebbbbbf fbbbbbe ebbbbbf fbbbbb ebbbbbe ebbbbbf fbbbbbe ebbbbbf fbbbbbe ebbbbbf bbbbbb fbbbbbe ebbbbbf fbbbbbe ebbbbbf bbbbbb ebbbbbe ebbbbbf fbbbbbe ebbbf be ``` <!-- end of image -->

This image seems promising for intersection detection. I wonder what's going on inside those areas? Perhaps intersections are hiding there. <!-- image --> ```palette Key,Color ,#fefefeff a,#86ad6aff b,#fdddb4ff c,#b2d7b1ff d,#6e9b49ff e,#f0f1e4ff f,#f9bf71ff g,#9ac692ff ``` ```image e da gdd ded aa de d ag dg cd ed d dc d cd dc de ga ad ed d d da de ed ag dc cd cd d de d ad dc d ga da ed f ed d fb dc de fb cd ag bf de cd ef gd d f d d f aa dc fe ed ga fb dg ed bf cd d ef dc de e f gd ag gggdgfgggggggggggggggggc de cd cccdcfcccccccccccccccccg aa d cccdgfcccccccccccccccccg ed d cccdgffccccccccccccccccg dg dc cccdgcfccccccccccccccccg ed ga cccdgcfccccccccccccccccg dc ed cccdgcfccccccccccccccccg gd d cccdgcfccccccccccccccccg de de cccdgcfccccccccccccccccg ad ag cccdgcffcccccccccccccccg d cd cccdgcffcccccccccccccccgdg d cccdgccfcccccccccccccccgd d cccdaccfcccccccccccccccdc dc cddd cccdaccfccccccccccccccad ga eadddg cccdaccfccccccccccccccdg ed egdddge cccaaccfcccccccccccccadg d cdddac cccaaccffccccccccccccdcg de cadddc cccaacccfcccccccccccdacg aaadddge cccaacccfccccccccccgdccg edae cccaacccfccccccccccdgccg cccaacccfcccccccccgdcccg cccaacccfcccccccccdgcccg cccadcccffcccccccadccccg cccadcccffcccccccdcccccg efff cccadccccfccccccdacccccg bffffebff cccgdccccfccccccdccccccg bfffb bffe cccgdccccfcccccdaccccccg effffe bffe cccgdccccfccccgdcccccccg bfffb bffe cccgdccccfccccdgcccccccg bfffb bffe cccgdccccffccadccccccccgffffe bffe cccgdccccffccdccccccffffb bffe cccgdcccccfcddcccffffccg bffe cccgdcccccfcdcffffcccccg bffe cccgdcccccfffffccccccccg bffb cccgdcccccfacccccccccccg bffb ccccdcccccdgcccccccccccg effb ccccdccccadccccccccccccg effb ccccdccccdcccccccccccccg effb ccccdcccddcccccccccccccg effb ccccdcccdccccccccccccccg effb ccccdccdaccccccccccccccg effb ccccdcgdcccccccccccccccg effe ccccdcdgcccccccccccccccg e ccccdadccccccccccccccccg ccccddcccccccccccccccccg ccccddcccccccccccccccccg eeeedeeeeeeeeeeeeeeeeee ``` <!-- end of image --> Time to investigate area A up close. <!-- image --> ```palette Key,Color ,#fefefeff a,#88ab68ff b,#fcd4a0ff c,#c8d9bbff d,#6e9a49ff e,#f0ecdaff f,#fcbd6eff g,#a8c292ff ``` ```image cddebfb cddebff cddeeff eddeeffe edde ffe edde ffb edde bfb edde bff edde bff edde eff eddc effe eddc ffe eddc ffb ddc bfb ddc bff ddc eff ddc effe ddc ffe ddc ffb ddc bfb ddc bfb ddc bff ddc eff ddc effe adg ffe c adg ffb a adg bfb gd adg bff edd adg eff gdd adg effe eddg adg ffe add adg ffb cddc adg bfb ada adg bfb cddc adg bff dda adg eff gdde gdg effe eddg gda ffe adde gda ffb cddc gda bfb ada gda bff cddc gda eff dda gda effe gdde gda ffe eddg gda ffb gdde gda bfb cddg gda bfb ada gda bff cddc gda eff dda gdd effe gdde cdd ffe eddg cdd ffb gdde cdd bfb eddg cdd bff ada cdd eff cddc cdd effe ada cdd ffe gdde cdd ffb eddg cdd bfb gdde cdd bfb eddg ebf cdde bff add ebbffff cdde eff cddc ebffffffbb cdde effe ada ebffffffbe edde ffe cddc ebfffffffbe edde ffbeddgebffffffbbe edde bfbgafffffffbe edde bffffffffbe edde effffbbe edde bfac edde ada eddc cddc eddc dda eddc gdde ddc eddg ddc adde ddc cddc ddc ada ddc cddc ddc dda ddc gdde ddc eddg ddc gdde ddc eddg ddg ada adg cddc adg dda adggdde adgddg adddde adddg addd ``` <!-- end of image --> The close-up clearly shows 1 intersection point in area A. Answer: A: 1; 1 = 1 It was tricky, but I finally found one single intersection in the image.

<!-- image --> ```palette Key,Color ,#fefefeff a,#87ab68ff b,#fdd9abff c,#c4d6b5ff d,#6d9a49ff e,#f0eddcff f,#fcbe6fff g,#a5c08eff ``` ```image e da gdd ded aa de d ag dg cd ed d dc d cd dc de ga ad ed d d da de ed ag dc cd cd d de d gd dc d ga da ed f ed d fe dg de bb cd ag bf de cd f gd d f d d f aa dc fe ed ga fb dg ed bf cd d ef dc de e f gd ag def de cd def aa d defe d d debb dg dc debf ed ga deef dc ed dc f gd d dc f de de dc fe aa ag dc fb d cd dc bf dg d dc ef ed d ac f dc dc cddd ag f cd ga eadddg ag f de ed egdddge ag fe ad d cdddac ag fb d de cadddc ag bf da aaadddg gg ef ed edae ga f dc ga f cd ga fe de ga fb gd ga bf d ebff ca ef da efffbebff cd f ed bfffb bff cd f dg effffe bffe cd f cd bfffb bffe cd fe de bfffb bffe cd fb gd effffe bffe cd bf d bfffb bffe ed ef aa bfffb bffe ed fedeffffe bffe ed ffffb effe ed fa effe ed dc effb ed gd effb d de effb d aa effb d d effb d dg effb d ed eff d dc dgd dde dd d ``` <!-- end of image -->

I have a feeling there might be some intersections in this image. Could these regions be concealing intersection points? Let's find out. <!-- image --> ```palette Key,Color ,#fefefeff a,#68767fff b,#292f4dff c,#c1c8daff d,#92a3b5ff e,#6a7db0ff f,#edf3f0ff g,#afd6afff ``` ```image ced fee eec cee ee ded ee ffffeecffffffffffffdfff fgggggeegggggggggggabbggf fgggggeegggggggggggbbbggf fgggggdeegggggggggbbbbagf fggggggeeggggggggabbdbbgf fggggggeedgggggggbbggbbgf fgggggggeeggggggbbbggbbdf fgggggggeedggggabbgggabbf bf fgggggggdeeggggbbdggggbbf bbb fggggggggeegggbbbgggggbbc bbb fggggggggdeegabbggggggabb bbb fgggggggggeegbbdgggggggbb bbb fgggggggggeebbbggggggggbbf bbb fggggggggggabbgggggggggaba bbb fggggggggggbbdggggggggggbb bbb fgggggggggbbbeggggggggggbbf bbb fggggggggdbbeeggggggggggaba bbb fggggggggbbddeegggggggggfbb bbb fgggggggbbbggeegggggggggfbb bbb fggggggdbbgggeedggggggggfaba bbb fggggggbbdggggeeggggggggffbb bbb fgggggbbbgggggeeggggggggf bb bbb fggggdbbggggggdeegggggggf abd bbb fggggbbagggggggeegggggggf cbb bbb fgggbbbggggggggeedggggggf bb bbb fggdbbggggggggggeeggggggf bbd bbb fggbbaggggggggggeedgggggf cbb bbb fgabbgggggggggggdeegggggf bb bbb fggagggggggggggggeegggggf bbc bbb ded dbb bbb fee bb bbb eef bbc bbb ded dbb bbb ee bb bbb eef bbc bbb cee dba bbb ee bb bbb eec bbf bbb fee aba bbb ee bb bbb ded bbf bbb fee aba bbb eef fbb bbb ded bb bbb ee abd bbb eef fbb bbb cee bb bbb ee bbd bbb eec cbb bbb cee bb bbb ee bbd bbb dec cbbbbb fee bbbb ee bbb ded fa ee eef cee ee eec cee ee dec fee eef deeeeeedcf deeeeeeeeeeeeedcf fcdeeeeeeeeeeeeedcf ccdeeeeeeeeeeeedcc fcdeeeeeeeeeeeeedcf fcdeeeeeeeeeeeeedcf fcdeeeeeeeeeeeeedc fcdeeeeeeed ccc ``` <!-- end of image --> My goal is to determine if there's an intersection inside area A. <!-- image --> ```palette Key,Color ,#fefefeff a,#636880ff b,#282e4cff c,#b3b9cdff d,#9198b3ff e,#6b7cafff f,#d9dce5ff g,#444a65ff ``` ```image eeeec dd ceeee gbba feeeef dbbbbf deeed fbbbbbd feeeef gbbbbba eeeec dbbbbbbb ceeee fbbbbbbbbc eeeec gbbbbabbba ceeed dbbbbdcbbbb feeeef fbbbba bbbbc deeed gbbbbf abbba feeee dbbbbd cbbbb eeeec fbbbba bbbbc ceeee gbbbbf abbbe eeeef dbbbbd cbbbg deeed fbbbbg fbbbb feeeef abbbbf abbb deeec dbbbbd dbbb ceeee fbbbbg fbbb eeeec abbbbf gbb ceeed dbbbbd dbb feeeef fbbbbg fbb deeed abbbbf gb feeeedbbbbd db eeeebbbbg fb ceegbbbbf g eabbbbd d dbbbbg c abbbbc cbbbbgc fgbbbbee abbbbaeec cbbbbaeeee gbbbgfeeeef abbbbc deeed cbbbba feeeef gbbbg eeeec abbbbc ceeee cbbbba eeeec gbbbgf ceeed ebbbbc feeeef cbbbba deeed gbbbbf feeee ebbbbc eeeec cbbbba ceeee gbbbbf eeeef dbbbbc deeed fbbbba feeeef gbbbbf deeec dbbbbd ceeee fbbbba eeeec gbbbbf ceeed dbbbbd feeeef fbbbba deeed abbbbf feeeef ``` <!-- end of image --> Aha! I've found 1 intersection inside area A! Answer: A: 1; 1 = 1 The image features one single intersection point.

<!-- image --> ```palette Key,Color ,#fefefeff a,#545972ff b,#282e4cff c,#c3c8daff d,#8a95b7ff e,#6a7cafff f,#e0e3ecff g,#a8afc7ff ``` ```image ceg ee eef cee ee ged ee eec d fee dbb eef bbb cee bbbbg ee dbbgbb deg bbf bb ee bba bbc eec dbb gbb b fee bbf bb bbb ee bba bbc bbb ged gbb dba bbb ee bbc bb bbb eebba bbf bbb fabb dba bbb bbg bb bbb bbbe bbf bbb gbbee eba bbb bbcded bb bbb bbb ee bb bbb cbb eec abe bbb bbg fee fbb bbb abb eef bb bbb cbb gee abd bbb bbg ee fbb bbb abb deg bb bbb cbb ee bbg bbb bbg eef cbb bbb abb cee bb bbb g ee bbg bbb deg gbb bbb ee bb bbb ee bbc bbb ged dba bbb ee bb bbb eef bbf bbb cee dba bbb ee bb bbb eec bbf bbb fee eba bbb ee bb bbb deg bb bbb ee abe bbb ee fbb bbb ged bb bbb ee abd bbb eef fbb bbb cee bb bbb ee abd bbb eec cbb bbb fee bb bbb ee bbg bbb deg gbbbbb fee bbbb ee bbb ged fa ee eef cee ee eec fee ee deg fee eef geeeeeedgf deeeeeeeeeeeedgc fcgeeeeeeeeeeeeedcf fgdeeeeeeeeeeeedgf fcdeeeeeeeeeeeeegcf cgdeeeeeeeeeeeedcf fcdeeeeeeeeeeeedgc fcgeeeeeeed fgc ``` <!-- end of image -->

Hmm, I'm not sure what to expect from this image. Let's see if any lines cross. These zones are intriguing. I bet there's something interesting happening within them. <!-- image --> ```palette Key,Color ,#fefefeff a,#79def8ff b,#5ae655ff c,#b1d8b1ff d,#abeafbff e,#e6f7f3ff f,#80e582ff g,#95cb96ff ``` ```image ad aaa aaaad aaeaaa ad aaae ead daad dad eaaa dae aaad da eaaa aa aaae aa daad aa eaaa aa aaad aa daaa aa aaae aa daad ed ad eaaa aae ead aaae aaa dad daaa eaaa dae aaa dadaa da aaad aa aa aa eaaa aa daa aa aaae ead aa aa daad dae dad aa eaaa aa aa aa aaad aa dad aa eaaa ead aa aa cggggaaagggggggggggg dae aad ad gcccccaaaacccccccccc aa aa ead gcccccccaaaccccccccc aa aae dad gccccccccaaacccccccc ead aa dae gccccccccccaaacccccc dae aae da gcccccccccccaaaccccc aa eaa aa gccccccccccccaaccccc aa aa aa gccccccccccccaaccccc ead eaa aa gccccccccccccaaccccc dae aa aa gccccccccccccaaccccc aa dad aa gcccccccccccccaacccc aa aa aa gcccccccccccccaacccc ead dad aa gcccccccccccccaacccc aae aa ead gcccccccccccccaacccc aa dadead gcccccccccccccaacccc aa aadae gcccccccccccccaacccc ead aaaae gcccccccccccccaacccc aae aaa gcccccccccccccaacccc aa aaa gcccccccccccccaagccc aa aa gcccccccccccfbfagccc ead aa gcccccccccgbbbfaaccc aae gccccccccbbbbccaaccc aa gccccccbbbbccccccccc aa gccccbbbbgcccccccccc ead gccfbbbfcccccccccccc aae ggbbbfcccccccccccccc aa ebbbbcccccccccccccccc aa bbbbcccccccccccccccccc ead fbbbgccccccccccccccccccc aae fbbbe gccccccccccccccccccc aa cbbbc gccccccccccccccccccc aa ebbbf gccccccccccccccccccc ead ebbbf gccccccccccccccccccc aa bbbb gccccccccccccccccccc aa fbbbe gccccccccccccccccccc aa fbbbc gccccccccccccccccccc ead cbbbbc gccccccccccccccccccc aa cbbbbbc gccccccccccccccccccc eeeeeaaeeeeeeee cbbbbbc eeeeeeeeeeeeeeeeeee gcccccaacccccccge cbbbbbc gcccccaacccccccce cbbbbbf gccccaaccccccccce ebbbbbf gccccaaccccccccce ebbbbbfe gccccaaccccccccce efbbbbfe gccccaaccccccccce efbbbbfe gcccaacccccccccce fbbbbbe gcccaacccccccccce fbbbbbe gcccaacccccccccfbbbbbc gcccaaccccccfbbbbbc gccaaccccfbbbbbfe gccaacfbbbbbfccce gccaabbbbfcccccce gccafbfccccccccce gccfcccccccccccce gccccccccccccccce gccccccccccccccce ``` <!-- end of image --> I'm now examining the contents of area A in detail. <!-- image --> ```palette Key,Color ,#fefefeff a,#79def9ff b,#59e755ff c,#a7f1a7ff d,#adeafbff e,#cef3fbff f,#75e97bff g,#d9f9d9ff ``` ```image eaaad daaae aaaa aaaa eaaad daaae aaaa aaaa eaaad daaae aaaa aaaa eaaad daaae aaaa aaaa eaaad daaae aaaa gc aaaa gcbbb eaaad gcfbbbbb daaae gcfbbbbbbbb aaaa gcfbbbbbbbbbfc aaaa gcfbbbbbbbbbfcg eaaad cfbbbbbbbbbfcg daaacfbbbbbbbbbfcg aaaabbbbbbbbbcg gaaaabbbbbbcg eaaafbbbcg fbffcg cfg ``` <!-- end of image --> The lines within area A do not intersect. Onward to the next region of interest. Let's see what secrets area B holds. <!-- image --> ```palette Key,Color ,#fefefeff a,#79def9ff b,#5ae755ff c,#a9f1abff d,#afebfbff e,#e1f8f7ff f,#7ae986ff g,#cef7ccff ``` ```image daaaaaae eaaaaaad daaaaad eaaaaaae eaaaaaad daaaaaae eaaaaaad daaaaad daaaaaae eaaaaaad daaaaae eaaaad eaaad aaad aaaa aaaa daaa daaae daaae daaad eaaad eaaad eaaad aaaa aaaa aaaa daaae daaae daaae daaad eaaad eaaad aaad aaaa aaaa aaaa eaaaac cbfaaaf cbbbfaaac gbbbbbfaaad gfbbbbbbfaaad efbbbbbbfgeaaad ecbbbbbbbg aaad cbbbbbbbc cbbbbbbbce gfbbbbbbfe gfbbbbbbfg efbbbbbbfg ecbbbbbbbc cbbbbbbbc gbbbbbbbce gfbbbbbbfe bbbbbbfg bbbbbg bbbc bc e ``` <!-- end of image --> Success! This area contains 1 intersection point! Answer: A: 0; B: 1; 0 + 1 = 1 The final count is: one intersection.

<!-- image --> ```palette Key,Color ,#fefefeff a,#77def9ff b,#5ae755ff c,#b3f3b3ff d,#b7edfbff e,#ddf7f6ff f,#87ec8bff g,#96e5faff ``` ```image gg aaa aaaad aaeaaa ag aaae ead daag dad aaa dae gaad ga eaaa aa aaae aa gaag aa eaaa aa aaad aa daaa aa aaae aa gaad ed ag eaaa aae ead aaae aaa dad daag eaaa dae aaa gadaa ga gaad aa aa aa eaaa aa dag aa aaae eag aa aa daag gae dag aa aaa aa aa aa gaad aa gad aa eaaa eag aa aa aaae gae gad ag gaag aa aa ead eaaa aa aae dad aaad eag aa dae daaa gae aae ga aaa aa eaa aa aa aa aa aa aa eag eaa aa ga gae aa aa dae aa dag aa ead aa aa aa eag eag dag aa aa gae aa ag aa aa gadead aa aa aadad aa ead gaaae aa gae aaa aa aa aaa aac aa aa cbfac ead aa ebbbfad gae ebbbb ad aa bbbb aa fbbbe ead cbbbc ga cbbbf aa ebbbf aa bbbb ead bbbbe ga fbbbc aa cbbbc aa cbbbf ead ebbbb ga bbbb aa fbbbe aa fbbbc ead cbbbbc ga cbbbbbc aa cbbbbbc aa cbbbbbc ead cbbbbbf ga ebbbbbf aa ebbbbbf aa efbbbbfe ead efbbbbbe ga fbbbbbe aa fbbbbbe aa fbbbbbc dad cbbbbbc aa cbbbbbc aa cbbbbbc aabbbbc eafbf f ``` <!-- end of image -->

This is the image I'm working with. The goal is to count the intersections. These regions highlight areas that look suspicious. Lines seem to converge within them. <!-- image --> ```palette Key,Color ,#fefefeff a,#1b7cf6ff b,#df3e79ff c,#e3d1e7ff d,#76b0f2ff e,#b1d7b1ff f,#da819eff g,#96c996ff ``` ```image fbb bbb bbf bbc bb cbb fbb bbb bbf bbc cbb fbb bbb bbf bbc bb cbb fbb bbb bbf bbc cbb ggggggggggggfbbggggggg eeeeeeeeeeeebbbeeeeeee eeeeeeeeeeeebbfeeeeeee eeeeeeeeeeeebbfeeeeeee eeeeeeeeeeeebbeeeeeeee eeeeeeeeeeefbbeeeeeeee eeeeeeeeeeefbbeeeeeeee aaaadddc eeeeeeeeeeebbbeeeeeeee daaaaaaaaaaaaaaddc eeeeeeeeeeebbfeeeeeeee aaadaaaaaaaaaaaaaaaaaaaaaddc eeeeeeeeeeebbeeeeeeeee aaa cdddaaaaaaaaaaaaaaaaaaaaaddc eeeeeeeeeeebbeeeeeeeee caad cddaaaaaaaaaaaaaaaaaaaaaaddeefbbeeeeeeeee aaa cddaaaaaaaaaaaaaaaaaaaaaaddeeee daac gddaaaaaaaaaaaaaaaaeee aaa eeeeeeeeeebfdaaaaaaeee aaa eeeeeeeeeebbeeeeeeeeee caad eeeeeeeeeebbeeeeeeeeee aaa eeeeeeeeefbbeeeeeeeeee daa eeeeeeeeebbbeeeeeeeeee aaa eeeeeeeeebbfeeeeeeeeee aaa eeeeeeeeebbeeeeeeeeeee caad eeeeeeeeebbeeeeeeeeeee aaa eeeeeeeefbbeeeeeeeeeee daa eeeeeeeebbbeeeeeeeeeee aaa eeeeeebbbbfeeeeeeeeeee aaa eeefbbbbbfeeeeeeeeeeee caad gfbbbbbggggggggggggggg aaa fbbbbbc daa fbbbbb aad fbbbbb aaa bbbbbf daac bbbbbf aaa cbbbbbf aaa cbbbbbc aad cbbbbbc aaa fbbbbbc daac fbbbbb aaa fbbbbb aaa bbbbbf aad bbbbbf aaa cbbbbbf daac cbbbbbf aaa cbbbbbc aaa fbbbbbc caad fbbbbbc aaa fbbbbb daac bbbbbb aaa bbbbbf eeaaaeeeeeeeeeg bbbbbf eeeadeeeeeeeeeg cbbbbbf eeeeeeeeeeeeeegcbbbbbc eeeeeeeeeeeeefbbbbbc eeeeeeeeeeefbbbbbc eeeeeeeeefbbbbb eeeeeeebbbbbbeg eeeeebbbbbbeeeg eeebbbbbfeeeeeg eebbbbfeeeeeeeg eeebfeeeeeeeeeg eeeeeeeeeeeeeeg eeeeeeeeeeeeeeg ``` <!-- end of image --> Here's a close-up of the area A. <!-- image --> ```palette Key,Color ,#fefefeff a,#1b7cf7ff b,#e03e78ff c,#ef9dbbff d,#c4ddfcff e,#67a8f9ff f,#e56392ff g,#f6cbdbff ``` ```image eaaaaa daaaaad aaaaae daaaaad eaae de cf cbbb cbbbbb gcbbbbbbb gfbbbbbbbbb gfbbbbbbbbbbc gfbbbbbbbbbfc gfbbbbbbbbbfc cfbbbbbbbbbfg cbbbbbbbbbbfg cbbbbbbbbbbfg gbbbbbbbbbbcg fbbbbbbbc gbbbbbc fbbc gc ``` <!-- end of image --> Area A does not contain any intersection points. I'm ready to analyze the next area. Could this be where the intersection is hiding, in area B? <!-- image --> ```palette Key,Color ,#fefefeff a,#197bf6ff b,#e03e79ff c,#f5c6d7ff d,#b9d5faff e,#69a7f8ff f,#ea84a9ff g,#8558b0ff ``` ```image fbbbbf fbbbbc bbbbb bbbbb cbbbbf cbbbbf fbbbbc fbbbbc bbbbb bbbbb cbbbbf fbbbbf fbbbbc bbbbb bbbbb cbbbbf cbbbbf fbbbbc fbbbbc bbbbb bbbbb aaeeeddd cbbbbf aaaaaaaaaaaeeeeddd fbbbbf aaaaaaaaaaaaaaaaaaaaaaggggdd aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaeeedddd aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaad dddeeeeaaaaaaaaaaaaaaaaaaaaaaaaaaaaad dddeeeaaaaaaaaaaaaaaaaaaaa fbgggeeeaaaaaaaaaa fbbbbc ddddeee bbbbb bbbbb cbbbbf fbbbbf fbbbbc bbbbbc bbbbb cbbbbf cbbbbf fbbbbc fbbbbc bbbbb bbbbb cbbbbf cbbbbf fbbbbc cfbbbbbc cfbbbbbbb cfbbbbbbbbf cfbbbbbbbbbbc cbbbbbbbbbbbc ``` <!-- end of image --> Bingo! This close-up reveals 1 intersection in area B! Answer: A: 0; B: 1; 0 + 1 = 1 My investigation reveals that there is exactly one intersection in this image.

<!-- image --> ```palette Key,Color ,#fefefeff a,#197bf7ff b,#df3e79ff c,#f1abc4ff d,#9ac5fbff e,#579df7ff f,#e876a0ff g,#eae1f0ff ``` ```image cbb bbb bbf bbc bb cbb fbb bbb bbc bbg gbb cbb bbb bbf bbc bb cbb fbb bbb bbc bbg gbb cbb bbb bbf bbc bb cbb fbb aaaaeddg bbb daaaaaaaaaaaaaaeddg bbf aaaeaaaaaaaaaaaaaaaaaaaaaedd bbg aaa gddeaaaaaaaaaaaaaaaaaaaaeedg gbb gaad gdeeaaaaaaaaaaaaaaaaaaaaeedg cbb aaa gdeaaaaaaaaaaaaaaaaaaaaaeddg eaag gddeaaaaaaaaaaaaaaa aaa bbeeaaaaa aaa bb gaad cbb aaa fbb eaag bbb aae bbf aaa bbg daad gbb aaa cbb eaag gbbb aae gbbbbf aaa cbbbbbc daad cbbbbbg aaa fbbbbbg eaa fbbbbb aae fbbbbb aaa bbbbbf daad gbbbbbf aaa gbbbbbc eaa cbbbbbc aae cbbbbbc aaa cbbbbbg daad fbbbbbg aaa fbbbbb eaa bbbbbf gaae bbbbbf aaa gbbbbbf daag gbbbbbc aaa cbbbbbc aaa cbbbbbg gaae fbbbbbg aaa fbbbbb daag fbbbbb aaa bbbbbf aaa gbbbbbf ad gbbbbbc cbbbbbc cbbbbbc cbbbbbg fbbbbbg fbbbbb bbbbbf gbbbbbf fbbbf bc ``` <!-- end of image -->

I'm analyzing this image to identify any points where lines intersect. I've spotted 2 narrow regions that might be worth examining further. Let's call them area A,, and B. <!-- image --> ```palette Key,Color ,#fefefeff a,#c6a553ff b,#fc0b96ff c,#b1d7b1ff d,#c17d06ff e,#e367a9ff f,#f2d1c7ff g,#9bc893ff ``` ```image fd dd ddd dddd adaad fdd ad dd fd bb dd fdf bb ddf fdf bbbf ada fdf bbbe be fdd df bb bb ebf dd da bb bb bb ddggggggggdaggggggbbggbbggggggggggggggbbgggg ddaccccccccdaccccccbbccebcccccccccccccebecccc addcccccccccdacccccbbcccebcccccccccccccbbccccc fddccccccccccddcccccbbccccbeccccccccccccbbccccc dd ccccccccccddccccbbcccccbbccccccccccccbeccccc ddf ccccccccccddccccbbcccccbbcccccccccccbbcccccc ada ccccccccccddcccbbccccccbbcccccccccccbbcccccc fdd ccccccccccddcccbbccccccebcccccccccccbecccccc dd ccccccccccddccbbcccccccebccccccccccbbccccccc dd ccccccccccddccbbccccccccbecccccccccbbccccccc ddf ccccccccccddcbbcccccccccbecccccccccbeccccccc ada ccccccccccddcbbcccccccccbbccccccccebcccccccc fdd ccccccccccddbbccccccccccbbccccccccbbcccccccc dd ccccccccccddbbccccccccccbbccccccccbecccccccc dd ccccccccccdbbcccccccccccebcccccccebccccddccc ddf ccccccccccabbccccccccccccbeccccccbbcccddcccc ada ccccccccccbbcccccccccccccbeccccccbbcccddcccc fdd ccccccccccbbcccccccccccccbbcccccebcccddccccc dd cccccccccbbdcccccccccccccbbcccccbbcccddccccc dd cccccccccbbdcccccccccccccbbcccccbbccddcccccc ddf ccccccccbbadgccccccccccccebccccebeccddcccccc ada ccccccccbbgdgccccccccccccebccccbbccddccccccc fdd cccccccbbcgdgcccccccccccccbecccbbccddccccccc dd cccccccbbccdacccccccccccccbbcccbecddcccccccc ddf ccccccbbcccdacccccccccccccbbccbbccddcccccccc dda ccccccbbcccdacccccccccccccbbccbbcddccccccccc add cccccbbccccdacccccccccccccebccbecddccccccccc fdd cccccbbccccdacccccccccccccebcbbcddcccccccccc dd ccccbbcccccddccccccccccccccbebbcddcccccccccc ddf ccccbbcccccddccccccccccccccbbbeddccccccccccc fd ada cccbbccccccddccccccccccccccbbbcddccccccccccc ad fdd cccbbccccccddccccccccccccccbbbddcccccccccccc dda dd ccbbcccccccddccccccccccccccbbeddcccccccccccc ddd dd ccbbcccccccddccccccccccccccebddccccccccccccc ggggdddgggggggggddagc cbbccccccccddccccccccccccccccddccccccccccccc ccccdddacccccccadaccg cbbccccccccddcccccccccccccccddcccccccccccccc ccccddddccccccgddcccg bbcccccccccddcccccccccccccccddcccccccccccccc ccccddadccccccddccccg bbcccccccccddccccccccccccccddccccccccccccccc ccccddcdaccccddcccccg ebccccccccccddccccccccccccccddccccccccccccccc ccccddcddcccddacccccg bbccccccccccddcccccccccccccddcccccccccccccccc ccccddcddccaddccccccg ebgccccccccccddcccccccccccccddcccccccccccccccc ccccdacgdagddcccccccg bbcccccccccccadccccccccccccddccccccccccccccccc ccccdaccddddcbbcccccg ebfcccccccccccadccccccccccccddccccccccccccccccc ccccdaccdddcebbbccccg bb cccccccccccadcccccccccccddcccccccccccccccccc ccccdaccgdacbbebbcccg ebf cccccccccccadcccccccccccddcccccccccccccccccc ccccdacccccebecebbccg bb cccccccccccadccccccccccddccccccccccccccccccc cccgdgcccccbbccccbbeg ebf cccccccccccgdgcccccccccddccccccccccccccccccc cccgdgcccccbecccccbbe bb gccccccccccgdgccccccccddgccccccccccccccccccc cccadcccccbbcccccccbbb ebf fdf dd cccadcccccbbccccccccbbb bb df dd cccadccccbbcccccccccgebb ebf da dd cccadccccbbcccccccccg fbbf bb da dd cccddcccbbccccccccccg bbe ebf da dd cccddcccbbccccccccccg bbb bb da dd cccddccebcccccccccccg bbb ebf da dd cccddccbbcccccccccccg ebb bb dd dd cccddcebccccccccccccg fbbf ebf dd dd cccddcbbccccccccccccg bbebb dd dd cccddebeccccccccccccg bbbf dd dd cccddbbcccccccccccccg bb dd dd cccddbecccccccccccccg dd dd cccdbbccccccccccccccg dd dd cccdbeccccccccccccccg dd dd cccbbcccccccccccccccg dddd gggbbgggggggggggggggc dddd f add add ad ``` <!-- end of image --> Let's put area A under the microscope. <!-- image --> ```palette Key,Color ,#fefefeff a,#d09c43ff b,#fe0996ff c,#e1bf86ff d,#c17b03ff e,#fe51b5ff f,#fe99d3ff g,#f4ded0ff ``` ```image dddddd gddddg gddddddc ddddc gdddddda addda gddddddd cddda gdddcdddg gddddg gdddgddda gddddg cdddgaddd adddc cddd cdddg addda cddd dddc cdddd cddd addd gddddg cddd cdddg gddddc cddd gdddc adddc adda addd addda adda cdddg cdddd adda gdddc gddddg adda addagddddc ff adda cdddaddda fbbe dddc gdddddda bbbbbg dddc ddddddg fbbbbbbf dddc cddddg bbbbbbbbf dddc gdddc fbbbfebbbbe dddc cac bbbb ebbbbe gdddc fbbbf fbbbbbg gdddg ebbb fbbbbbg gdddg fbbbf gbbbbbf gdddg ebbb ebbbb gdddg gbbbe ebbb cdddg ebbbg fbb cddd gbbbe fb cddd ebbbg g cddd bbbe cddd fbbbf cddd bbbe adda fbbbf adda bbbb adda fbbbf adda bbbb adda fbbbf adda ebbb dddc gbbbe dddc ebbbg dddc gbbbe dddc ebbbg dddc bbbe gdddg ebbbf gdddg bbbe gdddg fbbbf gdddg bbbb gdddgfbbbf cdddgbbbb cdddfbbbf cdddebbb cdddbbbe cddbbbb addbbbe adbbbbg adbbbe abbbbg abbbe ``` <!-- end of image --> No intersection in area A, but I'll keep looking. Time to investigate another area. I'm determined to find out if an intersection exists in area B. <!-- image --> ```palette Key,Color ,#fefefeff a,#d29847ff b,#fe0896ff c,#e3c48fff d,#c27c05ff e,#fe4db1ff f,#fe8fcfff g,#fbd2e1ff ``` ```image cddda dddc fbbbf gbbbf fbbbg cddddg dddc bbbb bbbf ebbb gddddc ddda fbbbf ebbe bbbe ddddc adda bbbb ebbb fbbbg ddda adda fbbbf fbbb ebbb ddd adda bbbb fbbbg bbbe ddg adda fbbbf gbbbf gbbbf dc adda bbbb bbbf ebbb c adda fbbbf bbbe bbbe addd bbbb ebbe gbbbf cddd fbbbf fbbb fbbbg cddd bbbb fbbbg bbbe cddd fbbbf gbbbg gbbbf cddd bbbb bbbf fbbbg cddd fbbbf bbbe ebbe cddd bbbb ebbe gbbbf cdddg fbbbf ebbb fbbbg cdddg bbbb fbbb ebbb gdddg fbbbf gbbbg bbbf gdddg bbbb gbbbf fbbbg gdddc fbbbf bbbf ebbb gdddc bbbb ebbe bbbe dddc fbbbf ebbb fbbbg dddc bbbb fbbb ebbb dddcfbbbf gbbbg bbbe dddcbbbb gbbbf gbbbf dddebbbf bbbf ebbb dddbbbb ebbe bbbe dddbbbf ebbe gbbbf cdc adbbbb fbbb fbbb ddda adbbbf fbbbg bbbe cdddc abbbb gbbbg gbbbf dddd abbbf bbbf fbbbg cdddc bbbb bbbe ebbe dddd fbbba ebbe gbbbf cdddc bbbbd fbbb fbbbg dddd fbbbad fbbbg ebbb cdddc bbbbdd gbbbg bbbf dddd fbbbadd bbbf fbbbg cdddc bbbbddd bbbe ebbb dddd fbbbeddd ebbe bbbe cdddc ebbbcdddg ebbb fbbbg dddd fbbbfcdddg fbbb ebbb cdddc ebbb gdddg gbbbg bbbe dddd fbbbf gdddg gbbbf gbbbf cdddc ebbb gdddc bbbf ebbb dddd fbbbf gdddc ebbe bbbe cdddc ebbb gdddc ebbb gbbbf dddd fbbbf dddc fbbb fbbb cdddc ebbb dddc fbbbg bbbe dddd fbbbf dddc gbbbf gbbbf cdddc ebbb dddc bbbf fbbbg dddd fbbbf dddc bbbe ebbe cdddc ebbb ddda ebbe gbbbf dddd fbbbf adda fbbb fbbbg cdddc ebbb adda fbbbg ebbb dddd gbbbf adda gbbbg bbbf cdddc ebbbg adda bbbffbbbg dddd gbbbf adda bbbeebbb cdddc ebbbg adda ebbebbbe dddd gbbbf addd ebbbbbbgcdddc ebbbg cddd fbbbbbb dddd gbbbe cddd gbbbbbecdddc ebbbg cddd gbbbbbfdddd gbbbe cddd bbbbbcdddc ebbbg cddd ebbbedddd gbbbe cdddg ebbbedddc ebbbg cdddg fbbbdddd gbbbe gdddg bbedddc ebbbg gdddg gdddd gbbbe gdddg cdddc ebbbg gdddc dddd gbbbe gdddc cdddc ebbbg dddc dddd gbbbe dddc cdddc ebbbg dddc dddd gbbbe dddc cdddc ebbbg dddc dddd bbbe ddda cdddc bbbg adda dddd bbe adda cdddc bbg adda dddd be adda cdddc bg adda dddd e adda cdddc g addd dddd cddd cdddc cddd dddd cddd cdddc cddd dddd cddd cdddc cddd dddd cdddg cdddc cdddg dddd gdddg cdddc ``` <!-- end of image --> Wow! I can see 1 intersection so clearly in area B! Answer: A: 0; B: 1; 0 + 1 = 1 The final count is: one intersection.

<!-- image --> ```palette Key,Color ,#fefefeff a,#cd9433ff b,#fe0997ff c,#e1c086ff d,#c17c03ff e,#fe49b1ff f,#ff95d2ff g,#f8dfddff ``` ```image ga dd ddd ddad adacd gdd cd dd cd bb ddg cdg bb ddc gdg bbbf cda gdc bbbe be gdd gdc bb bb fbg dd dc bb bb bb ddg dc bb bb bb adc dc bb eb fbf cda da bb fbg bb gdd da bb bf bb dd da bb be gbf ddg dd bb bb bb adc dd bb bb bb cdd dd bb eb gbf gdd dd bb fb eb dd dd bb gbf bb ddg dd bb be be ada dd bb bb eb cdd ddbb bb bb dd ddbb eb be g dd abb fb fbg da ddc abb gbf bb dd ada bb be be da gdd bb bb fbg dd dd bbd bb bb da ddg bbd bb bb dd ddc ebcdg eb fbf da cda bbgdg fbg bb dd gdd eb gdg bf bb da dd bb gdc bb gbf dd ddg eb dc bb bb dd adc bb dc bb bb dd cda ebg dc eb gbf dd gdd bb da fbgeb dd dd ebg da bfbb dd ddg bb da bebedd gd adc ebg dd bbb dd adg cdd bb dd bbbdd ada gdd ebg dd ebedd ddd dd bb dd fbad ddd ddg ebg dd gdd ddda ada bb dd dd dddd cdd ebg dd dd ddad dd bb dd ad dd dc dd ebg dd dd dd dd ddc bb ad ad da ad ada ebg ad dd da gdcgdd bb ad ad da dddd be ebg cd dd dc addgfbbb bb cd ad dc gdc bbebb ebg cd dd gdc fbf fbbg bb cdg ad gdg bb gbbf ebg gdg dd gdg gbe bbe bb gdg ad cdg bb bbb ebg gdc dd cd gbe ebb bb dc ad cd bb fbbg ebg dc dd ad bb gbbf bb dc ad ad eb bbe ebg da dd ad bb bbe bb da ad dd ebg bbb ebg da dd dd bb ebb bb da ad dd fbg fbbg ebg dd dd dd bb gbbfbb dd ad ddfbf bbbg dd dd ddbb bb dd ad dabf dd dd dbb dd adg dbe dd dd bb ddadg bb addd f addg add cdg g ``` <!-- end of image -->

I'm examining this image closely. My goal: find any and all intersections. I'd describe these as 'hotspots' for potential intersections. <!-- image --> ```palette Key,Color ,#fefefeff a,#6292deff b,#4865d9ff c,#8fb0e3ff d,#ebf2f6ff e,#b0d7b1ff f,#c0d1f1ff g,#95c996ff ``` ```image d fbbad faf bbbbbbad aaa fbbbbbbbad aac fbbbbbbbad daad fbbbbbbbad caa fbbbbbbbc aaa fbbbbbbbc aaf fbbbbbbbc faa fbbbbbbbc aaa fbbbbbbd aac fbbbb daad cbbf caa bbb aaa dbbb aaf abbd faa bbb aaa fbbc aac bbb daa bbb caa dd cbbf aaa daa bbb aaf faaa dbba faa aaaad abbd aaa aaaaa bbb aaf aaaaaf fbbc faa aadaaa bbb aaa faa daaf bba aac caa aaa abb aad aaa daac cbb caa aac aaa dbb ddddddddddddddaaaddddddd aad aaa bbf geeeeeeeeeeeeeaaceeeeeeg faa caad bba geeeeeeeeeeeecaaeeeeeeeg caa aaa bbb geeeeeeeeeeeeaaaeeeeeeeg aaa faaf cbb geeeeeeeeeeeeaaceeeeeeeg aac aaa fbb geeeeeeeeeeeeaaeeeeeeeeg aaf daaf bbd geeeeeeeeeeecaaeeeeeeeeg daa aaa bbc geeeabbbeeeeaaaeeeeeeeeg caa aac bbb gbbbbbbbaeeeaaceeeeeeeeg aaa caa abb dcbbbbbbbbbbbaecaaeeeeeeeeeg aac aaa fbb fbbbbbbbbaeeeebbbaaaaeeeeeeeeeg aaf caad dbb dcbbbbbbbbcgeeeeeeebbbbaceeeeeeeeeg daa aaa bbffbbbbbbbbad geeeeeeeebbbbeeeeeeeeeeg faa faaf bbbbbbbbbc geeeeeeeeebbbaeeeeeeeeeg aaa aaa bbbbbad geeeeeeeeeabbbaeeeeeeeeg aac daac dac geeeeeeeeeaabbbaeeeeeeeg aaf aaa geeeeeeeecaaebbbaeeeeeeg aad aac geeeeeeeeaaaeebbbaeeeeeg faa caa geeeeeeeeaaceeebbbaeeeeg caa aaa geeeeeeeeaaeeeeebbbaeeeg aaa caad geeeeeeeaaaeeeeeebbbaeeg aaf aaa geeeeeeeaaaeeeeeeebbbaeg aad faaf geeeeeeeaaeeeeeeeeebbbag faa aaa geeeeeecaaeeeeeeeeeebbba caa daac geeeeeeaaaeeeeeeeeeeebbbc aaa aaa geeeeeeaaceeeeeeeeeeeebbbd aac aac ddddddfaaddddddddddddddbd aad caa aaa daa aaa aac caa caad daad aaa aaa caa aac faaf aaa aaf aaa aaf daa daac faa faa aaa aaa aaa aac aac aac caa daad aaf aaa caa daa caad aaa faa aaa aaf caa faaf faa aaa aaaaccccccfffffffdddaaa aaf daaaaaaaaaaaaaaaaaaaaac aad caaaaaaaaaaaaaaaaaaaa faa caa aaa aac aad faa caa caa ``` <!-- end of image --> I'm eager to see what's happening in this magnified view of area A. <!-- image --> ```palette Key,Color ,#fefefeff a,#6192dfff b,#4764d9ff c,#aec0eeff d,#ecf1faff e,#809ce4ff f,#c8d6f3ff g,#95aee9ff ``` ```image caaaag eaaaac daaaaad faaaae gaaaac aaaaaf daaaaa caaaag eaaaaf daaaaad faaaae gaaaac dcgc aaaaaf dfgabbbbad faaaaa dcebbbbbbbbbad caaaag dfgbbbbbbbbbbbbbbad eaaaaf bbbbbbbbbbbbbbbbbbad daaaaad bbbbbbbbbbbbabbbbbbad faaaae bbbbbbbbbefd fbbbbbbad gaaaac bbbbbacf fbbbbbbadaaaaad bbefd fbbbbbbaaaaaa f fbbbbbbbaaag fbbbbbbbaaf fbbbbbbbad fbbbbbbb fbbbbbbe dabbbbbbe faabbbbbbe gaaabbbbbbe aaaaabbbbbbe daaaaacbbbbbbe caaaag cbbbbbbe eaaaaf cbbbbbbe daaaaad cbbbbbbe faaaae cbbbbbbe gaaaac cbbbbbbe aaaaaf cbbbbbbe faaaaa cbbbbbbe caaaag cbbbbbbe eaaaaf cbbbbbbe daaaaad cbbbbbbe faaaae cbbbbbbg gaaaac cbbbbbbg aaaaad cbbbbbbg faaaaa gbbbbbbg caaaag gbbbbbb eaaaaf gbbbbb daaaaad gbbbb caaaae gbbb gaaaac gbb ``` <!-- end of image --> Bingo! This close-up reveals 1 intersection in area A! Answer: A: 1; 1 = 1 One intersection, that's it, but I found it.

<!-- image --> ```palette Key,Color ,#fefefeff a,#6192dfff b,#4865d9ff c,#a2bcebff d,#dce6f7ff e,#83a2e5ff f,#c3d4f2ff g,#f0f4fbff ``` ```image g fbbeg fac bbbbbbeg eaa dbbbbbbbeg aae fbbbbbbbeg gaad fbbbbbbbeg caa fbbbbbbbeg aaa fbbbbbbbeg aaf fbbbbbbbeg faa fbbbbbbbe aaa fbbbbbbg aac fbbbb gaag cbbc eaa bbb aaa gbbb aaf abbd faa bbb aaa fbbe aac bbbg daag bbb eaa gg cbbc aae gaa bbb aad caaa gbba caa eaaag abbd aaa aaaaa bbb aac aaeaaf fbbe daa aagaaa bbb eaa faa daac bba aae eaa aaa abb gaad aaa gaae cbb caa aac eaa dbb aaa aad aaa bbf aaf faa caag bbe faa caa aaa bbb aaa aaa faaf ebb aae aac aaa fbb gaag aad daac bbd caa daa aaa bbe gebba aaa caa gaae bbb fbbbbbbba aaf aaa eaa abb gebbbbbbbbbbba faa aae aaa cbb fbbbbbbbbad bbbaaaa aaf caag gbbg gebbbbbbbbc bbbbac gaa aaa bbcfbbbbbbbbad bbbbg caa faaf bbbbbbbbbc bbbe aaa aaa bbbbbad abbbe aae daac gac aabbbe aaf aaa caa bbbe gaag gaae aaa bbbe faa eaa aac bbbe eaa aaa daa bbbe aaa caag eaa bbbe aac aaa aae bbbe aag faaf aad bbbe faa aaa caa bbbe eaa daac aaa bbbc aaa aaa aaf bbbg aac aae faa bg aad eaa aaa daa aaa aae caa caad gaag aaa aaa caa aae faaf aaa aaf aaa aaf daa daac faa caa aaa aaa aaa aae aac aae eaa gaag aaf aaa eaa gaag caad aaa faa aaa aaf eaa faaf faa aae aaaeeeecccccffffdddgaaa aac gaaaaaaaaaaaaaaaaaaaaac aag caaaaaaaaaaaaaaaaaaaa faa eaa aaa aac aad daa caa caa ``` <!-- end of image -->

I have a feeling there might be some intersections in this image. I've spotted 1 narrow regions that might be worth examining further. Let's call them area A. <!-- image --> ```palette Key,Color ,#fefefeff a,#846035ff b,#0e9ba0ff c,#55b5abff d,#743809ff e,#96c798ff f,#979168ff g,#b1d7b1ff ``` ```image geeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee eggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggg eggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggg eggggggggggggggggggggggggggggggggccggggggggggggggggggggggggggggggggg eggggggggggggggggggggggggggggggggbbggggggggggggggggggggggggggggggggg egggggggggggggggggggggggggggggggbbbegggggggggggggggggggggggggggggggg eggggggggggggggggggggggggggggggebcbbggggggggadgggggggggggggggggggggg eggggggggggggggggggggggggggggggbbgcbgggggggeddgggggggggggggggggggggg egggggggggggggggggggggggggggggebcggbbggggggdddaggggggggggggggggggggg d egggggggggggggggggggggggggggggbbgggbbgggggfdfddggggggggggggggggggggg dda eggggggggggggggggggggggggggggebcggggbcggggddgfdegggggggggggggggggggg gddd eggggggggggggggggggggggggggggbbgggggbbgggddgggddgggggggggggggggggggg dded egggggggggggggggggggggggggggcbcgggggcbegedagggddgggggggggggggggggggg adg da egggggggggggggggggggggggggggbbgggggggbbgddggggedfggggggggggggggggggggda dd eggggggggggggggggggggggggggcbegggggggcbadfgggggddgggggggggggggggggggdd gdg eggggggggggggggggggggggggggbbgggggggggbddggggggadggggggggggggggggggadg da egggggggggggggggggggggggggcbegggggggggddggggggggdagggggggggggggggggdd dd egggggggggggggggggggggggggbbgggggggggfdacgggggggddggggggggggggggggdd gdg eggggggggggggggggggggggggcbegggggggggddbbgggggggfdeggggggggggggggfdf dd eggggggggggggggggggggggggbbgggggggggadecbegggggggdaggggggggggggggddg dd egggggggggggggggggggggggbbgggggggggeddggbbgggggggddgggggggggggggadgg gdg egggggggggggggggggggggggbbgggggggggddgggcbgggggggfdfggggggggggggadgg dd eggggggggggggggggggggggbbgggggggggfdfggggbbgggggggddggggggggggggddgg dd eggggggggggggggggggggggbbgggggggggddgggggbbgggggggddggggggggggggddgg gdg egggggggggggggggggggggbbgggggggggddeggggggbcggggggedfgggggggggggddgg a egggggggggggggggggggggbbggggggggedagggggggbbgggggggddgggggggggggddgg eggggggggggggggggggggbbgggggggggddggggggggcbeggggggadgggggggggggddgg egggggggggggggggggggebcggggggggadfgggggggggbbgggggggdaggggggggggddgg egggggggggggggggggggbbgggggggggddggggggggggcbgggggggddggggggggggddgg cgeggggggggggggggggggebcggggggggddggggggggggggbbggggggfdegggggggggddgg bceggggggggggggggggggbbggggggggfdaggggggggggggbbgggggggddgggggggggdagg bcegggggggggggggggggebcggggggggddggggggggggggggbcggggggddgggggggggdagg bcegggggggggggggggggbbggggggggadeggggggggggggggbbggggggedfggggggggdagg bbeggggggggggggggggcbcggggggggddgggggggggggggggcbeggggggddggggggggdfgg bbeggggggggggggggggbbggggggggddgggggggggggggggggbbggggggadggggggggdfgg bbegggggggggggggggcbegggggggfdfgggggggggggggggggcbgggggggdfgggggggdfgg bbegggggggggggggggbbggggggggddgggggggggggggggggggbbggggggddgggggggdfgg bbeggggggggggggggcbegggggggddegggggggggggggggggggbbggggggadggggggedegg bbeggggggggggggggbbgggggggedagggggggggggggggggggggbcggggggdagggggedegg bbegggggggggggggcbegggggggddggggggggggggggggggggggbbggggggddgggggfdggg bbegggggggggggggbbgggggggfdfggggggggggggggggggggggcbegggggfdeggggfdggg bbeggggggggggggbbggggggggddggggggggggggggggggggggggbbggggggddggggfdggg cbeggggggggggggbbgggggggddgggggggggggggggggggggggggcbggggggddggggadggg cbegggggggggggbbgggggggedaggggggggggggggggggggggggggbbgggggedfgggadggg cbegggggggggggbbgggggggddgggggggggggggggggggggggggggbbggggggddgggadggg cbeggggggggggbbgggggggadfgggggggggggggggggggggggggggebcgggggadgggadggg gbeggggggggggbbgggggggddgggggggggggggggggggggggggggggbbggggggdaggddggg gbegggggggggbbgggggggddggggggggggggggggggggggggggggggebbgggggddggddggg gbeggggggggebcggggggfdagggggggggggggggggggggggggggggggcbbggggfdegddggg gbeggggggggbbgggggggddgggggggggggggggggggggggggggggggggbbcggggdagddggg begggggggebcggggggadeggggggggggggggggggggggggggggggggggbbggggddgddggg bcgggggggbbggggggeddggggggggggggggggggggggggggggggggggggbbgggfdfddggg bcggggggebcggggggddgggggggggggggggggggggggggggggggggggggebbgggddddggg bcggggggbbggggggfdfggggggggggggggggggggggggggggggggggggggcbcggddddggg bcgggggcbcggggggddggggggggggggggggggggggggggggggggggggggggbbegeddaggg bcgggggbbggggggddggggggggggggggggggggggggggggggggggggggggggbbggddaggg bbggggcbegggggedagggggggggggggggggggggggggggggggggggggggggggbbgadaggg bbggggbbggggggddggggggggggggggggggggggggggggggggggggggggggggcbbgdfggg bbgggcbegggggadfgggggggggggggggggggggggggggggggggggggggggggggbbcggggg bbgggbbggggggddgggggggggggggggggggggggggggggggggggggggggggggggbbggggg bbggcbegggggddgggggggggggggggggggggggggggggggggggggggggggggggggbbgggg bbggbbgggggfdagggggggggggggggggggggggggggggggggggggggggggggggggebbggg bbgbbggggggddgggggggggggggggggggggggggggggggggggggggggggggggggggcbcgg bbgbbgggggadeggggggggggggggggggggggggggggggggggggggggggggggggggggbbeg bbbbggggggddggggggggggggggggggggggggggggggggggggggggggggggggggggggbbe bbbbgggggddggggggggggggggggggggggggggggggggggggggggggggggggggggggggbb bbbgggggfdfggggggggggggggggggggggggggggggggggggggggggggggggggggggggcbb cbbgggggddggggggggggggggggggggggggggggggggggggggggggggggggggggggggggbbg cbeeeeeddeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeebb da bb dd bb fdg cbc dd bbg dd bb gda bb dd gbb adg cbc dd bb dd bb edf bc dd ad da g ``` <!-- end of image --> I'm analyzing this close-up of area A with precision. <!-- image --> ```palette Key,Color ,#fefefeff a,#986c4aff b,#0c9aa0ff c,#42b0b5ff d,#75380aff e,#c0a590ff f,#d7e1ddff g,#86cccfff ``` ```image cg bbbg gbbbb fbbbbbf gbbbbbc ef cbbbfbbbg edda bbbc cbbb fdddd bbbf fbbb adddde fbbg cbb eddddda cbbf gbbf dddadddf cbb gbbf ddda adda fbbg fbbg dddf eddd cbb cbb edda ddd gbbb fbbg ddd add bbbg bbbf fdda dda bbc bbbc addf edd gbbg gbbb eddd fdde bbc fbbbfdddd ada gbbf cbbaddde eddf gbbf cbdddf ddd a fbbb gadde dddf ed gbbb fddd ddda dd fbbbc addbf addd dd bbbc dddbbb ddd ddd bbbf edddbbbg eddf edde fbbg dddacbbc fdde fdda cbbf dddfgbbbf ada addf fbbg edde bbbc eddf eddd fbbg adde fbbb add adda cbb fdda cbb eddf adde gbbb addf fbbg dda ddde cbbb eddd cbc ddd ddde bbc dddf bbc ddda ddde gbbg edda gbbf edddf ddde bbc dddf fbbg fddde fddde gbbf edde bbb adda fdddf bbc fdda bbbg eddd fdddf fbbb eddd gbbb add fdddf gbbb dddd bbb fdde edddf fbbbc addde gbbf dda eddd cbbbf ddda fbbg edd eddd bbbf edde fbbg ada eddd fbbg fddd cbc eddf eddd cbbf addf gbbf fdde edda fbbg edda bbc ddd adda cbb dddf bbbf dddf adda cbb ddda cbbb addd adda gbbb dddf fbbbg fddd adda cbbb edda cbbc ddd adda bbbg ddd gbbb eddf adde gbbg fdda gbbf ada ddde bbc addf fbbg eddf ddde gbbf eddd cbb dde ddde bbc fdddd fbbg add ddde f fbbb ddda gbbf dda dddf f gbbb dddf bbc ddd dddf f fbbbc edde bbbf ddde dddf f cbbbf fdda bbbg ddda dddf f bbbc addf cbbb eddd dddf g fbbg dddf cbb add ddd g cbbf eddd gbbf eddf ddd g fbbg ddda bbc dda ddd g cbb dddf gbbf add ddd g cbb fddd cbb dda dda g gbbb adde fbbg edd dda c cbbb fdda bbc fdde dda c bbbg addf bbbf dda dda c bbc eddd bbbc dddf dda c bbc adddf fbbbg addd dde c gbbf ddda cbbb edddf dde b bbc dddf fbbb ddda dde b gbbf edde cbbg addd dde b gbbb addf fbbbf ddd dde b bbbc edda gbbc eddf fdde bf bbbf ddd bbbg fdde fddf bf fbbc addd cbbb ada fddf bf cbbf ddda fbbbf eddf fddf bf cbbf edde gbbc add eddf bf fbbg fddd cbbg eddfedd bg cbb adde fbbbf ddaedd bg fbbb fdda bbbb dddedd bg gbbbg eddd cbbg dddddd bg cbbb fddda cbbg edddda bg bbbg adddf fbbbf fdddda bg bbc ddda gbbb addda bc gbbg ddd bbbc eddda bc gbbf fdda bbbb adda bc bbc addf fbbbf fdda bc gbbf edde gbbc dde bc fbbb fddd cbbc edf bb bbbc ddda fbbbf bb bbbf dddf bbbb bb fbbc edde gbbb bb cbbf fdda cbbg bb fbbg addf bbbg bb fbbg dddf gbbc bb cbb eddd bbbc bb fbbb ddda cbbbg bb cbbb dddf fbbbb bbcbbb ddd gbbc bbbbbg adde cbbg bbbbc fdda cbb bbbbg addf fbb bbbc eddd bb bbc adddf c bbf ddda f ``` <!-- end of image --> Incredible, there's actually 1 intersection in area A! Answer: A: 1; 1 = 1 My investigation reveals that there is exactly one intersection in this image.

<!-- image --> ```palette Key,Color ,#fefefeff a,#956845ff b,#0e9ba1ff c,#57b9bdff d,#75380aff e,#c2a793ff f,#dee0dbff g,#9dd6d8ff ``` ```image cg bb bbbg fbcbb ad bb cb fdd fbc bb ddda d bb bb ededd dda gbg fbc dd edf fddd bb bb dd dd ddedf gbg gbg fda dd adf da bb bb dd fde fda dd gbg cbade dd dd edf bb bdd ad ade dd cbf dd da fdd dd bb edac dd dd edf cbf ddbb edf ede dd bb adfgbg da dd dd cb fdd bb dd ad fde bb dd cb edf ad dd bb ede bb dd dd dd bb dd bb ad dd fde bb ddf fbc fde dd af bc fda bb dd dd bb dd gbg ad dd fbc ade bb da dd bb dd cb dd dd cg fbc dd bb edf dd bc bb eda bb dd da bc gbg dd fbc dd da bc bb adf bb fde da bb gbg dd gbg dd de bb bb dd bb ad de bb gbg ede cb fde de bb bb dd bb dd fde bb cbf adf bb ad fdf bb bb fda fbc da fdf bb cbf dd bb dd ed bb bb ede gbg edf ed bb cb dd bb dd ed cb bb dd cb dd ad cb bb fda bb fde ad cb bb dd bb dd ad cb bb adf fbc ad ad gb bc dd bb da dd gb bb dd fbb dd dd gb fbc eda gbc edf dd fbf bb dd bbg da dd fbf fbc adf bb dd dd bg bb fdd bb edfdd bg gbg dd fbb dddd bg bb ede cbc addd bc gbg dd bbf fdda bc bb ddf bb dda bc gbg fda bb ada bc bb dd gbb de bb cbf ade cbg bb bb dd bb bb cbf dd bb bb bb eda fbb bb cb dd cbc bb bb adf bbf bbbb fdd bb bbbb dd bb bbb ede gbb cbc dd cbg cb ddf bbf fda bb dd fbb ade cbc dd bbg dd bb fda bb dd gbb adf cbc dd bbf dd bb ede fbc dd f adf fda f ``` <!-- end of image -->

This image might have some surprises. Let's look for intersections carefully. Could these regions be concealing intersection points? Let's find out. <!-- image --> ```palette Key,Color ,#fefefeff a,#d4a2b2ff b,#66ae0cff c,#c9668dff d,#8cc156ff e,#f0f2edff f,#b2d7b1ff g,#a4cea0ff ``` ```image e ebb bbb fbb bbd fbb a bbd ccc gbb ecccc bbd cccccc gbb ecce ccce bbd cc ccc ccce dbb ecc ecc ccce bbg ccce ccc ccceeeeeeeeeeeeeeeeedbbeeee ccca ecc cccggggggggggggggggbbdgggge cccc ccc cccgfffffffffffffbbbffffge acccc ecc cccgffffffffffffbbdffffge ccccc ccc gcccaffffffffffbbbfffffge ccecc ecc gfcccafffffffffbbgfffffge ecc cc cca gffcccafffffffbbbffffffge acc cce acc gfffcccaffffffbbgffffffge cca cca cca gffffcccaffffbbbfffffffge cc cca acc gfffffccccffgbbgfffffffge acc acc cca gffffffccccfbbbffffffffge cca acc acc gfffffffccccbbgffffffffge cce ecc cca gffffffffacccbfffffffffge ecc cc acc gfffffffffccccfffffffffge acc cc cca gfffffffffbdcccffffffffge cca cce acc gffffffffgbbacccfffffffge cc cca cca gffffffffbbbfacccffffffge ecc cca acc gfffffffdbbfffacccfffffge ccc acc cca gfffffffbbdffffgcccffffge cce ecc acc gffffffdbbffffffgcccfffge cc cc cca gffffffbbdffffffffcccffge acc cc acc gfffffdbbffffffffffcccfge cca cce cce gfffffbbdfffffffffffcccge cc cce ccc gffffdbbfffffffffffffccce ecc cca cce gffffbbdffffffffffffffccc ccc acc ccc ggggdbbggggggggggggggggccc cce acc cce eeeebbgeeeeeeeeeeeeeeeeece cc ecc ccc de dbb acc cc cce bbbe bbf cca cc ccc ebbbbbe dbb cce cce ecce ebbbebbb bbf ecc cca ccc fbbb bbb bbb acc cca ecce fbbb bbb bbe cca acc ccc dbbb ebbb bbb cc ecc ecc dbbb ebbb ebbe acc ecc ccc bbbd ebbb bbb eeeeeeccceeeeeeeeeeeeecceeeecceeeeeebbbd ebbbebbe ggggggccagggggggggggggccgggcccgggggbbbg ebbbbb gfffffccgfffffffffffffccgfgccfffffbbbge fbbbe gfffffccffffffffffffffccafcccffffbbbgge fbb gfffffccffffffffffffffcccaccfffgbbbffge gffffgccffffffffffffffacccccffgbbbfffge gffffaccffffffffffffffgccccffdbbbffffge gffffcccfffffffffffffffccccfdbbbfffffge gffffccafffffffffffffffcccfbbbbffffffge gffffccgfffffffffffffffcccbbbdfffffffge gffffccffffffffffffffffacbbbdffffffffge gffffccfffffffffffffffffbbbdfffffffffge gfffgccffffffffffffffffbbbgffffffffffge gfffaccffffffffffffffgbbbgfffffffffffge gfffcccfffffffffffffgbbbfffffffffffffge gfffccaffffffffffffgbbbffffffffffffffge gfffccgfffffffffffdbbbfffffffffffffffge gfffccfffffffffffdbbbffffffffffffffffge gfffccffffffffffbbbbfffffffffffffffffge gffgccfffffffffbbbdffffffffffffffffffge gffaccffffffffbbbdfffffffffffffffffffge gffcccfffffffbbbdffffffffffffffffffffge gffccaffffffbbbgfffffffffffffffffffffge gffccgffffgbbbgffffffffffffffffffffffge gffccffffgbbbffffffffffffffffffffffffge gffccfffgbbbfffffffffffffffffffffffffge gffccffdbbbffffffffffffffffffffffffffge gfaccfdbbbfffffffffffffffffffffffffffge gffaabbbbffffffffffffffffffffffffffffge gfffbbbdfffffffffffffffffffffffffffffge gffbbbdffffffffffffffffffffffffffffffge ggbbbdgggggggggggggggggggggggggggggggge eeebfeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee ``` <!-- end of image --> I'm focusing my attention on this specific region, area A. <!-- image --> ```palette Key,Color ,#fefefeff a,#e6b9caff b,#66ae0bff c,#ca648cff d,#8dc24aff e,#ebe7ddff f,#bddc96ff g,#d78ca9ff ``` ```image ccccg gcccc gcccca fbbb cccca acccc eccccc fbbbb ecccca acccce gcccca fbbbbb acccce ecccce eccccg dbbbbbb acccc ecccca gcccca dbbbbbbe gcccc cccca eccccg dbbbbbde gcccg ccccg gcccca edbbbbbde ccccg gcccg accccg ebbbbbbd cccca gcccc gcccce ebbbbbbd ecccca accccaccccg ebbbbbbf acccce accccccccce fbbbbbbf acccc eccccccccg fbbbbbbf gcccc ecccccccce fbbbbbbf gcccg cccccccg dbbbbbbe ccccg gcccccce dbbbbbbe cccca gcccccg dbbbbbde ecccca gccccceedbbbbbde acccce accccgebbbbbbd acccc eccccabbbbbbd gcccc accgbbbbbbf gcccg fbbbbbbf ccccg fbbbbbbf cccca fbbbbbbf ecccca dbbbbbbe acccce dbbbbbbe acccce dbbbbbde gcccc edbbbbbd gcccg ebbbbbbd ccccg ebbbbbbd cccca fbbbbbbf ecccca fbbbbbbf acccce fbbbbbbf acccce fbbbbbbf gcccc dbbbbbbe gcccg dbbbbbbe ccccg edbbbbbde cccca edbbbbbd ecccca ebbbbbbd acccce ebbbbbbd acccce fbbbbbbf gcccc fbbbbbbf gcccg fbbbbbbf ccccg fbbbbbbe cccca dbbbbbbe ecccca dbbbbbbe acccce edbbbbbde acccce edbbbbbd gcccc ebbbbbbd gcccg ebbbbbbd ccccg fbbbbbbf cccca fbbbbbbf ecccca fbbbbbbf acccce fbbbbbbe acccce dbbbbbbe gcccc dbbbbbbe eaaaedbbbbbde edbbbbbd ebbbbbbd ebbbbbbd fbbbbbbf fbbbbbbf ``` <!-- end of image --> No intersection found in area A, but I won't give up. I'm ready to analyze the next area. Let's take a closer look at area B. <!-- image --> ```palette Key,Color ,#fefefeff a,#db98b2ff b,#65ae0bff c,#ca658cff d,#88b840ff e,#eedcdfff f,#cee5b2ff g,#abd279ff ``` ```image ce fbbbbb cce dbbbbf ccce fbbbbd cccce dbbbbf ccccce fbbbbd cccccce dbbbbf ecccccce fbbbbd ecccccce dbbbbf ecccccce fbbbbd ecccccce dbbbbf ecccccca fbbbbd ecccccca bbbbbf ecccccca gbbbbd ecccccca bbbbbe cccccca gbbbbg cccccca bbbbbe accccca gbbbbg accccca ebbbbbe accccca gbbbbg accccca ebbbbbe accccca gbbbbg acccccabbbbb accccccbbbg accccccbb accccccg acccccc ddcccccce fbbdcccccce dbbbdcccccce fbbbbdacccccce dbbbbf ecccccce fbbbbd ecccccce dbbbbf ecccccce fbbbbd ecccccce dbbbbf ecccccce fbbbbd ecccccce bbbbbf ecccccce gbbbbd ecccccce bbbbbe ecccccce gbbbbd ecccccca bbbbbe ecccccca gbbbbg ecccccca bbbbbe ecccccca gbbbbg cccccca ebbbbbe cccccc gbbbbg acccc ebbbbb accc gbbbbg acc ebbbbb ac dbbbbg a ``` <!-- end of image --> As I suspected, there's 1 intersection within area B. Answer: A: 0; B: 1; 0 + 1 = 1 My investigation reveals that there is exactly one intersection in this image.

<!-- image --> ```palette Key,Color ,#fefefeff a,#e4b1c5ff b,#66ae0bff c,#ca648cff d,#90c24fff e,#eee2e0ff f,#c1de9cff g,#d586a5ff ``` ```image ebb bbb fbb bbd fbb a bbd ccc fbb cccc bbd cccccc fbb ecc ccc bbd cc ccc ccc dbb ecc ecc ccce bbf gcce ccc ccce dbb ccca ecc ccce bbf cccg ccg ccce dbb acccc ecc ccce bbf ccccc ccg ccca dbb ccecc ecc ccca bbe ecc cc ccg ccca bbb gcc cce acc gcca bbe cca cca ccg gcca bbb cc ccg acc gccg ebbe acc gcc ccg gccg bbb ccg acc acc gccgbb cce ecc cca gcccb ecc cc acc gccg gcc cc cca bdccc cca cce acc fbbaccc cc cca cca bbd accc ecc gcg gcc fbb eccc ccg acc cca bbd eccc cce ecc gcc fbb eccc cc cc cca bbd eccc acc cc gcc fbb eccc cca cc cce bbd eccc cc cce gcc dbb ccc ecc cca cce bbf ccc gcc gcg gcc dbb ccc cce acc cce bbf ce cc ecc ccc d dbb acc cc cce bbb bbf ccg cc ccc bbbbb dbb cce cce cce ebbb bbb bbf ecc cca ccc ebbb bbb bbb gcc ccg ecc fbbb bbb bbe cca acc ccc dbbb bbb bbb cc acc ecc dbbb ebbb bbe acc cc ccc bbbd ebbb bbb gcg cc ecc bbbd ebbbebbe cca cc ccg bbbf ebbbbb cce cce ecc bbbe fbbb cc cca ccg bbbe fbd cc gcgecc ebbb ecc accccg fbbb acc ecccc fbbb gcg cccg dbbb cca ccc dbbd cce ccgbbbd cc acbbbf cc bbbf ecc bbbe acc bbbe gcg ebbb cca fbbb cce fbbb cc dbbb cc dbbd ecc bbbd acc bbbf gcg bbbf cca bbbe cce ebbbe cc ebbb cc fbbb ecc fbbb acc dbbb aadbbd bbbd bbbf bbbf be ``` <!-- end of image -->

Based on a first glance, I suspect there could be intersection regions here. These areas seem to enclose narrow spaces where lines might be close. <!-- image --> ```palette Key,Color ,#fefefeff a,#c83707ff b,#906c70ff c,#cf7b56ff d,#631e2fff e,#ddc1beff f,#b0d7b0ff g,#9fbe95ff ``` ```image ee edddddddddddddddbbbgee eb eeegbbbddddddddddddddbbbgeee gffffffffffffffg eb eegbbbdddddddddddddddbbbbgggffffffff gb ebbbbbdddddddddddddddbbb ffffffbbffffffffffg gfffffffffffffff eegb ffffffbbffffffffffg gfffffffffffffff ffffffbbffffffffffg gfffffffffffffff ffffffbbffffffffffg gfffffffffffffff ffffffdgffffffffffg gfffffffafffffff ffffffdgffffffffffg gffffffaacffffff ffffffdgffffffffffg gffffffagaffffff ffffffdgffffffffffg gfffffagfaffffff ffffffdfffffffffffg gffffcaffaffffff ffffffdfffffffffffg gffffafffagfffff ffffffdfffffffffffg gfffacfffccfffff fffagfdfffffffffffg gffgafffffafffff ffffagdfffffffffffg gffaffffffafffff fffffadfffffffffffg gfacffffffafffff ffffffdcffffffffffg gfafffffffccffff ffffffdaafffffffffg gagfffffffgaffff ffffffdfaaffffffffg cagggggggggagggg ffffffdffcafffffffg a a ffffffdfffcaffffffg ae ae ffffffdffffcafffffg ea cc ffffffdfffffgagfffg a a ffffffdffffffgagffg cc a ffffffdffffffffacfg a a ffffffdfffffffffacg ae ce fffffgdffffffffffaa ca ea fffffgdfffffffffffaa a a fffffgdfffffffffffgca ae a fffffbbfffffffffffg caaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa ae fffffbbfffffffffffg cc bb a bb a bg a be ce be ea de a de a d ae d cc d a d a d a d ce d ea d a d a d ae d cc d a d a d a d ce d ec d a ed a ed a eb cc eb a gb a gb a dbb ce dbg ec dde a dde a bde a bde cc bd a gd a ed a ed d d d d d d ``` <!-- end of image --> Here's a close-up of the area A. <!-- image --> ```palette Key,Color ,#fefefeff a,#c8390aff b,#824957ff c,#d97150ff d,#621b2cff e,#cfa7a5ff f,#e9d3d1ff g,#a37881ff ``` ```image edg edg gdg gdg gdg gdg gde gde bde bde bde bdf bdf bdf ddf ddf ddf dd dd dd fdd fdd fdd f fdb faaf fdb faaaf edb caafedb caagdb caadb cadb gddc gddac gdgaac gdgfaaaf gdg faaaf gde caaf gde caae bde caae bde caae bde eaac bdf eaac bdf faac bdf faaaf ddf faaaf ddf faaaf ddf caaf dd caae dd caae dd eaac fdd eaa fdd ea fdd f fdb fdb edb edb edb edb edg ``` <!-- end of image --> Wow! I can see 1 intersection so clearly in area A! Let's shift our focus to the next area. Could this be where the intersection is hiding, in area B? <!-- image --> ```palette Key,Color ,#fefefeff a,#c93505ff b,#976975ff c,#df886cff d,#631e2fff e,#d1a7a3ff f,#ecd0c9ff g,#d35d36ff ``` ```image ddbbbbbbeeeefff dddddddddddddddddddddbbbbbbeeee ffeeeebbbbbbddddddddddddddddddd fffeeeebbbbbb ce caa faaaf gaaae eaacac aaefag cag aa faaf gaf gac cac caa eag faaf faa gag aaf eaaf gae aae cac cag fag faaf aa gac gaf caa cac faaf eag gag faa eaaf aaf aae gae cag cac faaf fag gac aa ``` <!-- end of image --> The evidence suggests that this is not an intersection point in area B. Answer: A: 1; B: 0; 1 + 0 = 1 There's one and only one intersection present in the image.

<!-- image --> ```palette Key,Color ,#fefefeff a,#c93606ff b,#854f5dff c,#db7959ff d,#611b2dff e,#d9b5b1ff f,#eddddcff g,#aa858eff ``` ```image eff fddddddddddddddbbgggeff eb feeggbbbdddddddddddddbbggeef eb ffeeggbbdddddddddddddbbggeeff gb feeggbbdddddddddddddbbbg gg ffegg gg gg be be a be cae df faea df af a d ca a d a af d ae cc af d ea a faed a a ad cc a dc fa ce dac af ea d aa ca a d ca a a d ca ae af d ea ea cc d faf a a d faf cc a d ae fa a fd ac af ce fd ac ca ea fb aa a a eb ca ae a eb caaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa af gb cc gg fa gg a gg a be ce be ea be a df a df af d cc d fa d a d a d ce d ea d a d a d af d cc d fa d a d a d ce d ec fd a fd a fb af eb cc eb fa gb a gg a dgg ce dbg ec dbe a bde a bde af gdf cc gdf fa gd a ed a fd fd d d d d d ``` <!-- end of image -->

This is the image I'm working with. The goal is to count the intersections. The image has some tight areas where segments are too close. I should investigate those closely. <!-- image --> ```palette Key,Color ,#fefefeff a,#e57e50ff b,#bf1cf4ff c,#f5cfbfff d,#e9b3faff e,#b0d6b0ff f,#e4a37fff g,#cc63ebff ``` ```image gbb bbb bbg dbb bbb bbb bbd gbb bbb bbg dbbd gbb aaa bbb faa bbg caa dbb caa bbb aac bbb aac bbd aaf gbb aaa bbb aaa bbg aaa dbbd faa gbb caa bbb caa bbg aac dbb aac bbb aaf bbb eeeeaaaeeeeeeeeeeee bbd eeeeaaaeeeeeeeeeeee gbb eeeeaaaeeeeeeeeeeee bbb eeeefaaeeeeeeeeeeee bbg eeeefaaeeeeeeeeeeee dbbd eeeeeaaeeeeeeeeeeee gbb eeeeeaaeeeeeeeeeeee bbb eeeeeaafeeeeeeeeeee bbg eeeeeaafeeeeeeeeeee dbb eeeeeaaaeeeeeeeeeee bbb eeeeeaaaeeeeeeeeeee bbb eeeeeaaaeeeeeeeeeee bbd eeeeefaaeeeeeeeeeee gbb eeeeefaaeeeeeeeeeee bbb eeggggggggggggeeeeed bbg eegbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbggggggggbb eegbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb eeeeeeaafeeeeeeeeee dddddddddddggggggggggbbbbbbbbbbbbbbbbbbbbbbbbbbbbg eeeeeeaaaeeeeeeeeee eeeeeeaaaeeeeeeeeee eeeeeeaaaeeeeeeeeee eeeeeefaaeeeeeeeeee eeeeeefaaeeeeeeeeee eeeeeeeaaeeeeeeeeee eeeeeeeaaeeeeeeeeee eeeeeeeaafeeeeeeeee eeeeeeeaafeeeeeeeee eeeeeeeaaaeeeeeeeee eeeeeeeaaaeeeeeeeee eeeeeeeaaaeeeeeeeee eeeeeeefaaeeeeeeeee eeeeeeefaaeeeeeeeee caa aac aac aaf aaa aaa faf aaa caaaa faa aaaaac caa aaaaac caa faaaaf aac caaaaa aac caaaaa aaf aaaaac aaa faaaaf aaa faaaaf aaa cccfffaaaaaaaaa faa cccfffaaaaaaaaaaaaaaaaaaaaaaaac caa cccfffaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaac caaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaffccc aaaaaaaaaaaaaaaaaaaaaffccc faaaffccc ``` <!-- end of image --> This is a magnified view of the region A. <!-- image --> ```palette Key,Color ,#fefefeff a,#e67e50ff b,#bf1cf4ff c,#f5cebdff d,#e5a7faff e,#cd40bbff f,#eca383ff g,#d15ef6ff ``` ```image caaaaf caaaaa caaaaa aaaaa aaaaac aaaaac faaaac faaaaf faaaaf caaaaf caaaaa caaaaa aaaaa aaaaac aaaaac faaaac faaaaf faaaaf caaaaf caaaaa caaaaa aaaaa aaaaac aaaaac faaaac faaaaf faaaaf caaaaf caaaaa dggggggeeeeedddddddddddddddddddd gbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb gbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb gbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb gbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb dggggggeeeeeeggggggbbbbbbbbbbbbb faaaaf caaaaf caaaaa caaaaa aaaaa aaaaac aaaaac faaaac faaaaf faaaaf caaaaf caaaaa caaaaa aaaaa aaaaac aaaaac faaaac faaaaf faaaaf caaaaf caaaaa caaaaa aaaaa aaaaac aaaaac faaaac faaaaf faaaaf ``` <!-- end of image --> I can confirm that 1 intersection exists in area A. Answer: A: 1; 1 = 1 The image features one single intersection point.

<!-- image --> ```palette Key,Color ,#fefefeff a,#e67e51ff b,#bf1bf4ff c,#f2c1abff d,#e39ef9ff e,#f6dce4ff f,#eca17fff g,#d059f2ff ``` ```image gbb bbb bbg dbbe bbb bbb bbd dbb bbb bbg ebbd gbb aaa bbb faa bbg caa dbb eaa bbb aae bbb aac bbd aaf dbb aaa bbb aaa bbg aaa ebbe faa gbb caa bbb eaa bbg aae dbb aac bbb aaf bbb aaa bbd aaa gbb aaa bbb faa bbg caa ebbe eaa gbb aae bbb aac bbd aaf dbb aaa bbb aaa bbb aaa bbd faa gbb caa bbb dgggggdddddddddeeeee bbg gbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbgggggggggbbe gbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb aaf eeeeeddddddddddgggggggggbbbbbbbbbbbbbbbbbbbbbbbbbbbg aaa aaa aaa faa caa eaa aae aac aaf aaa aaa aaa faa caa eaa aae aac aaf aaa aaa caf aaa eaaaa faa eaaaaae caa aaaaac eaa faaaaf aae caaaaa aac eaaaaae aaf aaaaac aaa faaaac aaa caaaaf aaa eecccffaaaaaaaaa faa eecccffaaaaaaaaaaaaaaaaaaaaaaaae caa eecccffaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaac eaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaffccee aaaaaaaaaaaaaaaaaaaaaffccee faaaffccee ``` <!-- end of image -->

I'm optimistic that I'll find some intersections in this image. I'm going to focus my attention on these specific areas. <!-- image --> ```palette Key,Color ,#fefefeff a,#78bbb5ff b,#d3cab8ff c,#51a8aeff d,#ecf4eeff e,#b2d7b2ff f,#a5d1a7ff g,#95c996ff ``` ```image bd bb bb dbd de bb cc bb ccc bb dccc bb ccac dbd aceac bb cc ac bb ccd ec dbd dca ecd bb cc dcd bb acd dcd bb cc dce bb cc ce dbd dca ce bb cc ca bb acd ca dbd dcc cc bb cc cc bb eca cc dbd cc cc bb acd cc bb dcc cc bb cc cc bb eca ac dbd cc ac bb acd ac bb dcc ec dbd cc ec bb dcce ecd dgggggbbggggggggggggggggggggggggggggccccgggggggggggggggggcggggggggggggggggggggf dfeeeeebbeeeeeeeeeeeeeeeeeeeeeeeeacccaeeeeeeeeeeeeeeeeeefcfeeeeeeeeeeeeeeeeeeeg dfeeeeebbeeeeeeeeeeeeeeeeeeeeeeacccaeeeeeeeeeeeeeeeeeeeeecaeeeeeeeeeeeeeeeeeeeg dfeeeeebbeeeeeeeeeeeeeeeeeeeeacccaeeeeeeeeeeeeeeeeeeeeeeecaeeeeeeeeeeeeeeeeeeeg dfeeeeeebbeeeeeeeeeeeeeeeeeacccaeeeeeeeeeeeebeeeeeeeeeeeecaeeeeeeeeeeeeeeeeeeeg dfeeeeeebbeeeeeeeeeeeeeeeacccaeeeeeeeeeeeeebbbeeeeeeeeeeecaeeeeeeeeeeeeeeeeeeeg dfeeeeeeebeeeeeeeeeeeeeacccfeeeeeeeeeeeeeeebbbbeeeeeeeeeecceeeeeeeeeeeeeeeeeeeg dfeeeeeeebbeeeeeeeeeeacccfeeeeeeeeeeeeeeeebbebbbeeeeeeeeecceeeeeeeeeeeeeeeeeeeg dfeeeeeeebbeeeeeeeeacccfeeeeeeeeeeeeeeeeeebbeebbeeeeeeeeecceeeeeeeeeeeeeeeeeeeg dfeeeeeeeebbeeeeeccccfeeeeeeeeeeeeeeeeeeebbeeeebbeeeeeeeecceeeeeeeeeeeeeeeeeeeg dfeeeeeeeebbeeeccccfeeeeeeeeeeeeeeeeeeeeebbeeeeebbeeeeeeecceeeeeeeeeeeeeeeeeeeg dfeeeeeeeebbeccccfeeeeeeeeeeeeeeeeeeeeeebbeeeeeeebbeeeeeecceeeeeeeeeeeeeeeeeeeg dfeeeeeeeeebccceeeeeeeeeeeeeeeeeeeeeeeeebbeeeeeeebbbeeeeecceeeeeeeeeeeeeeeeeeeg dfeeeeeeeeeccaeeeeeeeeeeeeeeeeeeeeeeeeeebeeeeeeeeebbeeeeecceeeeeeeeeeeeeeeeeeeg dfeeeeeeeeccfeeeeeeeeeeeeeeeeeeeeeeeeeebbeeeeeeeeeebbeeeecceeeeeeeeeeeeeeeeeeeg dfeeeeeefccfbbeeeeeeeeeeeeeeeeeeeeeeeeebbeeeeeeeeeeebbeeeaceeeeeeeeeeeeeeeeeeeg dfeeeeefccfebbeeeeeeeeeeeeeeeeeeeeeeeebbeeeeeeeeeeeeebbeeaceeeeeeeeeeeeeeeeeeeg dfeeeeacceeeebbeeeeeeeeeeeeeeeeeeeeeeebbeeeeeeeeeeeeebbbeacceeeeeeeeeeeeeeeeeeg dfeeeacceeeeebbeeeeeeeeeeeeeeeeeeeeeebbeeeeeeeeeeeeeeebbbeccceeeeeeeeeeeeeeeeeg dfeeacceeeeeebbeeeeeeeeeeeeeeeeeeeeeebbeeeeeeeeeeeeeeeebbeeccceeeeeeeeeeeeeeeeg dfeccceeeeeeeebbeeeeeeeeeeeeeeeeeeeebbeeeeeeeeeeeeeeeeeebbeeccaeeeeeeeeeeeeeeeg dfccceeeeeeeeebbeeeeeeeeeeeeeeeeeeeebbeeeeeeeeeeeeeeeeeeebbeeccaeeeeeeeeeeeeeeg dccaeeeeeeeeeeebeeeeeeeeeeeeeeeeeeebbeeeeeeeeeeeeeeeeeeeeebbeeccaeeeeeeeeeeeeeg ccaeeeeeeeeeeeebbeeeeeeeeeeeeeeeeeebbeeeeeeeeeeeeeeeeeeeeebbbeeccaeeeeeeeeeeeeg dccgeeeeeeeeeeeeebbeeeeeeeeeeeeeeeeebbeeeeeeeeeeeeeeeeeeeeeeebbeeeccaeeeeeeeeeeeg dccdfeeeeeeeeeeeeeebbeeeeeeeeeeeeeeeebbeeeeeeeeeeeeeeeeeeeeeeeebbeeeccaeeeeeeeeeeg eccddfeeeeeeeeeeeeeebbeeeeeeeeeeeeeeebbeeeeeeeeeeeeeeeeeeeeeeeeeebbeeeccaeeeeeeeeeg ecc dfeeeeeeeeeeeeeebbeeeeeeeeeeeeeeebbeeeeeeeeeeeeeeeeeeeeeeeeeeebbeeeccaeeeeeeeeg dcc dfeeeeeeeeeeeeeeebbeeeeeeeeeeeeeebeeeeeeeeeeeeeeeeeeeeeeeeeeeebbbeeeccaeeeeeeeg e dfeeeeeeeeeeeeeeebbeeeeeeeeeeeeebbeeeeeeeeeeeeeeeeeeeeeeeeeeeeebbeeeeccaeeeeeeg dfeeeeeeeeeeeeeeebbeeeeeeeeeeeeebbeeeeeeeeeeeeeeeeeeeeeeeeeeeeeebbeeeeccaeeeeeg dfeeeeeeeeeeeeeeeebbeeeeeeeeeeebbeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeebbeeeeccaeeeeg dfeeeeeeeeeeeeeeeebbeeeeeeeeeeebbeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeebbeeeeccaeeeg dfeeeeeeeeeeeeeeeeebeeeeeeeeeebbeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeebbbeeeeccaeeg dfeeeeeeeeeeeeeeeeebbeeeeeeeeebbeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeebbeeeeeceeeg dfeeeeeeeeeeeeeeeeebbeeeeeeeebbeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeebbeeeeeeeeg dfeeeeeeeeeeeeeeeeeebbeeeeeeebbeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeebbeeeeeeeg dfeeeeeeeeeeeeeeeeeebbeeeeeebbeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeebbeeeeeeg dfeeeeeeeeeeeeeeeeeebbeeeeeebbeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeebbbeeeeeg dfeeeeeeeeeeeeeeeeeeebbeeeebbeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeebbbeeeeg dfeeeeeeeeeeeeeeeeeeebbeeeebbeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeebbeeeeg dfeeeeeeeeeeeeeeeeeeeebeeeebeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeebbeeeg dfeeeeeeeeeeeeeeeeeeeebbeebbeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeebbeeg dfeeeeeeeeeeeeeeeeeeeebbeebbeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeg dfeeeeeeeeeeeeeeeeeeeeebbbbeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeg dfeeeeeeeeeeeeeeeeeeeeebbbbeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeg dffffffffffffffffffffffbbbffffffffffffffffffffffffffffffffffffffffffffffffffffg dddddddddddddddddddddddbbddddddddddddddddddddddddddddddddddddddddddddddddddddd ``` <!-- end of image --> My goal is to determine if there's an intersection inside area A. <!-- image --> ```palette Key,Color ,#fefefeff a,#a0cfd2ff b,#d6c9baff c,#51a8aeff d,#f0f0edff e,#cae4e5ff f,#7ebdc1ff g,#e5ddd3ff ``` ```image bb efccccf ecce bbg efccccad dcce gbb ecccccd dcce dbbg cccccad cca gbbd cccccad cca dbbg accccca d cca bbb accccca bbb fcf bbb daccccc bbbd fcf gbb accccfe gbbbbd fcf bbg dccccce dbbdgbb acc gbbd efccccfe bbb bbg acc bbb fccccfe bb dbbbd acc dbbd efccccf dbb dbbb eccd bbg fccccfd gbb bbb eccd bbb ecccccd gbbd bbbg ecce bbb ecccccad dbbg dbbbd dcce dbbeccccad bbb bbb dcce bbcccca bbb gbbg cca gfccf bbb bbbg cca acccf bbb dbbd cca cccfb dbbg bbb fcf dfcccbb bbb gbbb fcf cccce bbd bb bbb fcf ecccd bbb dbb bbbd acf cccf dbbg dbbg gbbb accd accf gbb gbbd gbb ccf accc dbbd bbg bbg cccf ccce bbb bbb dbbbd dccc dfccc bbb bbb gbbb cccf ecccd gbbd dbbd bbbg dccc ecccd dbbg bbb dbbbd dccf ecccf bbb dbbg dbbb cccf accc bbg bbg bbg dccc ccca gbb bb bbbg cccf ce bb gbb dbbb dccc c bb bbg bbbd eccf d bbg gbbd gbbb cccf gbbd gbbd bbb eccc bbg bbb dbbd cccf dbbd bbb gbbb ecccf bbg dbbg gbbg eccc bbb bbb bbb cccf bbb gbb dbbbd eccc gbbd bbg gbbb ecca gbb dbb bbg eccca dbbd gbb bbbd eccc bbg bbg dbbbd ccca dbb bbb bbb eccc bb gbbd gbbg ecc bbd bbb bbbg cf bbb bbb dbbb gbbd dbbg bbb gbb dbbg bbbg dbbd gbb dbbb bbg dbbg dbbd bbb bbb gbbg bbb bbb bbbg dbbg gbbd bbbd gbb bbb gbbb dbbd dbbd gbbg gbb bbg bb dbb bb bg bbd gbb bbgdbbg bbbgbbd bbbbd ``` <!-- end of image --> Incredible, there's actually 1 intersection in area A! Answer: A: 1; 1 = 1 There's one and only one intersection present in the image.

<!-- image --> ```palette Key,Color ,#fefefeff a,#93c8ccff b,#d6c9b9ff c,#51a8aeff d,#eceeebff e,#bddee0ff f,#74babeff g,#e3dbd0ff ``` ```image bd bb bb dbg ee bb cc gb ccc bg dccc bb ccfc gbd acefc bb cc ac bb cc ac dbd ecf ec bb cc ecd gb fce dce bg cc dce bb cc ce gb ecf ca bb cc ca bb fce cf dbd cc cf bb cc cc bb eca cc bg cc cc bb fcd cc gb dcc cc bg cc cc bb eca fc dbd cc fc bb fcd ac bb dcc ac dbg cc ec bb dcca ecd gb eccca ecd bg eccca dce bb eccca ce gbd eccca ca bb accce b ca bb accce bbb cf dbd accce bbbb cf bb accce bb gbg cc gb fcccd bb bbd cc bg fcccd gb bb cc bb fcccd bb bb cc gb fcccd gbd dbb cc bccc bb gbg cc cca dbd bbd cc ccad bb bb fc dccebb dbg bb fc dccd bb bb dbb ac ecc bg dbg gbb ecf acc bb bb bbg ccf fcc gb bg bbd ccf fcc bg bb bb ccf ccf bb bb bb ccf cca dbd gb dbb ccf cce bb bb gbg ccf dcce bb gbd bbd ccf dccd dbd bb bb ccf ecc bb gbd bb cca acc gb bb dbb cca ecc bg dbd gbg cca a bb bb bbd cca gbd dbg bb cca bb bb bb cca bb bg dbb cca dbd bb gbg cca bb bb bbd c bb bb bb bg bb bb bb gb dbb gb bb gbb bb gbd bbg bb bb bbd dbd dbd bb bb bb bg bb dbg dbgbb bbbg gbb bb ``` <!-- end of image -->

I'm on the case! Let's uncover any intersections hidden in this image. The image has some tight areas where segments are too close. I should investigate those closely. <!-- image --> ```palette Key,Color ,#fefefeff a,#7b2c39ff b,#5cb2eeff c,#a6b49aff d,#9fd2f1ff e,#99676dff f,#b0d6b1ff g,#eaf1f0ff ``` ```image g gae aae aaa caag bb gaac bbb aaa bbbd eaa bbbbg faag bbdbb aae bb bbb aaa bb bbb eaa bb gbbd gaaf bb dbbg aae bb bbb aaa bb bbb eaa bb bbb gaac bb gbbd aaa bb dbbg aaa bb bbb caag bb bbb aae bb bbd aaa bb gbbg eaa bb dbb faag bb bbb aae bb bbb aaa gbb gbbd eaa gbb dbbg gaaf gbb bbb aae gbb bbb aaa gbb bbb caag gbb gbbd gaac gbb dbbg aaa gbb bbb eaa gbb bbb faag bbd aae gbbg aaa dbb eaa bbb gaaf bbb aae gbbd aaa dbbg caag bbbggggggggggggggggggaac gbbbffffffffffffffffaaafg gfbbbffffffffffffffaaaffg gffbbdffffffffffffcaacffg gffbbbffffffffffffaaefffg gfffbbbffffffffffaaaffffg gffffbbbffffffffeaafffffg gfffffbbbffffffcaacfffffg gffffffbbffffffaaeffffffg dbd gffffffbbbffffaaafffffffg bbbb gfffffffbbbffeaaffffffffg dbbbd gffffffffbbbcaacffffffffg bbbb gfffffffffbbeaafffffffffg dbbbd gfffffffffdbbaffffffffffg gbbbb gfffffffffebbbffffffffffg bbbbg gfffffffffaabbbfffffffffg gbbbb gffffffffaaafbbbffffffffg bbbbg gfffffffaaafffbbdfffffffg dbbbd gffffffcaacfffbbbfffffffg bbbbg gffffffaaefffffbbbffffffg dbbbd gfffffaaafffffffbbbfffffg bbbb gffffeaafffffffffbbbffffg dbbbd gfffcaacffffffffffbbffffg gbbbb gfffaaafffffffffffbbbfffg bbbbg gffaaafffffffffffffbbbffggbbbb gfeaafffffffffffffffbbbfbbbbg gcaaeffffffffffffffffbbbbbd aaaccccccccccccccccccbbb g eaa dd gceaaaaa faag gceaaaaaaaaaaa aae gceaaaaaaaaaaaecg aa aaa caaaaaaaaaaaef aa eaa faaaaaef aa gaaf f aagaae aaaaa aaaa aaac aaa e ``` <!-- end of image --> I'm analyzing this close-up of area A with precision. <!-- image --> ```palette Key,Color ,#fefefeff a,#7b2c39ff b,#5cb2eeff c,#b98f96ff d,#98cef4ff e,#945c68ff f,#d7bfc3ff g,#dde8f2ff ``` ```image gbbbbbd eaaaae gbbbbbg caaaaag dbbbbbg faaaaaf dbbbbb eaaaac bbbbbd eaaaae gbbbbbd faaaaag gbbbbbg gaaaaaf dbbbbb eaaaac dbbbbd caaaae bbbbbd faaaaag gbbbbbg gaaaaac dbbbbbg eaaaae dbbbbb caaaaa bbbbbd faaaaaf gbbbbbd aaaaac gbbbbbg eaaaae dbbbbbg caaaaag dbbbbb gaaaaaf bbbbbd eaaaac gbbbbbd caaaae gbbbbbg faaaaag dbbbbb gaaaaaf dbbbbdeaaaae bbbbbeaaae gbbbbbeaaf dbbbbbac bbbbbb cabbbbbd faaabbbbbd eaaaebbbbbg caaaaedbbbbbg faaaaag dbbbbb gaaaaaf bbbbbd eaaaac gbbbbbd caaaae gbbbbbg faaaaag dbbbbb gaaaaac dbbbbd eaaaae bbbbbd caaaaag gbbbbbg faaaaaf dbbbbbg aaaaac dbbbbb eaaaae bbbbbd faaaaag gbbbbbd gaaaaaf gbbbbbg eaaaac dbbbbbg caaaae dbbbbb faaaaag bbbbbd gaaaaaf gbbbbbd eaaaae gbbbbbg caaaae dbbbbb faaaaaf dbbbbdd gaaaaac bbbbbb ``` <!-- end of image --> The lines cross each other within area A, forming 1 intersection. Answer: A: 1; 1 = 1 It was tricky, but I finally found one single intersection in the image.

<!-- image --> ```palette Key,Color ,#fefefeff a,#7b2c39ff b,#5cb2efff c,#bf989eff d,#9fd2f5ff e,#9c636eff f,#d8c1c4ff g,#e2ebf4ff ``` ```image g gae aae aaa caag bb gaac bbb aaa bbbd eaa bbbbg faag bbdbb aae bb bbb aaa bb bbb eaa bb gbbd faaf bb dbbg aae bb bbb aaa bb bbb caa bb bbb gaac bb gbbd aaa bb dbbg aaa bb bbb caag bb bbb aac bb bbd aaa bb gbbg eaa bb dbb faaf bb bbb aae bb bbb aaa gbb gbbd eaa gbb dbbg gaaf gbb bbb aae gbb bbb aaa gbb bbb caag gbb gbbd gaac gbb dbbg aaa gbb bbb eaa gbb bbb faag bbd aae gbbg aaa dbb eaa bbb faaf bbb aae gbbd aaa dbbg caa bbb gaac bbb aaa bbb aaa gbbd faag dbbg aae bbb aaa bbb eaa bbd faaf gbbg aae gbd dbb aaa bbbb bbb eaa dbbbd bbbgaaf bbbb gbbeaa dbbbd dbba gbbbb cbbb bbbbg aabbb gbbbb aaa bbb bbbbg eaa gbbd gbbbd faaf dbbg bbbb aae bbb dbbbd aaa bbb bbbb eaa bbd dbbbd gaaf gbbg gbbbb aae dbb bbbbg aaa bbb gbbbb caag bbb bbbbg gaac gbbbbbd aaa dbbb g eaa dd gceaaaaa faag gceaaaaaaaaaaa aae gceaaaaaaaaaaaef aa aaa caaaaaaaaaaaef aa eaa faaaaaef aa faaf f aa aae aaaaa aaaa aaac aaa e ``` <!-- end of image -->

I'm ready to tackle this image and find those intersections! I'm going to focus my attention on these specific areas. <!-- image --> ```palette Key,Color ,#fefefeff a,#63a798ff b,#ae1d21ff c,#b1d7b2ff d,#bd5958ff e,#e7bdbeff f,#95c39bff g,#e5ede9ff ``` ```image g cf ag ga cf ag ga ff g ag eb ga bg ff dd ag eb ga bg ff dd ag eb ga bg fc dd ag eb ga be fc dd ag eb gggggggggggggggggggggg ga be fccccccccccccccccccccccf ac dd fccccccccccccccccccccccf ag eb fccccccccccccccccccccccfca bfccccccccccccccccccccccac ddccccccccccccccccccccaf ffbcccccccccccccccccfacf fccbfccccccccccccccafccf fcccddccccccccccccaccccf fccccfbcccccccccfacccccf fccccccbfccccccafccccccf fcccccccddccccaccccccccf fccccccccfbcfacccccccccf fccccccccccafccccccccccf fcccccccccacddcccccccccf fcccccccfacccfbccccccccf fccccccafccccccbfccccccf fcccccacccccccccddcccccf fcccfacccccccccccfbccccf fccafccccccccccccccbfccf fcacccccccccccccccccddcf aacccccccccccccccccccfbf afccccccccccccccccccccccbe ga fccccccccccccccccccccccfdd ff fccccccccccccccccccccccf gb ag fccccccccccccccccccccccf be ga cffffffffffffffffffffffc dd ff gb ag be ga dd fc gdbbe ag edbde gc edbde a edbde a ebbdg gg ebbd a a cg a f f a gc a a gg a a cg a f c a c f a gc a ``` <!-- end of image --> I'm now examining the contents of area A in detail. <!-- image --> ```palette Key,Color ,#fefefeff a,#67a99bff b,#af1f23ff c,#9fc8bfff d,#bd4a4dff e,#e1b2b3ff f,#d07d7fff g,#e1e4e2ff ``` ```image bg g bbf ca dbd cac ebbe gaac gdbf caag dbdg cac ebbe gaac gdbf caag fbdg cac ebbe gaac gdbf caag fbdg cac ebbe gaag gdbf caag fbdg cac ebbe gaag gdbf caag fbdaac eaac caadbf gaac fbdg gaag ebbe caag gdbf gaac fbdg gaag ebbe caag gdbf gaac fbdg gaag ebbe caag gdbf gaac fbdg gaag ebbe cac gdbf gaac fbdg gaag ebbe cac gdbf aac fb ag e ``` <!-- end of image --> Success! This area contains 1 intersection point! Answer: A: 1; 1 = 1 I've found a single intersection point in the image.

<!-- image --> ```palette Key,Color ,#fefefeff a,#63a799ff b,#ae1d21ff c,#b9d7d1ff d,#c55d60ff e,#e8bfc0ff f,#90bfb5ff g,#e4e8e6ff ``` ```image g ff ag ga ff ag ga ff g ag eb ga bg ff dd ag eb ga bg ff dd ag eb ga bg ff dd ag eb ca be ff dd ag eb ca be ac dd ag eb ca be ac dd a eb ca be ac dd a eb ca be ac dd ga gb ca af ga dd ff gb ac be ga dd ff gb ag be ga dd ff gb ag be ga dd ff gb ag be ga dd ff gb ag be ga dd ff gdbbe ag edbde gc edbde a edbde a ebbdg cg ebbd a a cg a f f a gc f a gc a a cg a f f a f f a gc a ``` <!-- end of image -->

I'm analyzing this image to identify any points where lines intersect. I've spotted 1 narrow regions that might be worth examining further. Let's call them area A. <!-- image --> ```palette Key,Color ,#fefefeff a,#163ad8ff b,#1db01aff c,#adb9f1ff d,#4eba53ff e,#b1d7b1ff f,#94c995ff g,#6488c7ff ``` ```image fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffe ageeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeef aaaaeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeef gaaaaageeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeef caaaaaaeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeef aaaaaageeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeef eeaaaaaaeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeef eeegaaaaaaeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeef eeeeeaaaaaageeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeef eeeeeegaaaaaaeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeef eeeeeeeeaaaaaageeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeef eeeeeeeeegaaaaaaeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeef eeeeeeeeeeeaaaaaageeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeef bbdfeeeeeeeeeeeaaaaaaeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeef bbbbbbdfeeeeeeeegaaaaaaeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeef bbbbbbbbbbbfeeeeeeaaaaaageeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeef edbbbbbbbbbbbbbfeeegaaaaaaeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeef fbd eefdbbbbbbbbbbbbbdeaaaaaageeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeef bbbb eeeeeefdbbbbbbbbbbbbdaaaaaaeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeef bbbb eeeeeeeeeefdbbbbbbbbbbaaaaaageeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeef fbbbd eeeeeeeeeeeeeefdbbbbbbbbaaaaaafeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeef bbbb eeeeeeeeeeeeeeeeeefdbbbbbaaaaaaabdfeeeeeeeeeeeeeeeeeeeeeeeeeeeef bbbb eeeeeeeeeeeeeeeeeeeeeeedbbbaaaaaabbbbdfeeeeeeeeeeeeeeeeeeeeeeeef fbbbd eeeeeeeeeeeeeeeeeeeeeeeeeeeddaaaaaabbbbbbdfeeeeeeeeeeeeeeeeeeeef bbbb eeeeeeeeeeeeeeeeeeeeeeeeeeeeeeaaaaaadbbbbbbbbdfeeeeeeeeeeeeeeeef bbbb eeeeeeeeeeeeeeeeeeeeeeeeeeeeeeegaaaaaabbbbbbbbbbbdfeeeeeeeeeeeef fbbbd eeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeaaaaaagbbbbbbbbbbbbbbdfeeeeeeef bbbb eeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeefaaaaaaeefbbbbbbbbbbbbbbbdfeef bbbb eeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeegaaaaaaeeeefdbbbbbbbbbbbbbbbde fbbbd eeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeaaaaaafeeeeeefdbbbbbbbbbbbbbbbbbbbb eeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeegaaaaaaeeeeeeeeeefdbbbbbbbbbbbbbb eeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeaaaaaageeeeeeeeeeeeefdbbbbbbbbd eeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeegaaaaaaeeeeeeeeeeeeeef fbbb eeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeaaaaaageeeeeeeeeeeef eeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeefaaaaaaeeeeeeeeeeef eeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeegaaaaaaeeeeeeeeef eeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeaaaaaafeeeeeeef eeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeegaaaaaaeeeeeef eeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeaaaaaageeeef eeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeegaaaaafeeef eeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeaaaaaeeef eeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeegaaafeef eeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeaaaaeef eeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeegaaafef ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffaaaafe caaac aaaa caaac aaaa caaac aaaa caaac aaaa caaac aaaa caaac aaaa caaac aaaa caaac aaaa caaac aaaa caaac aaaa caaac aaaa caaac aaaa caaac aaaa caaac aaaa caaac aaaa caaac aaaa caaac aaaa caaag aaaa aaag aaac c ``` <!-- end of image --> I'm analyzing this close-up of area A with precision. <!-- image --> ```palette Key,Color ,#fefefeff a,#173ad8ff b,#1db01aff c,#90a1ecff d,#4cb857ff e,#cfe0e5ff f,#94d992ff g,#526de0ff ``` ```image c aac aaaac aaaaage aaaaaaac aaaaaaaage aaaaaaaaaac caaaaaaaaaae egaaaaaaaaag gaaaaaaaaaage caaaaaaaaaaac gaaaaaaaaaae eaaaaaaaaaac caaaaaaaaaae gaaaaaaaaaag caaaaaaaaaaac caaaaaaaaaac gaaaaaaaaage aaaaaaaaaaac caaaaaaaaaaa egaaaaaaaaag e caaaaaaaaaac bbdf egaaaaaaaaage bbbbbbbbbdf gaaaaaaaaaag bbbbbbbbbbbbdff eaaaaaaaaaac bbbbbbbbbbbbbbbbdfe caaaaaaaaaae bbbbbbbbbbbbbbbbbbbddfe eaaaaaaaaaag dbbbbbbbbbbbbbbbbbbbbbbbde caaaaaaaaaaac ffbbbbbbbbbbbbbbbbbbbbbbbdfe egaaaaaaaaaag efdbbbbbbbbbbbbbbbbbbbbbbbfe caaaaaaaaaac efdbbbbbbbbbbbbbbbbbbbbbbdaaaaaaaaaac efbbbbbbbbbbbbbbbbbbbbaaaaaaaaaaaae efdbbbbbbbbbbbbbbbbbbaaaaaaaaaaag efbbbbbbbbbbbbbbbbdaaaaaaaaaac efdbbbbbbbbbbbbbbaaaaaaaaaage eddbbbbbbbbbbbdaaaaaaaaaadffe effdbbbbbbbbaaaaaaaaaaaabbdfe ffdbbbbaaaaaaaaaaabbbbbbbdfe fdbbbaaaaaaaaaaabbbbbbbbbdfe efddaaaaaaaaaadbbbbbbbbbbdfe gaaaaaaaaaaabbbbbbbbbbbbbdfe caaaaaaaaaaadbbbbbbbbbbbbbbbfe egaaaaaaaaaabbbbbbbbbbbbbbbbbbdfe caaaaaaaaaadbbbbbbbbbbbbbbbbbbbbff gaaaaaaaaaagddbbbbbbbbbbbbbbbbbbbbbbddfe caaaaaaaaaaacffdbbbbbbbbbbbbbbbbbbbbbbbbdde egaaaaaaaaaae ffdbbbbbbbbbbbbbbbbbbbbbbbbddfe caaaaaaaaaac fdbbbbbbbbbbbbbbbbbbbbbbbbbbdfe egaaaaaaaaage efdbbbbbbbbbbbbbbbbbbbbbbbbb aaaaaaaaaaac fdbbbbbbbbbbbbbbbbbbbbbb gaaaaaaaaaage effdbbbbbbbbbbbbbbbbb caaaaaaaaaac efdbbbbbbbbb egaaaaaaaaage effdbbbb aaaaaaaaaaac ffd egaaaaaaaaaage caaaaaaaaaaac gaaaaaaaaaae eaaaaaaaaaac gaaaaaaaaaag caaaaaaaaaaac egaaaaaaaaaae caaaaaaaaaac gaaaaaaaaage aaaaaaaaaaac caaaaaaaaaaae caaaaaaaaaac egaaaaaaaaac aaaaaaaaaae gaaaaaaaag eaaaaaaaae caaaaaag caaaaaae caaaaaae aaaaaag aaaaaaa aaaaaaa ``` <!-- end of image --> The evidence is clear: there's 1 intersection in area A. Answer: A: 1; 1 = 1 There's one and only one intersection present in the image.

<!-- image --> ```palette Key,Color ,#fefefeff a,#1639d8ff b,#1db01aff c,#97a6edff d,#6acb67ff e,#c4eac3ff f,#c7cff5ff g,#556fe1ff ``` ```image faf aaaa gaaaaac faaaaaa gaaaaag faaaaaaf gaaaaag aaaaaaf caaaaaa aaaaaac faaaaaa gaaaaag bbde faaaaaaf bbbbbbde gaaaaag bbbbbbbbbbbe aaaaaaf ebbbbbbbbbbbbbbe caaaaaa dbd edbbbbbbbbbbbbbe aaaaaac bbbb edbbbbbbbbbbbbbaaaaaa bbbb edbbbbbbbbbbaaaaaag dbbbd edbbbbbbbbaaaaaaf bbbb dbbbbbaaaaaaabde bbbb dbbbaaaaaabbbbde dbbbd daaaaaaabbbbbbde bbbb aaaaaabbbbbbbbbde bbbb faaaaaabbbbbbbbbbbde dbbbd gaaaaagbbbbbbbbbbbbbbde bbbb faaaaaa edbbbbbbbbbbbbbbde bbbb gaaaaag edbbbbbbbbbbbbbbbde dbbbd aaaaaaf edbbbbbbbbbbbbbbbbbbbb caaaaaa edbbbbbbbbbbbbbb aaaaaac edbbbbbbbbd caaaaaa edbbb aaaaaag faaaaaa gaaaaag aaaaaaf caaaaaa aaaaaac caaaaaf aaaaa caaaf aaaa caaaf aaaa caaaf aaaa caaaf aaaa caaaf aaaa caaaf aaaa caaaf aaaa caaaf aaaa caaaf aaaa caaac aaaa faaac aaaa faaac aaaa faaac aaaa faaac aaaa faaac aaaa faaac aaaa faaac aaaa faaac aaaa faaac aaaa faaac aaaa faaac aaac fc ``` <!-- end of image -->

I'm examining this image closely. My goal: find any and all intersections. These zones indicate regions where lines appear to be in close proximity. <!-- image --> ```palette Key,Color ,#fefefeff a,#6886daff b,#78432eff c,#0232caff d,#9ac397ff e,#b1d7b1ff f,#997a66ff g,#eaeeefff ``` ```image bb dbbbg bbbb fbbbg bbbb fbbbg bbbb fbbbg bbbb g fbbbg gca bbbb gccca fbbb gcccca bbbb cccca fbbb cccca bbbb ccccc fbbb ccccc bbbb ccccc fbbb ddddddddddddddddddddddddde ccccc bbbf geeeeeeeeeeeeeeeeeeeeeeeeed ccccc fbbb geeeeeeeeeeeeeeeeeeeeeeeeed ccccc bbbf geeeeeeeeeeeeeeeeeeeeeeeeed ccccc fbbb geeeeeeeeeeeeeeeeeeeeeeeeed ccccc bbbf geeeeeeeeeeeeeeeeeeeeeeeeed acccc bbbb geeeeeeeeeeeeeeeeeeeeeeeeed acccc bbbf geeeeeeeeeeeeeeeeeeeeeeeeed accccg bbbb geeeeeeeeeeeeeeeeeeeeeeeeed accccg bbbf geeeeeeeeeeeeeeeeeeeeeeeeedeccccg bbbbg geeeeeeeeeeeeeeeeeeeeeeeeedccccg bbbbbe geeeeeeeeeeeeeeeeeeeeeeeedcccce bbbbbbbd geeeeeeeeeeeeeeeeeeeeeeeecccca fbbbbbbbf geeeeeeeeeeeeeeeeeeeeeeecccca ebbbbbbbbg geeeeeeeeeeeeeeeeeeeeeecccca gbbbbbbbbe geeeeeeeeeeeeeeeeeeeeeccccc gbbbbbbbbd geeeeeeeeeeeeeeeeeeeecccccd fbbbbbbbf geeeeeeeeeeeeeeeeeeeccccced dbbbbbbbbg geeeeeeeeeeeeeeeeeeccccceed ebbbbbbbbeeeeeeeeeeeeeeeeeeccccceeed gbbbbbbbbfeeeeeeeeeeeeeeccccceeeed fbbbbbbbfeeeeeeeeeeeccccceeeeed dbbbbbbbbeeeeeeeeccccceeeeeed ebbbbbbbbdeeeeccccceeeeeeed gedbbbbbbbbfeacccceeeeeeeed geeeefbbbbbbccccceeeeeeeeed geeeeeefbbbbccccdeeeeeeeeed geeeeeeeedbccccbbbdeeeeeeed geeeeeeeeaccccbbbbbbdeeeeed geeeeeeedccccabbbbbbbbfeeed geeeeeedccccaeeefbbbbbbbfed ac geeeeeeccccaeeeeeefbbbbbbbbg acccg geeeeeccccaeeeeeeeeedbbbbbbbbe cccc geeeeccccaeeeeeeeeeeeeebbbbbbbbd accc geeeccccceeeeeeeeeeeeeeeefbbbbbbbf ccca geeccccceeeeeeeeeeeeeeeeeeddbbbbbbbbg cccc geccccceeeeeeeeeeeeeeeeeeed gbbbbbbbbg gccce gccccceeeeeeeeeeeeeeeeeeeed gbbbbbbbbd cccc ccccceeeeeeeeeeeeeeeeeeeeed fbbbbbbbf acccg ccccceeeeeeeeeeeeeeeeeeeeeed dbbbbbbbb cccc ccccceeeeeeeeeeeeeeeeeeeeeeed ebbbbbbbb accc ccccceeeeeeeeeeeeeeeeeeeeeeeed gbbbbbg ccca acccceeeeeeeeeeeeeeeeeeeeeeeeed fbb cccc accccgeeeeeeeeeeeeeeeeeeeeeeeeed g gccca accccggeeeeeeeeeeeeeeeeeeeeeeeeed cccc accccg geeeeeeeeeeeeeeeeeeeeeeeeed ecccg eccccg geeeeeeeeeeeeeeeeeeeeeeeeed cccc gccccg geeeeeeeeeeeeeeeeeeeeeeeeed accc gcccce geeeeeeeeeeeeeeeeeeeeeeeeed ccca gcccca geeeeeeeeeeeeeeeeeeeeeeeeed cccc gcccca geeeeeeeeeeeeeeeeeeeeeeeeed ccca cccca geeeeeeeeeeeeeeeeeeeeeeeeed cccc cccca geeeeeeeeeeeeeeeeeeeeeeeeed gcccg ccccc gdeeeeeeeeeeeeeeeeeeeeeeeed cccc ccccc ggggggggggggggggggggggggg accc ccccc cccc ccccc accc ccccc ccca ccccc cccc ccccc gcccccccc ccccccc accccc ccccg accg ``` <!-- end of image --> I'm eager to see what's happening in this magnified view of area A. <!-- image --> ```palette Key,Color ,#fefefeff a,#4165d7ff b,#77422eff c,#0130c9ff d,#c4ada3ff e,#8fa4e7ff f,#9b7363ff g,#d9daeaff ``` ```image g gc gcc gacc accc acccc accccc acccccc accccccc acccccccc ecccccccca eccccccccag ecccccccccg ecccccccccg ecccccccccg ecccccccccg gcccccccccg fd gcccccccccg bbbd gccccccccce bbbbbdg gccccccccce bbbbbbbfg gccccccccce bbbbbbbbbfd gccccccccce bbbbbbbbbbbfd acccccccce bbbbbbbbbbbbbbd acccccccce fbbbbbbbbbbbbbbbfg acccccccca gfbbbbbbbbbbbbbbbfg acccccccca gdbbbbbbbbbbbbbbbfd acccccccca dbbbbbbbbbbbbbbbbdacccccccca dfbbbbbbbbbbbbbccccccccca gfbbbbbbbbbbccccccccca gdbbbbbbbbcccccccccg dbbbbbcccccccccbbd dfbcccccccccbbbbbdg ecccccccccbbbbbbbbfg gcccccccccbbbbbbbbbbbfd gcccccccccbbbbbbbbbbbbbbbd gcccccccccedfbbbbbbbbbbbbbbbdg gccccccccce gfbbbbbbbbbbbbbbbfg gccccccccce gfbbbbbbbbbbbbbbbfd gccccccccce dbbbbbbbbbbbbbbbf gacccccccce dfbbbbbbbbbbbbb acccccccce gfbbbbbbbbbbb acccccccca gfbbbbbbbbb acccccccca gdbbbbbbb acccccccca dfbbbb acccccccca dfbb acccccccca gf ecccccccca ecccccccca ecccccccccg ecccccccccg ecccccccccg ecccccccccg cccccccccg ccccccccg ccccccce cccccce ccccce cccce ccce cce ca a ``` <!-- end of image --> The lines cross each other within area A, forming 1 intersection. Answer: A: 1; 1 = 1 It was tricky, but I finally found one single intersection in the image.

<!-- image --> ```palette Key,Color ,#fefefeff a,#3e62d6ff b,#78422dff c,#0130caff d,#bfa69bff e,#8aa0e6ff f,#98705fff g,#d9d9e7ff ``` ```image bb dbbbg bbbb dbbbg bbbb dbbb bbbb fbbb bbbb g fbbb gce bbbb gccce fbbb cccce bbbb cccca fbbb cccca bbbb cccca fbbb cccca bbbf ccccc fbbb ccccc bbbf ccccc fbbb ccccc bbbf acccc fbbb acccc bbbf acccc fbbb acccc bbbf ecccc bbbb eccccg bbbf eccccg bbbbg gccccg bbbbbd gcccce bbbbbbbd gcccce fbbbbbbbf cccce dbbbbbbbb cccca gbbbbbbbbg cccca fbbbbbbbd cccca fbbbbbbbf ccccc dbbbbbbbb ccccc gbbbbbbbbg ccccc bbbbbbbbd ccccc fbbbbbbbf ccccc dbbbbbbbf acccc gbbbbbbbbg acccc gbbbbbbbbd acccc fbbbbbbccccc dbbbbccccg dbccccbbbg gccccbbbbbbd gccccefbbbbbbbd gcccce dbbbbbbbf ac gcccce dbbbbbbbbg eccc cccce gbbbbbbbbg ccca cccca fbbbbbbbd accc cccca fbbbbbbbf ccca cccca dbbbbbbbb cccc ccccc gbbbbbbbbg gccce ccccc bbbbbbbbd cccc ccccc fbbbbbbbf ecccg ccccc dbbbbbbbf cccc ccccc gbbbbbbbb accc acccc bbbbbg ccca acccc fbb cccc acccc g ccce ecccc cccc eccccg ecccg eccccg cccc gccccg eccc gcccce ccca gcccce accc cccce ccce cccca cccc cccca gcccg cccca cccc cccca eccc ccccc ccca ccccc accc ccccc ccce ccccc cccc acccc gcccccccc ccccccc eccccc cccc eccg ``` <!-- end of image -->

I'm ready to tackle this image and find those intersections! I'd describe these as 'hotspots' for potential intersections. <!-- image --> ```palette Key,Color ,#fefefeff a,#40c766ff b,#81d993ff c,#b1d8b1ff d,#61cd7cff e,#6bec88ff f,#95ca96ff g,#9cd9a4ff ``` ```image a dab aab daab aaab badab aa ad gad ad aa ad cad ad aa ad caa aa aa aa caa aa aa aa aa aa aac aa aa aa aac aa aa aa dag aa aa aa dag aa aa aa bab aa aa aa gad aa aa aa gffffffffffffffffffdaafffffffffffaaffffffffffffffffffffffffffffffffffffffffffffffffg fccccccccccccccccccaaccccccccccccaaccccccccccccccccccccccccccccccccccccccccccccccccf fcccccccccccccccccfaaccccccccccccaaccccccccccccccccccccccccccccccccccccccccccccccccf fcccccccccccccccccaagccccccccccccaaccccccccccccccccccccccccccccccccccccccccccccccccf fccccccccccccccccgaacccccccccccccaaccccccccccccccccccccccccccccccccccccccccccccccccf fccccccccccccccccaagcccccccccccccaaccccccccccccccccccccccccccccccccccccccccccccccccf fcccccccccccccccgaaccccccccccccccaaccccccccccccccccccccccccccccccccccccccccccccccccf fcccccccccccccccaafccccccccccccccaaccccccccccccccccccccccccccccccccccccccccccccccccf fcccccccccccccccaacccccccccccccccaaccccccccccccccccccccccccccccccccccccccccccccccccf fccccccccccccccaabcccccccccccccccaaccccccccccccccccccccccccccccccccccccccccccccccccf fccccccccccccccaaccccccccccccccccaaccccccccccccccccccccccccccccccccccccccccccccccccf fcccccccccccccdabccccccccccccccccaaccccccccccccccccccccccccccccccccccccccccccccccccf fcccccccccccccaacccccccccccccccccaaccccccccccccccccccccccccccccccccccccccccccccccccf fccccccccccccdadcccccccccccccccccaaccccccccccccccccccccccccccccccccccccccccccccccccf fccccccccccccaaccccccccccccccccccaaccccccccccccccccccccccccccccccccccccccccccccccccf fcccccccccccdadccccccccccccccccccaaccccccccccccccccccccccccccccccccccccccccccccccccf fcccccccccccaacccccccccccccccccccaaccccccccccccccccccccccccccccccccccccccccccccccccf fccccccccccbaacccccccccccccccccccaaccccccccccccccccccccccccccccccccccccccccccccccccf fccccccccccaaccccccccccccccccccccaaccccccccccccccccccccccccccccccccccccccccccccccccf fcccccccccbaaccccccccccccccccccccaaccccccccccccccccccccccccccccccccccccccccccccccccf fcccccccccaacccccccccccccccccccccaaccccccccccccccccccccccccccccccccccccccccccccccccf fccccccccfaacccccccccccccccccccccaaccccccccccccccccccccccccccccccccccccccccccccccccf fccccccccaagcccccccccccccccccccccaaccccccccccccccccccccccccccccccccccccccccccccccccf fcccccccgaaccccccccccccccccccccccdagcccccccccccccccccccccccccccccccccccccccccccccccf fcccccccaagccccccccccccccccccccccdagcccccccccccccccccccccccccccccccccccccccccccccccf fccccccgaacccccccccccccccccccccccdagcccccccccccccccccccccccccccccccccccccccccccccccf fccccccaabcccccccccccccccccccccccdagcccccccccccccccccccccccccccccccccccccccccccccccf fccccccaaccccccccccccccccccccccccdagcccccccccccccccccccccccccccccccccccccccccccccccf fcccccaabccccccccccccccccccccccccdafcccccccccccccccccccccccccccccccccccccccgbeeebccf fcccccaacccccccccccccccccccccccccdafccccccccccccccccccccccccccccccccccgbeeeeeeeebccf fccccdadcccccccccccccccccccccccccdafcccccccccccccccccccccccccccccgbeeeeeeeebgccccccf fccccaaccccccccccccccccccccccccccdafcccccccccccccccccccccccccgeeeeeeeeegcccccccccccf fcccdadccccccccccccccccccccccccccdabccccccccccccccccccccgeeeeeeeeegccccccccccccccccf fcccaacccccccccccccccccccccccccccbabcccccccccccccccgbeeeeeeeebcccccccccccccccccccccf fccdadcccccccccccccccccccccccccccbabccccccccccgbeeeeeeeebgcccccccccccccccccccccccccf fccaaccccccccccccccccccccccccccccbabcccccgbeeeeeeeebgccccccccccccccccccccccccccccccf fcbaaccccccccccccccccccccccccccccbabcbeeeeeeeebgcccccccccccccccccccccccccccccccccccf fcaacccccccccccccccccccccccccccgbdadeeeeeegccccccccccccccccccccccccccccccccccccccccf fbaacccccccccccccccccccccgbeeeeeedadebcccccccccccccccccccccccccccccccccccccccccccccf faaccccccccccccccccgbeeeeeeeeeebgbadcccccccccccccccccccccccccccccccccccccccccccccccf baacccccccccccgeeeeeeeeeebgccccccfadccccccccccccccccccccccccccccccccccccccccccgdfccf aagcccccgbeeeeeeeeeegccccccccccccfadccccccccccccccccccccccccccccccccccccccbaaaaadccf aagbeeeeeeeeeebgcccccccccccccccccfadcccccccccccccccccccccccccccccccccgdaaaaaaadbcccf aeeeeeeebgcccccccccccccccccccccccgadcccccccccccccccccccccccccccccbdaaaaaaadgcccccccf eebgcccccccccccccccccccccccccccccgadccccccccccccccccccccccccgdaaaaaaaabccccccccccccf fccccccccccccccccccccccccccccccccgadccccccccccccccccccccfdaaaaaaadgccccccccccccccccf fccccccccccccccccccccccccccccccccgadccccccccccccccccbaaaaaaaabcccccccccccccccccccccf fccccccccccccccccccccccccccccccccgadcccccccccccfdaaaaaaadfcccccccccccccccccccccccccf fccccccccccccccccccccccccccccccccgaacccccccbaaaaaaaabccccccccccccccccccccccccccccccf fcccccccccccccccccccccccccccccccccaaccgdaaaaaaadfccccccccccccccccccccccccccccccccccf fcccccccccccccccccccccccccccccccccaaaaaaaaadgccccccccccccccccccccccccccccccccccccccf fcccccccccccccccccccccccccccccccccaaaadbcccccccccccccccccccccccccccccccccccccccccccf fcccccccccccccccccccccccccccccccccbgcccccccccccccccccccccccccccccccccccccccccccccccf fccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccf fccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccf ``` <!-- end of image --> This close-up of area A is like examining a piece of evidence. <!-- image --> ```palette Key,Color ,#fefefeff a,#40c766ff b,#8ce4a2ff c,#c8f3d3ff d,#63d182ff e,#6bec88ff f,#e5f8eaff g,#abecbbff ``` ```image aaag baa aag gaa gaa gaa caaa gaa daab gaa aab gaa caaf gaa faaa gaa baad caa aad caa faac caa baa caa gaad caa aaag caa aag caa gaa faa caaa faa daab faa aab faa faaf faa faaa faa baad faa aad aa faac aa aaa aa gaad aa gaaa aa daag aa aaa aa caaa aa caaaf aaf eaab aaf aad aaf faac aaf faaa aaf baad aaf aaac aaf aag aac ff gaa aac fgbec gaaa aac fbeeeeeeeeb daag aac fcbeeeeeeeeeebg aab aac cgeeeeeeeeeeebgf caaf aac fcbeeeeeeeeeeebcf caaa aag fcbeeeeeeeeeebcf baab aag fgbeeeeeeeeeegc aad aag fgbeeeeeeeeeeegc faac aag cgeeeeeeeeeeebgf faaa aag cgeeeeeeeeeeegc baad aag fcbeeeeeeeeeeegc aad aag cgeeeeeeeeeeebcf aag aadeeeeeeeeeeegc daa fggeeeeeaadeeeeegc gaaa fcgeeeeeeeeeaadebgf aaaf cgeeeeeeeeeeeeebgcfaab aab cgbeeeeeeeeeeeebgc aab daa fcbeeeeeeeeeeeeegc aab fbdaaab aaa fgbeeeeeeeeeeeeegcf aab fgdaaaaaad aaccgeeeeeeeeeeeeebgf aab fbdaaaaaaaaadbf aaeeeeeeeeeeeebgf aab cgaaaaaaaaaaagc adeeeeeeeebcc aab fbdaaaaaaaaadbf eeegc aad fbdaaaaaaaaadgf c aad cgdaaaaaaaaadbf aad fgdaaaaaaaaadbf aad cgdaaaaaaaaaagc aad cgaaaaaaaaaaagc aad fbdaaaaaaaaadbf aad fbdaaaaaaaaadgf aad fgdaaaaaaaaadbf aaaaaaaaaaaadbf aaaaaaaaaagc baaagc cf ``` <!-- end of image --> Bingo! This close-up reveals 1 intersection in area A! Answer: A: 1; 1 = 1 There's one and only one intersection present in the image.

<!-- image --> ```palette Key,Color ,#fefefeff a,#40c766ff b,#82de9aff c,#beefcbff d,#60d17fff e,#6bed88ff f,#def6e4ff g,#9fe9b2ff ``` ```image af dab aab daab aaab badad aafad badfad aa fad gad ad aa ad caa aa aaf aa faa aa aaf aa faa aa aac aa aa aa aac aa aa aa dag aa aa aa dab aa aa aa bab aa aa aa gad aa aa aa gad aa aa aa caa aa aaf aa faa aa aaf aa faa aa aac aa aa aa dag aa aa aa dag aa aa aa bab aa aa aa bad aa aa aa gad aa aa aa caa aa aa aa caa da aaf da faa daf aaf daf faa daf aac daf aa baf dag bac fgeeeg aa bac fgeeeeeeeeg dag bac fgeeeeeeeegf aa bac ceeeeeeeebc bab gac cbeeeeeeebc aa gac fgeeeeeeeecf bad gag fgeeeeeeeegf aa gag fgeeeeeeeegf gad gag ceeeeeeeebc aa cgdadeeeeebc caa fgeeeeeedadbcf aaf fcbeeeeeeeeegfcab faa cbeeeeeeeeegc cab fbc aaf cgeeeeeeeeebc cab gdaaaad faafgeeeeeeeeebcf cab fbaaaaaaadc fadeeeeeegf fab cdaaaaaaabf eegc fab fgaaaaaaadc fad cdaaaaaaabf fad gaaaaaaaag fad cbaaaaaaabc fad gdaaaaaaag ad fbaaaaaaadc aaaaaaaaabf aaaadc cf ``` <!-- end of image -->

Let's examine this image for potential line intersections. I've noticed 2 areas of interest. These could be potential intersection zones. <!-- image --> ```palette Key,Color ,#fefefeff a,#a48484ff b,#7f35ccff c,#7e484dff d,#b1d6b0ff e,#9f76d0ff f,#98c598ff g,#dbc9e2ff ``` ```image gg ggaaccccccccccc cccccccccccccccccccc cccccccccccccccccccc cccccccaagg ccc ccc ccc ccc ccc cccg cccg accd acca acca dcca gccc gccc ccc ge ccc ebbb ccc bbbbbe ccc bbbbbbbe ccc gbbbbeebbbg ccc gbbbbg bbbbg ccc ebbbb bbbb ccc bbbbb bbbb cccg bbbbb bbbb cccg bbbbe gbbbb accd gbbbbg gbbbe acca gbbbbg ebbbe acca ebbbb bbbbg dcca bbbbb bbbb gccc bbbbb bbbb fddddddddfcccddddddddddf bbbbe bbbb fdddddddddcccdddddddddddgbbbbg bbbb fdddddddddcccddddddddddebbbbg gbbbb fdddddddddcccdddddddddbbbbb gbbbe fdddddddddcccddddddddbbbbb ebbbg fdddddddddcccdddddddbbbbe bbbbg fdddddddddcccddddddbbbbe bbbb fdddddddddcccddddebbbbfd bbbb fdddddddddcccdddebbbbddd bbbb fdddddddddcccfdbbbbbdddd bbbe fdddddddddcccfbbbbbddddd gbbb fdddddddddcccbbbbedddddd bbb fdddddddddacccbbeddddddd bbbg fdddddddddacccbddddddddd ebbe fddddddddebcccdddddddddd gbbb fdddddddbbbcccdddddddddd bbb fddddddbbbbcccdddddddddd bbb fdddddbbbbecccdddddddddd bbbg fdddfbbbbedcccdddddddddd ebbe fddebbbbdddcccdddddddddd gbbb fdbbbbbddddcccdddddddddd bbb fbbbbbdddddcccdddddddddd bbb bbbbbddddddcccdddddddddd bbbg bbbbedddddddcccdddddddddd ebbe gbbbbfddddddddcccdddddddddd gbbb ebbbbddddddddddcccfddddddddd bbb bbbbbfddddddddddcccfddddddddd bbb bbbbb fddddddddddcccaddddddddd bbbg bbbbe fddddddddddaccaddddddddf ebbe gbbbbe acca bbb gbbbbg dcca bbb ebb gcccca bbb b ccccccccg dfffffffbbbefffff acccccccccca fdddddddebbbddddd gcccccccccccd fddddddddbbbddddd accccccccccag fddddddddbbbddddd gaccccccccccd fddddddddbbbddddd dccccccccccag fddddddddbbbedddd gacccccccccca fddddddddebbbdddd dcccccccccccg fdddddddddbbbdddd acccccccccca fdddddddddbbbdddd gcccccccccccd fdddddddddbbbdddd accccccccccag fdddddddddebbeddd gaccccccccccadddddddddebbbddd dcccccccccccfddddddbbbddd gaccccccccccadddbbbddd dcccccccccccbbbddd fddaccccccccccfdd fdddddfcccccccddd fdddddddddacccddd fddddddddddddfddd fdddddddddddddddd ``` <!-- end of image --> Here's a close-up of the area A. <!-- image --> ```palette Key,Color ,#fefefeff a,#a0777cff b,#7f35cbff c,#7e474dff d,#cab4b6ff e,#c8a8e9ff f,#a069d8ff g,#e7dcecff ``` ```image gcccccc gcccccc gccccccg ccccccg ccccccg ccccccd acccccd f acccccd gfb acccccd gbbb acccccd ebbbb accccca ebbbbb dccccca fbbbbbb dccccca fbbbbbbb dccccca gfbbbbbbbb dccccca gbbbbbbbbbe dcccccc ebbbbbbbbbg gcccccc ebbbbbbbbbg gcccccc fbbbbbbbbfg gccccccg fbbbbbbbbf ccccccg gbbbbbbbbbe ccccccg gbbbbbbbbbe ccccccdebbbbbbbbbg acccccfbbbbbbbbfg acccccbbbbbbbbf acccccbbbbbbbf accccccbbbbbe accccccbbbbe accccccbbbg fbccccccbfg fbbccccccf gfbbbcccccc gbbbbbcccccc ebbbbbbcccccc ebbbbbbbcccccc fbbbbbbbbccccccg fbbbbbbbbfccccccg gfbbbbbbbbe ccccccg gbbbbbbbbbe ccccccd ebbbbbbbbbg acccccd ebbbbbbbbbg acccccd fbbbbbbbbf acccccd gfbbbbbbbbf acccccd gbbbbbbbbbe accccca gbbbbbbbbbe dccccca ebbbbbbbbbg dccccca bbbbbbbbfg dccccca bbbbbbbf dccccca bbbbbbf dcccccc bbbbbe gcccccc bbbbe gcccccc bbbg gccccccg bfg ccccccg f ccccccg ccccccd acccccd acccccd acccccd ``` <!-- end of image --> I observe 1 intersection inside area A. Alright, let's examine the next area. I'm focusing my attention on this specific region, area B. <!-- image --> ```palette Key,Color ,#fefefeff a,#a68087ff b,#7f34ccff c,#7e484dff d,#c9b2b4ff e,#c6a6e8ff f,#a470d9ff g,#e4d7e7ff ``` ```image bbbbbbe fbbbbbf ebbbbbb gbbbbbb bbbbbbg fbbbbbe fbbbbbf ebbbbbb gbbbbbb bbbbbbg fbbbbbe fbbbbbf ebbbbbb gbbbbbbg bbbbbbe fbbbbbe fbbbbbf ebbbbbb gbbbbbbg bbbbbbe fbbbbbf ebbbbbf dg ebbbbbb cccad gbbbbbbg ccccccadg bbbbbbe ccccccccccadg fbbbbbf ccccccccccccccag ebbbbbf cccccccccccccccccadg gbbbbbb cccccccccccccccccccccabbbbbbg gdacccccccccccccccccccccafe dacccccccccccccccccccccd gdacccccccccccccccccg dacccccccccccccc gdaccccccccca gaccccccd gdaccg g ``` <!-- end of image --> The evidence suggests that this is not an intersection point in area B. Answer: A: 1; B: 0; 1 + 0 = 1 The image features one single intersection point.

<!-- image --> ```palette Key,Color ,#fefefeff a,#a1797eff b,#7f34ccff c,#7e474dff d,#c0a5a8ff e,#be98e5ff f,#9b62d7ff g,#dfcfe3ff ``` ```image gg ggdaccccccccccc cccccccccccccccccccc cccccccccccccccccccc cccccccaddg ccc ccc ccc ccc ccc cccg cccg accd accd dcca dcca gccc gccc ccc ge ccc fbbb ccc bbbbbf ccc bbbbbbbe ccc gbbbbefbbbg ccc ebbbbg bbbbg ccc fbbbb bbbb ccc bbbbb bbbb cccg bbbbb bbbb cccg bbbbf gbbbb accd gbbbbe ebbbf accd ebbbbg fbbbe dcca fbbbb fbbbg dcca bbbbb bbbb gccc bbbbf bbbb gccc bbbbf bbbb ccc gbbbbe bbbb ccc ebbbbg gbbbb ccc fbbbb ebbbf ccc bbbbb fbbbe ccc bbbbf bbbbg ccc gbbbbe bbbb ccc gbbbbg bbbb ccc fbbbb bbbb cccg fbbbb bbbf cccgbbbbb gbbb accbbbbf bbb acccbbe bbbg acccbg fbbe fbccc gbbb bbbccc bbb bbbbccc bbb bbbbfccc bbbg gbbbbe ccc fbbf ebbbbg ccc gbbb fbbbb ccc bbb bbbbb ccc bbb bbbbf ccc bbbg bbbbe ccc ebbf gbbbbg ccc gbbb ebbbb cccg bbb fbbbb cccg bbb bbbbb accd bbbe bbbbf accd ebbf gbbbbe dcca bbb gbbbbg dcca bbb fbb gccccd bbb b ccccccccg fbbe dcccccccccca ebbf gcccccccccccd bbb dccccccccccag bbb gaccccccccccd bbb dccccccccccag fbbe gaccccccccccd ebbb dcccccccccccg bbb acccccccccca bbb gcccccccccccd bbbg dccccccccccag fbbe gaccccccccccd gbbb dccccccccccag bbb gaccccccccccd bbb dcccccccccccbbbg accccccccccg gccccccc dccc g ``` <!-- end of image -->

This image looks interesting. I wonder if there are any intersections hidden in there? My next step is to analyze the details within each area. <!-- image --> ```palette Key,Color ,#fefefeff a,#67855dff b,#412d4cff c,#98c398ff d,#b1d6b1ff e,#869484ff f,#eaeeeaff g,#605669ff ``` ```image fffffffffffffff cddddddddddddddc dddddddddddddddc dddbdddddddddddc dddbbddddddddddc ddddbbdddddddddc ddddebgddddddddc dddaegbcdddddddc dddaedbbdddddddc dddaeddbbddddddc dddaeddcbgdddddc dddaadddgbeddddc dddaaddddbbddddc dddaadddddbbdddc dddaaddddddbbddc dddaaddddddebgdc dddaadddddddgbcc cddaaddddddddbbc fffeafffffffffbb ca fbg ca ebc da bbf da bb da fbb fa dbe fa gbf faf bb af bb ad fbg ad ebc ad bbf ac bb ac fbb ae dbe ae gbf aa bb aa bb aa fbg aa ebc aa bbf ea bb ea fbb ca dbe dad gbf aa bb aa bb dad fbg aa ebc aa bbf dad bb aa fbb aa dbe dad gbf aa bb aa bb dad fbg aa ebc aa bbf caf bb cccccccccccccccccccccccd aa fbb fdddddddddddddddddddddddc ae dbe fdddddddddddddddddddddddc caf gbbf fdddddddddddddddddddddddc aa dbbgfdddddddddddddddddddddddc fae gbbeddddddddddddddddddddddc caf fbbbdddddddddddddddddddddc aa fabbadddddddddddddddddddc fae fddbbbcdddddddddddddddddc d caf fdddcbbgddddddddddddddddcfcaaaad aa fdddddgbbedddddddddddcaaaaaaed fae fdddddddbbbddddddeaaaaaaef eaf fddddddddebbgeaaaaaacdddc aa fdddddddeaaaaaaecdddddddc fae fddceaaaaaaccbbbddddddddc eaf fdaaaaaaecddddddabbeddddddc aa feaaaaaacdddddddddddddbbbcddddc fae daaaaaacf fddddddddddddddddcbbgdddc eaaaaaedf fcaaaaaad fddddddddddddddddddgbbedc fdcaaaaaaaaaaef fddddddddddddddddddddbbbc fdd fdddddddddddddddddddddebbe fdddddddddddddddddddddddbbbf fdddddddddddddddddddddddcfbbg fdddddddddddddddddddddddc ebbe fdddddddddddddddddddddddc bbe fdddddddddddddddddddddddc d cccccccccccccccccccccccd ``` <!-- end of image --> I'm focusing my attention on this specific region, area A. <!-- image --> ```palette Key,Color ,#fefefeff a,#68855eff b,#412d4cff c,#a0a69fff d,#c9cbcaff e,#7a6d82ff f,#e7e7e7ff g,#5a4964ff ``` ```image ff dggf fbbbe cbbbc ebbbd fgbbbf dbbbg cbbbe caadebbbc caad gbbbd caac fbbbgf caac dbbbe caac cbbbc caac ebbbd caac fgbbbf daac dbbbg daac cbbbe daaa ebbbc daaa gbbbd daaa fbbbgf faaa dbbbe faaa cbbbc faaa ebbbd faaaf fgbbbf aaaf dbbbg aaaf cbbbe aaaf ebbbc aaad gbbbd aaad fbbbgf aaad dbbbe ``` <!-- end of image --> This close-up reveals that there are no intersections in area A. Right then, let's explore the next spot. Let's see if area B yields any clues. <!-- image --> ```palette Key,Color ,#fefefeff a,#66845cff b,#412e4cff c,#9ca39aff d,#dedfdeff e,#818681ff f,#bcc0bbff g,#615369ff ``` ```image gd bbed bbbbf gbbbbgd cbbbbbc dgbbbbgf fbbbbbed ebbbbbc dgbbbbgd cbbbbbe d debbbbbf dfceaa fgbbbbgd dfcaaaaaaa cbbbbbc dfceaaaaaaaaaaa dgbbbbgf dfcaaaaaaaaaaaacfd fbbbbbeceaaaaaaaaaaaecfd degaaaaaaaaaaaacfd dfeaaaaaaaaaaaecfd dfceaaaaaaaaaaaagbbe dfcaaaaaaaaaaaecfddebbbbbf dfceaaaaaaaaaaacfd fgbbbbgd aaaaaaaaaaecfd cbbbbbc aaaaaacfd dgbbbbgf aecfd fbbbbbed debbbbbc dgbbbbgd cbbbbbe debbbbbf fgbbbbgd cbbbbb dgbbb fbb de ``` <!-- end of image --> The lines cross each other within area B, forming 1 intersection. Answer: A: 0; B: 1; 0 + 1 = 1 I have found one intersection!

<!-- image --> ```palette Key,Color ,#fefefeff a,#67845dff b,#412e4cff c,#aab1a9ff d,#cdd2ccff e,#879086ff f,#ecedecff g,#63536cff ``` ```image bf bb fbb cbe acgbd ac bb ac bb ae dbg ae ebc aa bbf aa bb aa fbb aa cbe aa gbd ea bb ea bb ca dbg ca ebc ca bbf da bb da fbb da cbe fa gbd faf bb ad bb ad dbg ad ebc ac bbf ac bb ac fbb ae cbe ae gbd aa bb aa bb aa dbg aa ebc aa bbf ea bb ea fbb ca cbe dad gbd aa bb aa bb dad dbg aa ebc aa bbf cad bb aa fbb aa cbe cad gbd aa bb aa bb cad dbg aa ebc aa bbf cad bb aa fbb ae cbe cad gbbf aa cbbg fae gbbd caf fbbb aa cbbe fae bbbf d caf dbbg fcaaaad aa ebbc deaaaaaed fae bbb fcaaaaaacf eaf cbbaeaaaaaed aa fcaaaaaacf fae deaaaaaedfbbb eaf fcaaaaaacf ebbe aa deaaaaaed bbbf fae caaaaaacf dbbg eaaaaaedf deaaaaaac gbbc fdcaaaaaaaaaaed fbbb fdc cbbe gbbd fbbg ebbc bbe d ``` <!-- end of image -->

I'm approaching this image with caution. Intersections might be tricky to spot. I wonder what's going on inside those areas? Perhaps intersections are hiding there. <!-- image --> ```palette Key,Color ,#fefefeff a,#c0ddf2ff b,#a7cc83ff c,#76b7e4ff d,#e9f3eaff e,#96ca95ff f,#93c6dfff g,#b1d7b0ff ``` ```image eeeeeeeeeeeeeeeeeeeeeeeeeeeee dgggggggggggggggggggggggggggggd dgggggggggggggggggggggggggggggd cfa dgggggggggggggggggggggggggggggd cccccccad dgggggggggggggggggggggggggggggd daccccccccfd dgggggggggggggggggggggggggggggd afcccccccfa dgggggggggggggggggggggggggggggd afccccccccagggggggggggggggggggggggggggggd daccccccccfggggggggggggggggggggggggd dfccccccccffggggggggggggggbbbbbd dgggggffccccccccfgggggbbbbbbbbbbbbgd dgggggggggggfccccfebbbbbbgggggddbbbbbbd dgggggggggggggbbbbbbbgggggggggd gbbbbbgd dgggggggggbbbbbbbgccggggggggggd dbbbbbbd dgggggbbbbbbbgggggfcfgggggggggd gbbbbbgd debbbbbbbggggggggggccgggggggggd dbbbbbbd dbbbbbbbggggggggggggggfcfggggggggd gbbbbbgd dbbbbbbgeggggggggggggggggggccggggggggd dbbbbg dbbbbbbgd dggggggggggggggggggggccgggggggd g dbbbbbbgd dggggggggggggggggggggccgggggggd dbbbbbbgd dgggggggggggggggggggggccggggggd dbbbbbbgd dgggggggggggggggggggggccggggggd bbbgd dggggggggggggggggggggggccgggggd d dggggggggggggggggggggggfcgggggd eeeeeeeeeeeeeeeeeeeeeeecceeee aca cc acf cc dcf cc cc ccd cc fca cc aca cc acf cc dcf cc cc ccd cc fca cc aca cc acf cc dcf cc cc fcd cc fca cc aca cc acf cc dcf cc cc fcd cc fca cc aca cc acf cc dcf cc cc fcd cc fca cc aca cc acf f ``` <!-- end of image --> This close-up might reveal an intersection in area A. <!-- image --> ```palette Key,Color ,#fefefeff a,#cee5f5ff b,#a5cb81ff c,#77b7e4ff d,#cae0b5ff e,#e0edd4ff f,#a0cde9ff g,#b1d297ff ``` ```image a cccffaa ccccccccffaa ccccccccccccccfaa edggd aafccccccccccccccccffaa edgbbbbbb aaffcccccccccccccccffaa edgbbbbbbbbbb affccccccccccccccccfaa edgbbbbbbbbbbbggb aafcccccccccccccccca edgbbbbbbbbbbbgde aaffcccccccccgbbbbbbbbbbbbgde aaffgbbbbbbbbbbbbgde edgbbbbbbbbbbbgde edgbbbbbbbbbbbbgf edgbbbbbbbbbbbgdefccca edgbbbbbbbbbbbgde cccc edgbbbbbbbbbbbgde fccca edgbbbbbbbbbbbgde cccc edgbbbbbbbbbbbgde acccf bbbbbbbbbbbgde cccc bbbbbbbgde acccf bbbgde cccca de acccf fccca acccf fccca cccc fccca cccc acccf cccc acccf cccca acccf fccca ``` <!-- end of image --> Oh my, look at that! It's 1 intersection in area A! Answer: A: 1; 1 = 1 One intersection, that's it, but I found it.

<!-- image --> ```palette Key,Color ,#fefefeff a,#c0def2ff b,#a6cc81ff c,#77b7e4ff d,#e6f2f8ff e,#deecd0ff f,#9ac9ebff g,#b6d598ff ``` ```image cfa cccccccad daccccccccfd dafcccccccfa afccccccccad dfccccccccfd dafcccccccfa egbbbbe afccccccccad egbbbbbgbbbbbgd dfcccccbbbbbbge egbbbbbe egbbbbbge ebbbbbgd egbbbbbgecc egbbbbbe egbbbbbge aca ebbbbbgd egbbbbbge cc egbbbbbe egbbbbbge acf ebbbbbgd egbbbbbge cc egbbbg egbbbbbge dcf e egbbbbbge cc egbbbbbge dcc ebbbbbbge ccd bbbge cc e fcd cc aca cc acf cc dcf cc cc ccd cc fcd cc aca cc acf cc dcf cc cc ccd cc fca cc aca cc acf cc dcf cc cc ccd cc fca cc aca cc acf cc dcc cc cc ccd cc fca cc aca cc acf cc dcc cc cc ccd cc fca cc aca cc acf f ``` <!-- end of image -->

I'm approaching this image with caution. Intersections might be tricky to spot. These spots are like clues. Let's see what they reveal about potential intersections. <!-- image --> ```palette Key,Color ,#fefefeff a,#ae1d4dff b,#cb75dbff c,#ebcaeaff d,#d59bd2ff e,#ba5c77ff f,#b1d6b1ff g,#97c896ff ``` ```image c eae aaaa daaae aaaac caaaa eaaad aaaa cbbc daaae bbbbbc aaaac dbbbbbbb caaaa cbbbb bbb eaaad dbbd bbb aaaa b bbb daaae cbbb aaaac cbbb caaaa cbbb eaaad cbbb aaaa dbbd daaae dbbd aaaac bbbdgggggggggggggggggggggf caaaa bbbdffffffffffffffffffffg eaaad bbbffffffffffffffffffffg aaaa gbbbfffffffffffffffffffg daaae gfbbbffffffffffffffffffg aaaac gffbbbfffffffffffffffffg caaaa gfffbbbffffffffffffffffg eaaad gffffbbbfffffffffffffffg aaaa gfffffbbbffffffffffffffeaaae gffffffbbbfffffffffgeaaaaac gffffffdbbbfffffeaaaaaaaa gfffffffdbbbgeaaaaaaaefg gffffffffbbbbaaaaaeffffg gffffgeaaabbbbeffffffffg gfeaaaaaaaabbbdffffffffg ceaaaaaaaeffffbbbdfffffffg daaaaaaaaeffffffffbbbfffffffg cbb ceaaaaaaaefffffffffffffbbbffffffg dbb eaaaaaaaad gffffffffffffffbbbfffffg bbd ceaaaaaaae gfffffffffffffffbbbffffg bbc aaaaaaaad gffffffffffffffffbbbfffg bb daaae gfffffffffffffffffbbbffg bb d gffffffffffffffffffbbbfg cbb gfffffffffffffffffffbbbg dbb gfffffffffffffffffffdbbb bbd gffffffffffffffffffffdbbb bbc dbbd bb dbbd bb bbbd cbb bbbc dbb bbbc bbb bbbc bbc bbb bbc bbb bb bbb cbb bbb dbb bbb bbb cbbb bbd cbbb bbc cbbb bb dbbd cbb dbbd cbb bbbd bbb bbbc bbd bbbc bbc bbbc bb bbb bb bbb cbb bbb dbb bbb bbd bbb bbc cbbb bb cbbb bb cbbb cbb dbbd dbb dbbd bbd bbbd bbc bbbcbbc bbbbb bbbb bbb d ``` <!-- end of image --> This is a magnified view of the region A. <!-- image --> ```palette Key,Color ,#fefefeff a,#ae1d4dff b,#cb75dbff c,#e9c5e7ff d,#db9cb1ff e,#c45c7eff f,#daa0e6ff g,#f4e3f4ff ``` ```image bbbf bbbbc bbbbbc bbbbbbc gbbbbbbg cbbbbbbg cbbbbbbg cbbbbbbg fbbbbbbg fbbbbbb fbbbbbf fbbbbbf fbbbbbf bbbbbbf gbbbbbbf gbbbbbbc gbbbbbbc gbbbbbbc gdea gbbbbbbg cdeaaaa cbbbbbbg gdeaaaaaaaa cbbbbbbg cdeaaaaaaaaaaa cbbbbbbg gdeaaaaaaaaaaaaaaa fbbbbbbgcdeaaaaaaaaaaaaaaaedg fbbbbbbaaaaaaaaaaaaaaedc cbbbbbbbaaaaaaaaaaedg gdeaaabbbbbbbaaaaaedc cdeaaaaaaabbbbbbbaedg gdeaaaaaaaaaaaabbbbbbf cdeaaaaaaaaaaaaaaaebbbbbbf gdeaaaaaaaaaaaaaaaedc gbbbbbbc aaaaaaaaaaaaaaaedg gbbbbbbc aaaaaaaaaaaedc gbbbbbbc aaaaaaaaedg gbbbbbbc aaaaedc cbbbbbbg aedg cbbbbbbg cbbbbbbg fbbbbbbg fbbbbbb fbbbbbf fbbbbbf fbbbbbf fbbbbbf gbbbbbbf gbbbbbbc gbbbbbbc gbbbbbbc gbbbbbb cbbbbb cbbbb cbbb fbb ``` <!-- end of image --> There is 1 intersection point visible in this close-up of area A. Answer: A: 1; 1 = 1 After careful examination, I conclude that there is one intersection.

<!-- image --> ```palette Key,Color ,#fefefeff a,#ae1d4dff b,#cb75dbff c,#e7c0e5ff d,#d996acff e,#c2577aff f,#d797e4ff g,#f4e3f4ff ``` ```image g eae aaaa daaae aaaac gaaaa eaaad aaaag cbbg daaae gbbbbbg aaaac fbbbfbbbg caaaa gbbbbg bbb eaaad fbbf bbb aaaag b gbbb daaae gbbb aaaac gbbb caaaa cbbb eaaad cbbb gaaaa fbbf daaae fbbf aaaac bbbc caaaa bbbc eaaad bbbg gaaaa bbbg daaae bbbg aaaag bbb caaaa bbb eaaad gbbb gaaaa gbbb daaae gbbb ceaaaaag cbbb daaaaaaaa cbbbceaaaaaaaeg bbbbaaaaad ceaaabbbbeg daaaaaaaabbbc ceaaaaaaaeg bbbc daaaaaaaad bbbg cbb ceaaaaaaaeg bbbg fbb daaaaaaaad bbbg bbf ceaaaaaaaeg bbb bbc aaaaaaaad bbb bbg daaaeg gbbb gbb c gbbb cbb gbbb fbb cbbb bbf cbbb bbc fbbf bbg fbbf bb bbbf cbb bbbc fbb bbbg bbb bbbg bbc bbbg bbg bbb bb bbb gbb gbbb fbb gbbb bbb gbbb bbf cbbb bbg cbbb bb fbbf gbb fbbf cbb bbbf fbb bbbc bbf bbbc bbc bbbg bb bbbg gbb bbb cbb bbb fbb gbbb bbf gbbb bbc gbbb bbg cbbb bb cbbb cbb fbbf fbb fbbf bbf fbbf bbc bbbcbbg bbbbb bbbb bbb fg ``` <!-- end of image -->

This image seems promising for intersection detection. I need to zoom in on these areas to get a better look. <!-- image --> ```palette Key,Color ,#fefefeff a,#b1d8b2ff b,#96afa8ff c,#dceee1ff d,#98e3a8ff e,#c6ddd0ff f,#eff6f0ff g,#a6cda9ff ``` ```image fgaaaaaaaaaaaaaaaaaaa fgaaaaaaaaaaaaaaaaaaa fgaaaaaaaaaaaaaaaaaaa fgaaaaaaaaaaaaaaaaaaa fgaaaaaaaaaaaaaabaaaa fgaaaaaaaaaaaaaabaaaa fgaaaaaaaaaaaaaabaaaa fgaaaaaaaaaaaaaggaaaa ffcedddddddddddaaabaaaaa fcceeadddddddddaeecccgaaaaaaaaadaaabaaaaa ffcceeaddddddddaaeccff fgaaaaaaaaadaaabaaaaa fcceeadddddddddaeeccf fgaaaaaaaaadaaabaaaaa dddddaaeccff fgaaaaaaaaadaaagaaaaa fgaaaaaaaaaaaaggaaaaa fgaaaaaaaaaadabaaaaaa fgaaaaaaaaaadabaaaaaa fgaaaaaaaaaadabaaaaaa fgaaaaaaaaaadabaaaaaa fgaaaaaaaaaadggaaaaaa fgaaaaaaaaaadgaaaaaaa fgaaaaaaaaaaabaaaaaaa fgaaaaaaaaaaagaaaaaaa fgaaaaaaaaaaadaaaaaaa fgaaaaaaaaaaadaaaaaaa fgaaaaaaaaaagdaaaaaaa fgaaaaaaaaaabdaaaaaaa fgaaaaaaaaaabdaaaaaaa fgaaaaaaaaaabaaaaaaaa fgaaaaaaaaaabadaaaaaa fgaaaaaaaaaagadaaaaaa fgaaaaaaaaaggadaaaaaa fgaaaaaaaaabaadaaaaaa fgaaaaaaaaabaadaaaaaa fgaaaaaaaabgaadaaaaaa fgaaaaaaagbaaaadaaaaa fgaaaaaaabaaaaadaaaaa fgaaaaaabaaaaaadaaaaa fgaaaaabaaaaaaadaaaaa fgaaaaggaaaaaaadaaaaa fgaaaabaaaaaaaadaaaaa fgaaabaaaaaaaaaaaaaaa fgaabaaaaaaaaaaadaaaa fggbggggggggggggdgggg fcbffffffffffffdffff b d b gc ca b b bf ee fb b bf ee fb b ec b ec b ec b ec b ec b ec b bbe ec fgbgf b ebbe ec fgbgf b ebbe ef cgbaf b ebbe ef cgbaf b ebbe ef cbbaf b ebbe af cbbaf b ebf ``` <!-- end of image --> Eureka! Let's inspect this close up of area A <!-- image --> ```palette Key,Color ,#fefefeff a,#b6ecc2ff b,#96afa8ff c,#d3eddaff d,#98e4a8ff e,#c6d2d0ff f,#e9f4ecff g,#acbfbbff ``` ```image f be fbc ebf eb gg bg fbe cbc ffffccccaaf ebf ccaaaaaddddddddddddddda gb dddddddaaaaccccffff ad gg ff ad be cdf fbe fdc cbf fdc eb da gb da bg ad be ad fbc cdf ebf fdc eb dc gg da bg ad fbe ad cbc cdf ebf cdf gb fdc gg da be dafbe adcbf adeb cdgb fdbg fdbe ddc ddf dd dd bdf fbdc cbdc ebda gbaa ggad becdf fbecdf cbffdc eb da gb da bg ad fbe ad fbc cdf ebf cdf eb fdc gg da bg da cbe ad fbb ad gbf cdf ebc fdc cbe fdc fbg da gbf da gbc ad ebe cd fbg cdf fbbf fdc gbf da ebe da cbg ad fbb ad gbf cdf ebe cdf cbg fdc fbg da gbf da ``` <!-- end of image --> Incredible, there's actually 1 intersection in area A! Answer: A: 1; 1 = 1 There's one and only one intersection present in the image.

<!-- image --> ```palette Key,Color ,#fefefeff a,#b5ecc0ff b,#95ada8ff c,#d4eddbff d,#97e5a8ff e,#c8d4d2ff f,#eaf3edff g,#afc0bdff ``` ```image f b b g cc fccaaaddddddda g ffccaadddddddddaaccff d b fccaaaddddddddaaaccff d b ffccaaaddddddddaaccff d b dddddaaaccff a e cf ef c g a b d b d g dfe ae fb d d d cd ga bcf bfc b a fe d ef d g d b a gf cf cg fc b a b d bf d ee d fb a b cf b a gc d fg d b d b gf cg b b bf ee fb b b ee fg b ec b ec b ec b ec b ec b ec b bbe ef fgbgf b ebbe ef fgbgf b ebbe ef fgbgf b ebbe ef fgbgf b ebbe gf fgbgf b ebbc gf cgbgf b ebf ``` <!-- end of image -->

Alright, let's get to work and investigate this image for intersections. I need to zoom in on these areas to get a better look. <!-- image --> ```palette Key,Color ,#fefefeff a,#9743cbff b,#b38acfff c,#66258dff d,#b0d7b1ff e,#8c65a8ff f,#96c598ff g,#d8c0e6ff ``` ```image g a a gb c a c a c gb gc a be a ee gb eb a cg a c a c a c a gcddddddddddddddddddddddf gaa fcdddddddddddddddddddddf gaaag decddddddddddddddddddddf baag ddeedddddddddddddddddddf baab dddceddddddddddddddddddf gaabg ddddcfdddddddddddddddddf gbaag dddddcdddddddddddddddddf baab ddddddcddddddddddddddddf gaab dddddddcdddddddddddddddf gaaag ddddddddcddddddddddddddeaag ddddddddfcdddddddddbaabf dddddddddecddddbaaeddddf ddddddddddeeaaabdddddddf ddddddddeaaceddddddddddf ddddbaabddddcfdddddddddf baaadddddddddcdddddddddf gbaabdddddddddddddcddddddddf ab dddddddddddddddcdddddddf a ddddddddddddddddcddddddf a ddddddddddddddddfcdddddf a dddddddddddddddddfcddddf b ddddddddddddddddddeedddf gg dddddddddddddddddddeeddf b ddddddddddddddddddddcfdf a dddddddddddddddddddddcff a ddddddddddddddddddddddcf a fffffffffffffffffffffffc a c b gc gg gc b be a eb a cg a cg a c b c gg c b gc a gc a be a eb a ceebbggg b gggbbeeeccccccccccceeebbggg gg gggbbe b c a c a c a e a gg b e gg c b c a c e bg e c c c e bg b c c c ``` <!-- end of image --> I'm eager to see what's happening in this magnified view of area A. <!-- image --> ```palette Key,Color ,#fefefeff a,#9641cbff b,#bc92d6ff c,#65238dff d,#eae0f1ff e,#814aa1ff f,#a570c6ff g,#d3b9e3ff ``` ```image f cb ecg dccg gccd gced bce bce fcf ecf ecb decg dccg dccd gccd bce bce fcf ecf ecb decg d dccg dgbaa dccd gbfaaafb gccd dbfaaaabgd gced dgbaaaafgd bce gbaaaafbd fcebfaaaabg dgfcccabgd dgbaaaafecb gbfaaafbg decg dbfaaaabgd dccg dgfaaaafgd dccd dgbaaaafbd gccd aaaabg gced bgd bce fcf fcf ecb decb dccg dccd gccd gced bce fce fcf ecb ecb dccg dccd gccd gce bc f ``` <!-- end of image --> I am surprised, so clear, 1 intersection has appeared in area A. Answer: A: 1; 1 = 1 My investigation reveals that there is exactly one intersection in this image.

<!-- image --> ```palette Key,Color ,#fefefeff a,#9742cbff b,#bc8fd7ff c,#65238dff d,#ece2f3ff e,#8652a5ff f,#a676c4ff g,#d3b9e4ff ``` ```image d a a gb e a c a dc gb gc a be a ff gb eb a cg a cd a c a c a dc gaad gc gfaag be dbaag ff baabd eb gaafd cg dfaag cd dbaab c gaabd c gaafg dc dfaag dc baab ge gaafd fefaag dbaaeb baabd cg gaafd cd dfaag c ab c a dc a dc a ge db fe gg eb b cg a cd a c a c a c b dc gg gc b fe a ef a cg a cd a c b c gg c bd dc a gc a be a ef a eeffbggdd b dggbffeeccccccccccceeffbggd gg ddggbfe bd c a c a c a e a gg f e gg c bd c a c d e bg df c c c e bg df c c c ``` <!-- end of image -->

The hunt for intersections begins! Let's analyze this image closely. I'd describe these as 'hotspots' for potential intersections. <!-- image --> ```palette Key,Color ,#fefefeff a,#0f8f3eff b,#4f8915ff c,#92c692ff d,#b2d7b1ff e,#49a96bff f,#7ca853ff g,#e7f2e6ff ``` ```image gcd bbbbbbcg gbbbbbbbbbbfd gbbbbbbbbbbbbbbbfg dbbbgcbbbbbbbbbbbbbbbcg dbbb gfbbbbbbbbbbbbbbd cbbb dfbbbbbbbbbb fbbb gcbbbbbbd fbbb bbbf bbbf fbbb bbbf gbbb bbbf bbbd bbbc bbbb bbbd dbbb bbbd bbbg bbbg bbbf bbb fbbb bbb gbbb bbb bbbd bbb bbbf gbbb cbbb gbbb bbb dbbb bbbc eeeg cbbb bbbb aaag cbbb dbbb aaa fbbb bbbg aaa fbbb bbbf aaa bbbf fbbbbbd aaa bbbf gbbbbbbbbg aaa bbbc dbbbbbbbbbbg aaa bbbc cbbbbbbbbbfg aaa bbbd cbbbbbbbbbfg ccccccccccccccaaaccc bbbd cbbbbbbbbbfg gddddddddddddddaaaddd bbbg cbbbbbbbbbfg gdddddddddddddcaaaddd bbb cbbbbbbbbbfg gdddddddddddddcaaaddd bbb fbbbbbbbbbf gdddddddddddddcaaaddd bbb fbbbbbbbbbf gdddddddddddddcaaaddd bbb fbbbbbbbbbfddddddddddddcaaaddd gbbb gfbbbbbbbbbfdddddddddeaaaddd dbbb gfbbbbbbbbbfddddddeaaaddd ggdbbbggggg gfbbbbbbbbbfdddeaaaddd ddfbbbdddddc caag gdcbbbbbbbbbbfeaaaddd ddfbbbdddddc aaaaa gddddcbbbbbbbbaaaaddd ddfbbbdddddc eaaaaaac gdddddddcbbbbbaaaabdd ddbbbbdddddc aaaaaaaaad gddddddddddcbbaaaacdd ddbbbbdddddceaaa eaaaaaa gdddddddddddddaaaaddd ddbbbfdddddcaaae aaaaaae gdddddddddddddaaaaddd ddbbbfdddddaaaa gaaaaaac gdddddddddddddaaaeddd ddbbbfdddddaaae caaaaaag gdddddddddddddaaaeddd ddbbbcddddeaaa eaaaaaa gdddddddddddddaaaeddd ddbbbcddddaaae gaaaaaae gdddddddddddddaaaeddd ddbbbcdddeaaa daaaaaad gdddddddddddddaaaeddd dddddddddaaae caaaaaag gdddddddddddddaaaeddd ddddddddeaaa aaaaaae gdddddddddddddaaaeddd ddddddddaaae gaaaaaac gdddddddddddddaaacddd dddddddeaaac daaaaaad gdddddddddddddaaacddd dddddddaaaec eaaaaaa gdddddddddddddaaacddd ddddddeaaadc aaaaaae cccccccccccccaaacccc ccccccaaaecd gaaaaaac aaag eaaa caaaaaag aaag aaae eaaaaaa aaag caaaaa gaaaaaae aaa aaaaae daaaaaad aaa aaaaa eaaaaaag aaa caaae aaaaaae aaa aaa gaaaaaac aaa geg caaaaaag aaa eaaaaaa aaa aaaaaae gaaa daaaaaad gaaa caaaaaag gaaa eaaaaaa daaa gaaaaaac daaa daaaaaad daaa eaaaaaag daaa aaaaaae caaa gaaaaaac caaa caaaaaaeaaa eaaaaaaaa aaaaaaa daaaaa caad ``` <!-- end of image --> Let's see what secrets area A holds. <!-- image --> ```palette Key,Color ,#fefefeff a,#0f8e3eff b,#4f8914ff c,#a4c185ff d,#bcdabdff e,#44a769ff f,#7ea853ff g,#d9e7d1ff ``` ```image cbbbbbbd cbbbbbbg cbbbbbbg cbbbbbbg fbbbbbb fbbbbbb fbbbbbb fbbbbbb bbbbbbf bbbbbbf bbbbbbf bbbbbbf bbbbbbf gbbbbbbc gbbbbbbc d gbbbbbbc e dbbbbbbd da dbbbbbbd ea cbbbbbbd daa cbbbbbbg eaa cbbbbbbg daaa cbbbbbbg eaaa gccccff daaaa eaaaa daaaaa eaaaaa daaaaaa eaaaaaa daaaaaaa eaaaaaae daaaaaaag eaaaaaae daaaaaaag eaaaaaae ``` <!-- end of image --> I had hoped to find an intersection in area A, but there isn't one. Time to investigate another area. My goal is to determine if there's an intersection inside area B. <!-- image --> ```palette Key,Color ,#fefefeff a,#108f3eff b,#4f8914ff c,#97c18aff d,#a7d6b8ff e,#60b47fff f,#669833ff g,#d8e8d6ff ``` ```image aaaaaae aaaaaae aaaaaae gaaaaaae gaaaaaae gaaaaaac gaaaaaac gaaaaaac gaaaaaac daaaaaad daaaaaad daaaaaad daaaaaad bcg daaaaaad bbbfcg daaaaaad bbbbbbfcg daaaaaad bbbbbbbbbfcg caaaaaag bbbbbbbbbbbbfcg caaaaaag bbbbbbbbbbbbbbbfcg caaaaaag bbbbbbbbbbbbbbbbbbfcg caaaaaag gcfbbbbbbbbbbbbbbbbbbfcg eaaaaaag gcfbbbbbbbbbbbbbbbbbbfcgeaaaaaag gcfbbbbbbbbbbbbbbbbbbaaaaaaa gcfbbbbbbbbbbbbbbbaaaaaaa gcfbbbbbbbbbbbbaaaaaaacg gcfbbbbbbbbbaaaaaaabf gcfbbbbbbaaaaaaabc gcfbbbaaaaaaabg gcfaaaaaaaf aaaaaaac aaaaaaag aaaaaaa aaaaaae aaaaaae aaaaaae aaaaaae aaaaaae aaaaaae aaaaaae gaaaaaae gaaaaaae gaaaaaae gaaaaaac gaaaaaac gaaaaaac gaaaaaad daaaaaad daaaaaad daaaaaad daaaaaad daaaaaad daaaaaad ``` <!-- end of image --> Amazing! This area was hiding 1 intersection all along! Answer: A: 0; B: 1; 0 + 1 = 1 There's one and only one intersection present in the image.

<!-- image --> ```palette Key,Color ,#fefefeff a,#0f8f3eff b,#4f8914ff c,#93c38fff d,#c1dcbeff e,#4bab6eff f,#7ca751ff g,#e3efe2ff ``` ```image gcd bbbbbbcg gbbbbbbbbbbfd gbbbbbbbbbbbbbbbfd dbbb cbbbbbbbbbbbbbbbcg cbbb gfbbbbbbbbbbbbbbd cbbb dfbbbbbbbbbb fbbb gcbbbbbbd fbbb bbbf bbbf fbbb bbbf gbbb bbbc bbbc bbbc bbbb bbbd cbbb bbbd bbbg bbbg bbbf bbb fbbb bbb dbbb bbb bbbd bbb bbbf gbbb cbbb dbbb bbb dbbb bbbc eeeg cbbb bbbb aaag cbbb dbbb aaa fbbb bbbg aaa fbbb bbbf aaa bbbf fbbbbbd aaa bbbf gbbbbbbbbd aaa bbbc dbbbbbbbbbbg aaa bbbc cbbbbbbbbbfg aaa bbbd cbbbbbbbbbfg aaa bbbd cbbbbbbbbbfg gaaa bbbg cbbbbbbbbbfg gaaa bbb cbbbbbbbbbf daaa bbb fbbbbbbbbbf daaa bbb fbbbbbbbbbf daaa bbb fbbbbbbbbbf daaa gbbb gfbbbbbbbbbc caaa dbbb gfbbbbbbbbbc caaa dbbb gfbbbbbbbbbc caaa cbbb caag gfbbbbbbbbbccaaa cbbb aaaaa gfbbbbbbbaaaa fbbb eaaaaaac gbbbbbaaaaf fbbb aaaaaaaaad dbbaaaag bbbf eaaa eaaaaaa eaaa bbbf aaae aaaaaae aaaa bbbc eaaa gaaaaaac aaae bbbc aaae caaaaaag aaae bbbd eaaa eaaaaaa aaae bbbd aaae aaaaaae aaae bbbg eaaa daaaaaad aaac aaae caaaaaag aaac eaaa aaaaaae aaac aaae gaaaaaac aaad eaaa caaaaaad aaad aaae eaaaaaa aaad eaaa aaaaaae aaad aaae gaaaaaac aaag eaaa caaaaaag aaag aaae eaaaaaa aaag caaaaa gaaaaaae aaa aaaaae daaaaaad aaa aaaaa eaaaaaag aaa caaae aaaaaae aaa aaa gaaaaaac aaa geg caaaaaag aaa eaaaaaa aaa aaaaaae gaaa daaaaaac gaaa caaaaaag gaaa eaaaaaa daaa gaaaaaac daaa daaaaaad daaa eaaaaaa caaa aaaaaae caaa gaaaaaac caaa caaaaaaeaaa eaaaaaaaa aaaaaaa daaaaa caad ``` <!-- end of image -->

This image seems promising for intersection detection. I've spotted 1 narrow regions that might be worth examining further. Let's call them area A. <!-- image --> ```palette Key,Color ,#fefefeff a,#6e0431ff b,#998387ff c,#b8a5a8ff d,#f0f1eeff e,#8a3d5dff f,#afd6afff g,#d8cacfff ``` ```image gb eaaab aaaaaaac deaaaaaaaac deaaaaaaaac geaaaaaaaag gaaaaaaaaag gaaaaaaaaeg caaaaaaaaed caaaaaaaaed caaaaaaaaed baaaaaaaab baaaaaaaab baaaaaaaa deaaaaaa deaaae gaaac baaad aaaa aaaa daaae caaag eaaa aaaa aaae daaab baaad eaaa aaaa aaae gaaac eaaad aaaa aaaa daaab caaag eaaad aaaa aaaa aaaa daaaa daaaa daaaa gaaaa gaaaa gaaaa caaae caaae caaae dfffeaaaefffffffffffffff dffffeaaaeffffffffffffff dfffffeaaabfffffffffffff dffffffeaaabffffffffffff dfffffffeaaabfffffffffff dffffffffaaaabffffffffff dbbbcgd dfffffffffaaaacfffffffff bbbbbbbbbbbcd dffffffffffaaaacffffffff gbbbbbbbbbbbbbbbbbcg dfffffffffffaaaacfffffff bbbd gcbbbbbbbbbbbbbbbbbbcffffffffffaaaafffffff cbbb dgcbbbbbbbbbbbbbbbbbcfffffaaaaffffff bbbd gcbbbbbbbbbbbbbbbbbbaaaafffff bbbb dfcbbbbbbbbbbbbbaaaabfff dbbb dfffffffcbbbbbbbbaaaafff bbbc dffffffffffffffcbbaaabff dbbb dffffffffffffffffffabfff bbbg dfffffffffffffffffffffff gbbb dfffffffffffffffffffffff bbbg dfffffffffffffffffffffff gbbb dfffffffffffffffffffffff bbbd dfffffffffffffffffffffff cbbb dfffffffffffffffffffffff bbb dfffffffffffffffffffffff bbbb dfffffffffffffffffffffff dbbb dfffffffffffffffffffffff bbbc dfffffffffffffffffffffff dbbb dfffffffffffffffffffffff bbbg ddddddddddddddddddddddd gbbb bbbbbbbcccccggggddd bbbg bbbbbbbbbbbbbbbbbbbbbbbbbbbbbb bbbbbbbbbbbbbbbbbbbbbbbbbbbbbd dddggggccccbbbbbbbbbbc ``` <!-- end of image --> Let's see what secrets area A holds. <!-- image --> ```palette Key,Color ,#fefefeff a,#6e0331ff b,#998287ff c,#b8a0a8ff d,#e9e1e4ff e,#802a4eff f,#964b6bff g,#d3c0c7ff ``` ```image baaaaaaaf baaaaaaaf baaaaaaaf faaaaaaab faaaaaaab faaaaaaab faaaaaaac faaaaaaac eaaaaaaac deaaaaaaac deaaaaaaag deaaaaaaag deaaaaaaag deaaaaaaag deaaaaaaag gaaaaaaaad gaaaaaaaed gaaaaaaaed gaaaaaaaed bccgdd gaaaaaaaed bbbbbbbbcggd caaaaaaaed bbbbbbbbbbbbbbccgdd caaaaaaaed bbbbbbbbbbbbbbbbbbbbccggd caaaaaaaf bbbbbbbbbbbbbbbbbbbbbbbbbbbcfaaaaaaaf bbbbbbbbbbbbbbbbbbbbbbbbbbbbbeaaaaaaaf dggccbbbbbbbbbbbbbbbbbbbbbbbbeaaaaaaaebc ddgccbbbbbbbbbbbbbbbbbbbeaaaaaaaeb dggcbbbbbbbbbbbbbbeaaaaaaaf dggccbbbbbbbbeaaaaaaab ddgccbbbeaaaaaag dgeaaaac faag fg ``` <!-- end of image --> 1 intersection present within area A. Answer: A: 1; 1 = 1 My investigation reveals that there is exactly one intersection in this image.

<!-- image --> ```palette Key,Color ,#fefefeff a,#6e0331ff b,#998388ff c,#bca2abff d,#ebe3e6ff e,#82274eff f,#9a5170ff g,#d3c2c8ff ``` ```image db eaaab aaaaaaac dfaaaaaaaac deaaaaaaaac deaaaaaaaag geaaaaaaaeg gaaaaaaaaed caaaaaaaaed caaaaaaaafd caaaaaaaaf baaaaaaaaf baaaaaaaab faaaaaaaa faaaaaa dfaaae gaaac faaad eaaa aaaa daaaf caaag faaa aaaa aaae daaab baaad eaaa aaaa aaaf gaaac faaa aaaa aaae daaab caaag eaaa aaaa aaaa aaaa aaaa daaaa daaaa daaaa gaaaa gaaae gaaae caaae caaaf baaaf faaaf faaab faaac eaaac eaaag dbbbcgd eaaag bbbbbbbbbbbgd aaaad gbbbbbbbbbbbbbbbbbcg aaaad bbbd dcbbbbbbbbbbbbbbbbbcgd aaaad cbbb dgcbbbbbbbbbbbbbbbbbcd aaaad bbb gcbbbbbbbbbbbbbbbbbcaaaa bbbb dgbbbbbbbbbbbbbaaaab bbb dgcbbbbbbbaaaa bbbc dcbbaaag dbbb ag bbbg gbbb bbbg gbbb bbbd cbbb bbb bbbb bbb bbbc dbbb bbbg gbbb bbbbbbbbcccggggddd bbbd bbbbbbbbbbbbbbbbbbbbbbbbbbbbbb bbbbbbbbbbbbbbbbbbbbbbbbbbbbbd ddddgggccccbbbbbbbbbbc ``` <!-- end of image -->

I'm approaching this image with caution. Intersections might be tricky to spot. I need to zoom in on these areas to get a better look. <!-- image --> ```palette Key,Color ,#fefefeff a,#a12837ff b,#e1e0ddff c,#ba636dff d,#d6a2a8ff e,#b1d7b1ff f,#f1f2efff g,#9ac496ff ``` ```image fgggggggggggggggggggggggf feeeeeeeeeeeeeeeeeeeeeaaa feeeeeeeeeeeeeeeeeeeeaaaad bbbbbbbbbbffffffffffffff feeeeeeeeeeeeeeeeeeeaaaaaa bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbeeeeeeaaaaaaa bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbeeeeeaaaagaaa bbb ffffffffffffffbbbbbbbbbbbbbbbbbbbbbbbbbbbbeeeeaaaagecaad bbb feeeeeeeeebbbeeeaaaageegaaa fbbf feeeeeeeeeebbeeaaaageeeeaaa bbb feeeeeeeeeebbbaaaageeeeeaaaf bbb feeeeeeeeeebbaaaageeeeeedaac bbb feeeeeeeeeebaaaageeeeeeefaaa bbb feeeeeeeeeeaaaaeeeeeeeeefaaa fbbb feeeeeeeeeaaaaeeeeeeeeeefaaab fbbf feeeeeeeeaaaabeeeeeeeeeefdaac bbb feeeeeeeaaaabbeeeeeeeeeef aaa bbb feeeeeeaaaabbbeeeeeeeeeef aaa bbb feeeeeaaaaebbbeeeeeeeeeef caad bbb feeeeaaaaeebbbeeeeeeeeeef baaa fbbf feegaaaaeeebbbeeeeeeeeeef aaa bbbf fegaaaaeeeebbbeeeeeeeeeef aaaf bbb fgaaaaeeeeebbbeeeeeeeeeef daac bbb baaaaeeeeeeebbeeeeeeeeeef faaa bbb baaaaeeeeeeeebbbeeeeeeeeef aaa bbb daaaaeeeeeeeeebbbeeeeeeeeef aaab fbbf daaaaeeeeeeeeeebbbeeeeeeeeef daac bbb daaaagggggggggggbbbgggggggggf aaa bbb daaaa bbb aaa bbb daaaa bbb caad bbb daaaa bbb baaa fbbb caaac bbb aaa fbbf caaac bbb aaaf bbb caaac bbb caad bbb caaac bbb faaa bbb caaac bbbf aaa bbb caaac fbbf aaab fbbf caaac fbbf daac bbbf aaaad fbbf aaa bbb aaaad bbb aaa bbb aaaad bbb caad bbb aaaad bbb baaa bbb aaaad bbb aaa fbbf aaaab bbb aaa bbbf aaaab bbb cad bbb aaaab bbb bbb aaaab bbb aaaab bbb aaaaf bbb aaaaf bbbf aaaaf fbbf aaaaf fbbf faaaa fbbf faaaa bbb faaaa bbb faaaa bbb baaaa bbb baaaa bbb baaaa bbb baaaa bbb baaaa bbb daaaa bbb daaaa bbb daaaa fbbf daaaa fbbf daaaa fbbf caaac fbbb caaac bbb caaac bbb faaac bbb fac bbb bf f bbb bbbb bbb fbbbbbf bbb fbbbbbb bbb bbbbbb bbb bbbbbb bbb bbbbbbf fbbf fbbbbbf fbbffbbbbbb fbbbbbbbb fbbbbbb bbbbf bbf ``` <!-- end of image --> Let's take a closer look at area A. <!-- image --> ```palette Key,Color ,#fefefeff a,#a12736ff b,#e1e0ddff c,#c47d86ff d,#deb5baff e,#a93a48ff f,#f1eeeeff g,#b45762ff ``` ```image f fga feaa feaaa beaaaa beaaaaa beaaaaaa fffffffffffffffffffffff beaaaaaaa bbbbbbbbbbbbbbbbbbbbbbbbb beaaaaaaaa bbbbbbbbbbbbbbbbbbbbbbbbbf beaaaaaaaga bbbbbbbbbbbbbbbbbbbbbbbbbb beaaaaaaadba bbbbbbbbbbbbbbbbbbbbbbbbbb daaaaaaaad e bbbbbbbbbbbbbbbbbbbbbbbbbb daaaaaaaad c ffffffffffffffffffffbbbbbbf daaaaaaaad d fbbbbbf daaaaaaaad f fbbbbbf daaaaaaaeb fbbbbbf daaaaaaaeb fbbbbbf daaaaaaaeb fbbbbbfdaaaaaaaeb fbbbbbcaaaaaaaeb bbbbcaaaaaaaeb bbbcaaaaaaaeb bbcaaaaaaaef bcaaaaaaaef caaaaaaagf caaaaaaagf caaaaaaagf caaaaaaagf caaaaaaagbf gaaaaaaagbbf gaaaaaaagbbbf fgaaaaaaagbbbbf fgaaaaaaagbbbbbf fgaaaaaaacfbbbbbf fgaaaaaaac bbbbbb fgaaaaaaac bbbbbb fgaaaaaaac bbbbbb feaaaaaaac bbbbbb feaaaaaaac bbbbbb feaaaaaaac bbbbbb beaaaaaaac bbbbbb beaaaaaaad fbbbbbf beaaaaaaad fbbbbbf beaaaaaaad fbbbbbf beaaaaaaad fbbbbbf eaaaaaaad fbbbbbf aaaaaaad fbbbbbf aaaaaad fbbbbbf aaaaad bbbbbb aaaad bbbbbb aaad bbbbbb aeb bbbbbb ``` <!-- end of image --> Case closed! This is definitely 1 intersection point in area A. Answer: A: 1; 1 = 1 I have found one intersection!

<!-- image --> ```palette Key,Color ,#fefefeff a,#a12736ff b,#e1e0deff c,#c07079ff d,#e0babfff e,#af4855ff f,#f1efeeff g,#d1959dff ``` ```image f eaa eaaad bbbbbbbbbffffffffffffff eaaaae bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb aaaaaaa bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb aaaadaaa bbb ffffffffffffffbbbbbbbbbbbbbbbbbbbbbbbbbbb aaaad caag bbb fbbf aaaad faaa fbbf fbbf aaaab aaa bbb fbbfaaaab aaaf bbb bbaaaab gaac bbb baaaaf aaa bbb aaaaf aaa fbbb aaaaf eaad fbbf aaaab daae bbb aaaabb aaa bbb faaaabbb aaa bbb faaaa bbb caag bbb faaaa bbb baaa fbbf faaaa bbb aaa bbbf baaaa bbb aaaf bbb baaaa fbbf gaac bbb baaaa fbbf aaa bbb daaaa fbbf aaa bbb daaaa bbb aaab fbbf daaaa bbb daae bbb daaaa bbb aaa bbb gaaae bbb aaa bbb gaaae bbb eaad bbb gaaae bbb baaa fbbb caaae bbb aaa fbbf caaae bbb aaa bbb caaae bbb caag bbb caaac bbb faaa bbb eaaac bbb aaa bbb eaaac fbbf aaab fbbf eaaac fbbf gaac fbbf eaaag fbbf aaa bbb eaaag bbb aaa bbb aaaag bbb eaad bbb aaaad bbb daae bbb aaaad bbb aaa fbbf aaaad bbb aaa bbb aaaad bbb cag bbb aaaab bbb bbb aaaab bbb aaaab bbb aaaaf bbb aaaaf fbbf aaaaf fbbf aaaaf fbbf faaaa fbbf faaaa bbb faaaa bbb faaaa bbb baaaa bbb baaaa bbb baaaa bbb daaaa bbb daaaa bbb daaaa bbb daaaa bbb gaaaa fbbf gaaae fbbf gaaae fbbf caaae fbbf caaae bbb caaae bbb faaac bbb fac bbb bf f bbb fbbb bbb fbbbbbf bbb fbbbbbb bbb bbbbbb bbb bbbbbb bbb bbbbbbf fbbf fbbbbbf fbbffbbbbbb fbbbbbbbb bbbbbb bbbbf bbf ``` <!-- end of image -->

Hmm, I'm not sure what to expect from this image. Let's see if any lines cross. There are 1 regions I'd like to highlight in the image. <!-- image --> ```palette Key,Color ,#fefefeff a,#f32620ff b,#09ec1bff c,#f2a8a2ff d,#3ded4bff e,#f2625cff f,#b1d8b1ff g,#91d292ff ``` ```image aa a a a a a ec ac a a ac ce a ac a a ac a a ac ac a ac a a ac ee a ae a a ae ca a ae a a ee a a ee ec a ee a a ea ce a ea a a b ea a a bg gffffffffffffffffffffffgca ac e db gffffffffffffffffffffffea a cac e gb gfffffffffffffffffffffca ee eace e bf gffffffffffffffffffffcag a ac a ce bdgfffffffffffffffffffcafg ca a ce gbffffffffffffffffffcaffg a cc gbgffffffffffffffffafffg a cc gfbdffffffffffffffaffffg a cc gffdbffffffffffffafffffg cc cc gfffgbgfffffffffaffffffg ce ec gfffffbdfffffffafffffffg a ec gffffffbbfffffaffffffffg a ec gfffffffgbfffafffffffffg a e gfffffffffbgaffffffffffg a e gffffffffffbbffffffffffg e e gfffffffffafdbfffffffffg cc a gffffffffafffgbgfffffffg e a gfffffffacfffffbdffffffg a a gffffffacfffffffdbfffffg a a gfffffacfffffffffgbgfffg a a gffffacffffffffffffbdffg a a gfffaeffffffffffffffdbfg ec a gffaeffffffffffffffffgbg cc a gfaefffffffffffffffffffbg e a gaeffffffffffffffffffffgbd a a aefffffffffffffffffffffg gb a a eeffffffffffffffffffffffg bf a a eegffffffffffffffffffffffg bd a a ee gffffffffffffffffffffffg db ec a ea fggggggggggggggggggggggf fbf ce a ea bd a a ea db a a ca fb a a ca bg a a c db e a gb cca bf cea bd aa gb ae bf ae bd ae db ae fb ea bg db gb bf bd gb bf bd db fb bg f db b fb df bg b bdbf gb ``` <!-- end of image --> I wonder what we'll find inside area A? <!-- image --> ```palette Key,Color ,#fefefeff a,#f32822ff b,#09ed1bff c,#faadabff d,#49ee54ff e,#f56a64ff f,#9af7a2ff g,#eaecdbff ``` ```image c ca caa caac caac g caac bf caac bbf caac fbbdg gaac gdbbg gaac dbbf gaae fbbd gaae gbbbg gaae dbbf gaae fbbd gaae fbbdg gaae gdbbf aae fbbf eae fbbdg eae gdbbf eae dbbf eae fbbd eaa gbbbg eaag dbbfeaag fbbdag ebbdg eaadbbf eaag fbbd eaag fbbdg caag gdbbf caag dbbf caac fbbdg caac gbbbg caac dbbf caac fbbd caac gbbdg caac gdbbf caac fbbd caac fbbdg caac gdbbf gaac dbbf gaac fbbd gaae gdb gaae d gaae gaae gaae gaae aae ae e ``` <!-- end of image --> Case closed! This is definitely 1 intersection point in area A. Answer: A: 1; 1 = 1 I've found a single intersection point in the image.

<!-- image --> ```palette Key,Color ,#fefefeff a,#f4241eff b,#0fed21ff c,#f98e8bff d,#67f372ff e,#f6544fff f,#b8f9bdff g,#fbc9c8ff ``` ```image ae a a ag a ag ec ag a a ag ce a ag a a ag ga a ac ag a ac a a ac cc a ac a a ae ge a ee a a ee a a ee ec a ee a a ee ce a ca a a b ca ga e bd ca ag e bb ca a gag ge fb ca cc eagc ge bf ga a ac a ge bb ga ga a gc db ga a gc fbf ga a cc bd ga e cc db ga cc cc fbf a ge cg bd a a cg bb a a eg fb a a eg bfa a eg bb eg e agdb cc a ag bf ge a ag bd a a ag db a a ag fbf a a ac bd a a ac bb eg a ac fb cc a ac bd e a ac bb a a ee db a a ee bf a a ee bd a a ee db cg a ee fbf gc a ca bd a a ca db a a ca fb a a ca bd a a c bb e a db cca bf gea bb ae db ae fbf ae bd ae db ae fb ea bd bb fb bf bb db fbf bd db fbf bd f bb b fb bf bf b bbbf db ``` <!-- end of image -->

This is the image I'm working with. The goal is to count the intersections. I need to zoom in on these areas to get a better look. <!-- image --> ```palette Key,Color ,#fefefeff a,#94ca95ff b,#c9fcfbff c,#b0d7b1ff d,#d0ead2ff e,#edf9f4ff f,#a0f9f6ff g,#239f2bff ``` ```image fb fef fe f fe f fe f fe bb fe eb fe f fe f fb f fb fe fb bb fb f fb f fb f fb f c fb bb cg fb eb cg fb f cg fb f cg fb f cg ff fe cg ff bb cg bf f cg bf f cg bf f cg bf f dg bf bb dg bf eb dg bf f dg bf f dg bf f dg bf fe dg bf bb dg b f dg f dg f dg f dg bb dg eb dg eeeeeeeeefeeeeeeeeeeeedg eaccccccccfcccccccccccaga ecccccccccfccccccccccagca ecccccccccfcccccccccagcca eccccccccccfcccccccagccca eccccccccccfcccccccgcccca eccccccccccfccccccgccccca b eccccccccccfcccccgcccccca effe eccccccccccfccccgccccccca ff ef eccccccccccfcccgcccccccca bfe f ecccccccccccfcgccccccccca bfb f ecccccccccccfgcccccccccca ff bb ecccccccccccgccccccccccca ff f eccccccccccgfccccccccccca bfe f ecccccccccgcfcccccccccccaefb fe eccccccccgcccfccccccccccff eb ecccccccgccccfccccccccffa f eccccccgcccccfcccccccfcca f ecccccgccccccfcccccffccca bb eccccgaccccccfcccffccccca f ecccgacccccccfcffccccccca f eccgacccccccccffcccccccca f ecgacccccccccccccccccccca eb gga egaccccccccccccccccccccca f aggd gaaaaaaaaaaaaaaaaaaaaaaac f egga gd bb cggc gd f agge gd f dgga gd f aggd gd bb egga gd f cggcgd f egd be f f f bb f f ``` <!-- end of image --> I wonder what we'll find inside area A? <!-- image --> ```palette Key,Color ,#fefefeff a,#60b966ff b,#b9fbf9ff c,#9dfaf8ff d,#eaf5eaff e,#defdfcff f,#43ad4bff g,#1f9e27ff ``` ```image bce df ece dfg ecb dfga cb dfga cc dfga bce dfga bce dfga ecb dfga ecb dfga cc dfga bc dfga bce dfga ece dfga ecb dfga cb dfga cc dfga bce dfga bce dfga ecb dfgad ecb dfgad ccdfgfd bcfgfd bfgfd dfgfd dagfb dagfcb agfdcc agfd bce agfd bce agfd ecb agfd ecb ec agfd cc ebcc agfd bc bccbe agfd bce eccce agfd ece ecccb agfd ecb bccbe agfd cb bccce agfd cc eccce agfd bce ebccb agfd bce bccbe agfd ecbccce agfd ecccb agfd bb agfd agfd agfd ``` <!-- end of image --> The lines cross each other within area A, forming 1 intersection. Answer: A: 1; 1 = 1 After careful examination, I conclude that there is one intersection.

<!-- image --> ```palette Key,Color ,#fefefeff a,#62ba68ff b,#c0fbfaff c,#aadaadff d,#d5ecd7ff e,#e5fbf8ff f,#9ffaf8ff g,#219e29ff ``` ```image fb fef fe f fe f fe f fe be fe eb fe f fe f fe f fe be fe eb fb f fb f fb f fb f c fb be cg fb eb cg fb f cg fb f cg fb f cg bb be cg bb eb cg bf f cg bf f cg bf f cg bf f cg bf be dg bf eb dg bf f dg bf f dg bf f dg ef be dg ef eb dg b f dg f dg f dg f dg be dg eb dg f dg f dg f dg be eg eb eg f eg f eg b f eg effe f eg ff eb be eg bfe f ebege efb f fge fb bb ege ff f egf bfe f gebe efb be ge eb ff eb ge f bf f ge f bfe f ge f efb be ge f ff f gd bebfe f gd efb f gd eb ggc gd f cggd gd f eaga gd be cggc gd f agae gd f dggc gd f aggd gd eb dgga gd f cggcgd f ad be f f f eb f f ``` <!-- end of image -->

This image seems promising for intersection detection. There are 1 areas where the lines seem to converge. We should take a closer look at area A. <!-- image --> ```palette Key,Color ,#fefefeff a,#49cb2eff b,#2b1587ff c,#95d38eff d,#b1d7b1ff e,#d7e6daff f,#70d45cff g,#7e76b2ff ``` ```image ee aaa aaa aaa aaa aaa gd aaf bbbbe aac bbbbbbbe eaac bbbbbbbbbbe daad gbbb ebbbbbbe caae gbbbe ebbbbbbe faa ebbbd ebbbbbbe aaa bbbg ebbbbbbe aaa ebb ebbbbbb aaa ebbbbbb aaa ebbbbbb aaa dbbbbbb aaa dbbbbbb aaf gbbbbbb aac gbbbbbb eaad gbbbbbg daad gbbbbbg caae gbbbbbg faa gbbbbbg aaa gbbbbbg aaa gbbbbbg aaa gbbbbbg aaa gbbbbbg cccccccccccaaaccccc bbbbbbg dddddddddddaaaddddd bbbbbbg dddddddddddaafddddd bbbbbbd dddddddddddaafddddd bbbbbbd ddddddddddcaafddddd bbbbbbd ddddddddddcaacddddd bbbbbbe ddddddddddfaadddddd bbbbbbe ddddddddddfaadddddd ebbbbbbcdddddddddaaadddddd dfa ebbbbbbcdddddddaaadddddd aaa ebbbbbbddddddaaadddddd faa ebbbbbbddddaaadddddd eaac dcbbbbbbddaaadddddd aaa dddcbbbbbbaaadddddd aaa dddddgbbbbbbfdddddd aaa dddddddgbbbbbbddddd faae dddddddddgbbbbbbddd eaac dddddddddcaabbbbddd aaa dddddddddfaadgbbddd aaa dddddddddfaaddddddd aaa dddddddddaaaddddddd caae caaaa dddddddddaaaddddddd eaac daaaaaaaaf dddddddddaaaddddddd aaa daaaaaaaaaaaaa dddddddddaaaddddddd aaa efaaaaaaaaafd caaf dddddddddaaaddddddd aaa efaaaaaaaaaad aaa dddddddddaaaddddddd caae caaaaaaaaaac daaa dddddddddaafddddddd eaac caaaaaaaaaac aaae dddddddddaafddddddd aaa daaaaaaaaaafe eaaa ddddddddcaacddddddd aaa efaaaaaaaaafe aaae ddddddddcaacddddddd aaa efaaaaaaaaaad eaaa ddddddddfaadddddddd caae caaaaaaaaaac aaad ccccccccaaacccccccc eaac caaaaaaaaaac aaa aaa aaadaaaaaaaaaafe aaac aaa aaaaaaaaaafe aaa aaa aaaaaaad faac aaa eaac aaa aaa faaf aaa aaa aaf caaf eaac aaa eaad daaa daae aaae caa eaaa faa aaae aaa eaaa aaa aaadaaa aaaaaa aaaaaa aaaaa faaaf aaac faad aa ``` <!-- end of image --> Let's see if area A yields any clues. <!-- image --> ```palette Key,Color ,#fefefeff a,#49cb2fff b,#291486ff c,#aee8a2ff d,#a59ecaff e,#dae8ddff f,#7fda6cff g,#5e579dff ``` ```image caaaaae faaaaae faaaaa faaaaa faaaaa aaaaaf aaaaaf aaaaaf eaaaaac eaaaaac caaaaac caaaaae caaaaae faaaaae faaaaa faaaaa e faaaaa bge aaaaaf bbbge aaaaaf bbbbbge aaaaaf bbbbbbbge eaaaaac bbbbbbbbbge eaaaaac bbbbbbbbbbbge caaaaac egbbbbbbbbbbbge caaaaae egbbbbbbbbbbbde caaaaae egbbbbbbbbbbbde faaaaae egbbbbbbbbbbbd faaaaa egbbbbbbbbbbbgaaaaa egbbbbbbbbbbbgaaa dgbbbbbbbbbbbgf dgbbbbbbbbbbbd dgbbbbbbbbbbbd dgbbbbbbbbbbbd dbbbbbbbbbbbbd caabbbbbbbbbbbd caaaabbbbbbbbg caaaaadbbbbbbd faaaaae dbbbg faaaaa dbd faaaaa faaaaa aaaaaf aaaaaf aaaaaf eaaaaac eaaaaac caaaaac caaaaae caaaaae faaaaae faaaaa faaaaa aaaaaa aaaaaf aaaaaf eaaaaaf eaaaaac eaaaaac caaaaac caaaaae caaaaae faaaaae ``` <!-- end of image --> Oh my, look at that! It's 1 intersection in area A! Answer: A: 1; 1 = 1 One intersection, that's it, but I found it.

<!-- image --> ```palette Key,Color ,#fefefeff a,#49cb2eff b,#2a1486ff c,#a3e596ff d,#a9a1cdff e,#d8e9daff f,#75d761ff g,#6555a8ff ``` ```image ee aaa aaa aaa aaa aaa gd aaf bbbbd aaf bbbbbbbe eaac gbbbbbbbbbe caae gbbb ebbbbbbe caae dbbbe ebbbbbbe faa ebbbd ebbbbbbe aaa bbbg ebbbbbbe aaa ebg ebbbbbb aaa ebbbbbb aaa dbbbbbb aaa dbbbbbb aaa dbbbbbb aaf dbbbbbg aaf dbbbbbg eaac dbbbbbg caae dbbbbbg caae gbbbbbg faa gbbbbbg aaa gbbbbbg aaa gbbbbbg aaa gbbbbbd aaa gbbbbbd aaa gbbbbbd aaa gbbbbbd aaf bbbbbbd aaf bbbbbbd eaac bbbbbbd caae bbbbbbd caae bbbbbbe faa ebbbbbbe aaa cfa ebbbbbbe aaa aaa ebbbbbbe aaa faae ebbbbbbe aaa eaac ebbbbbb aaa aaa ebbbbbbaaa aaa dbbbbbbf aaa dbbbbbb faae dbbbbbb eaac caabbbb aaa caaedbg aaa faa aaa aaa faae caaaa aaa eaac caaaaaaaaf aaa aaa caaaaaaaaaaaaa aaa aaa efaaaaaaaaafe caaf aaa aaa efaaaaaaaaaac aaa aaa caae caaaaaaaaaac caaa aaf eaac caaaaaaaaaace aaae eaac aaa caaaaaaaaaafe eaaa eaac aaa efaaaaaaaaafe aaae caae aaa efaaaaaaaaaac eaaa caae caae caaaaaaaaaac aaac faa eaaf caaaaaaaaaac aaa aaa aaacaaaaaaaaaafe aaac aaa aaaaaaaaaafe aaa aaa aaaaaaac faac aaa eaac aaa aaa faaf aaa aaa aaf caaf eaac aaa eaac caaa caae aaae caa eaaa faa aaae aaa eaaa aaa aaacaaa aaaaaa aaaaaa aaaaa faaaf aaac faac aa ``` <!-- end of image -->

I have a feeling there might be some intersections in this image. I've noticed 1 areas of interest. These could be potential intersection zones. <!-- image --> ```palette Key,Color ,#fefefeff a,#84d985ff b,#62d364ff c,#acba86ff d,#d5e3c9ff e,#eef6edff f,#b3d8b1ff g,#a8d2a4ff ``` ```image egfffffffffffffffffffffge egfffffffffffffffffffffge egfffffffffffffffffffffge dfa egfffffffffffaagfffffffge edgabbbbbbbb egffffffffffbbbbbbbbagfge edgabbbbbbbbbbbbbbbbe egffffffffccbbbbbbbbbbbbbafe efabbbbbbbbbbbbbbbbbbbbbbbbae egfffffffcccbbbbbbbbbbbbbbbbbbbafdfabbbbbbbbbbbbbbbbbbbbbbbbafe egffffffgcccbbbffgaabbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbagde egffffffcccbbbbffffffffgfabbbbbbbbbbbbbbbbbagde egfffffccccbbbaffffffffge efabbbafd egffffcccccbbbfffffffffge egfffgccccgbbbfffffffffge egfffccccfabbbfffffffffge egffccccffbbbbgffffffffge egfccccfffbbbccffffffffge egccccgfffbbbccffffffffge egccccfffgbbbccffffffffge eccccffffabbbccgfffffffge ccccfffffbbbacccfffffffge ccccgfffffbbbgcccfffffffge dccccffffffbbbfcccfffffffge eccccffffffabbbfcccgffffffge ccccgffffffbbbafccccffffffge ccccegffffffbbbgfgcccffffffge gcccdegffffffbbbfffcccffffffge dcccg egfffffgbbbfffcccgfffffge cccc egfffffabbbfffccccfffffge cccc egfffffbbbafffgcccfffffge cccce eggggggbbbgggggcccgggggge fcccd eeeeeebbbeeeeecccdeeeee ecccc fbbb cccf cccc bbba dccc cccc bbbd ccc gcccd bbb ccce dcccg dbbb cccf ecccc abbb dccc ccc bbbf ccc fe bbbe ccce bbb cccf fbbb dccc bbba ccc bbbd ccce bbb cccd dbbb dccc abbb eccc fcd bbbf ccc cccd bbbe cccd eccc gbbb fccc cccc bbbg eccc ccce dbbb ccc eccc bbba cccd cccc ebbb fccc ccce bbbb eccc dccc bbbe ccc cccf abbb cccd ccc bbbf fccc dccc gbbb eccc cccf bbbg ccc ccc dbbb ccccf fccc bbba dcccccf cccd ebbb dccccccd eccc bbbb dccccccd gccc bbbe fccccccd cccd abbb fcccccce eccc bbbf gcccccce cccc fbbb ccccccce ccce bbbg ccccccc dccc dbbb eccccccc cccc bbba eccccccg ccce ebbb eccccccf dccc bbbb dccccccf cccf bbbe dccccccd ccc abbb dccccccd dccc bbbf fccccccdcccf fbbb fccccccccd bbbg gcccccce dbbb ccccc bbba ccc ebbb bbbb bbbe abbb bbbf ebbb f ``` <!-- end of image --> Let's zoom in on area A to get a clearer view. <!-- image --> ```palette Key,Color ,#fefefeff a,#87d683ff b,#62d264ff c,#acba86ff d,#d0e4c6ff e,#e8f1e3ff f,#aae5aaff g,#c0cba5ff ``` ```image efffde ebbbbbbbaffde abbbbbbbbbbbbbaffde ebbbbbbbbbbbbbbbbbbbbaff gcgfbbbbbbbbbbbbbbbbbbbbbbb gcccabbbbbbbbbbbbbbbbbbbbbbb gccccbbbbbbbbbbbbbbbbbbbbbbbb dcccccbbbbbbadfabbbbbbbbbbbbbb eccccccbbbbbbd edfabbbbbbbb eccccccabbbbbbe eddfabb gccccccbbbbbbb e gcccccccbbbbbba dccccccccbbbbbbf eccccccccabbbbbbd cccccccccabbbbbb gcccccccddbbbbbba dcccccccg ebbbbbba ecccccccg dbbbbbbf ecccccccce fbbbbbbc gccccccce abbbbbbc gcccccccd bbbbbbbce dcccccccg ebbbbbbacd ecccccccc dbbbbbbccg cccccccce fbbbbbbccc gcccccccd abbbbbbccce dcccccccg bbbbbbacccd ecccccccg ebbbbbbacccg ecccccccce fbbbbbbccccc gccccccce abbbbbbccccce gcccccccd bbbbbbbcccccd cccccccg ebbbbbbacccccg ccccccc dbbbbbbgcccccc cccccce fbbbbbbdcccccce cccccd abbbbbaeccccccd ccccg bbbbbbf ccccccg cccg ebbbbbbd gcccccc ccce fbbbbbbe dcccccce cce abbbbbb eccccccd cd bbbbbba ccccccg g ebbbbbbf gcccccc dbbbbbbd dcccccce fbbbbbb eccccccd abbbbba ccccccg bbbbbbf gcccccc ebbbbbbd dcccccce fbbbbbbe eccccccd abbbbbb ccccccg bbbbbba gcccccc ebbbbbbf dcccccce dbbbbbbd eccccccd ``` <!-- end of image --> There is 1 intersection point visible in this close-up of area A. Answer: A: 1; 1 = 1 I've found a single intersection point in the image.

<!-- image --> ```palette Key,Color ,#fefefeff a,#8add8bff b,#62d364ff c,#acba86ff d,#d7e5ccff e,#ebf3e6ff f,#b3e9b4ff g,#c4ceaaff ``` ```image dfa ffe edfabbbbbbbb abbbbbbafe efabbbbbbbbbbbbbbbbb ggbbbbbbbbbbbbbafe efabbbbbbbbbbbbbbbbbbbbbbbbae gccbbbbbbbbbbbbbbbbbbbafdfabbbbbbbbbbbbbbbbbbbbbbbbafe ecccbbb efabbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbafe cccbbbb efabbbbbbbbbbbbbbbbbafde ccccbbbf efabbbafd cccccbbb dcccgdbbb ecccc fbbb cccc bbbbd cccc bbbcg gcccd bbbcc dcccg dbbbcc cccc abbbcce cccc bbbaccg cccce bbbdccc gcccg bbb ccc ecccc fbbb ccce cccc bbba cccg cccc bbbd dccc gcccd bbb ccc dcccg dbbb ccce cccc abbb cccg cccc bbbf dccc cccce bbb ccc gcccg bbb ccce ecccc fbbb cccg cccc bbba dccc cccc bbbd ccc gcccd bbb ccce dcccg dbbb cccg cccc abbb dccc ccc bbbf ccc ge bbb ccce bbb cccg fbbb dccc bbba ccc bbbd ccc bbb cccg dbbb gccc abbb ccc gcg bbbf ccc cccd bbb cccd eccc fbbb gccc cccc bbba eccc ccce dbbb ccc eccc bbba cccd cccc ebbb gccc ccce bbbb eccc dccc bbbe ccc cccg abbb cccd ccc bbbf gccc dccc fbbb eccc cccg bbba ccc ccc dbbb ccccg gccc bbba gcccccg cccd ebbb dccccccd ccc bbbb dccccccd gccc bbbe gccccccd cccd abbb gcccccce eccc bbbf gcccccce cccc fbbb ccccccc ccce bbba ccccccc eccc dbbb ccccccc cccc bbba eccccccg ccce ebbb eccccccg dccc bbbb dccccccg cccg bbbe dccccccd ccc abbb dccccccd dccc bbbf gccccccdcccg fbbb gccccccccd bbba gcccccc dbbb ccccc bbba ccc ebbb bbbb bbbe abbb bbbf ebbb f ``` <!-- end of image -->

The hunt for intersections begins! Let's analyze this image closely. I'd describe these as 'hotspots' for potential intersections. <!-- image --> ```palette Key,Color ,#fefefeff a,#f28f06ff b,#54c6baff c,#d1c27dff d,#7fceb9ff e,#dfa942ff f,#b1d7b1ff g,#95c995ff ``` ```image aaa eaac fgggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggf aaa gfffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffg caaa gfffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffg aaa gfffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffg aaa gfffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffg eaae gfffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffg aaa gfffffffffffffffffffffffffffffffffffffffffffffffffffffffffffbfffg aaa gffffffffffffffffffffffffffffffffffffffffffffffffffffffffffbbbffg aaac gffffffffffffffffffffffffffffffffffffffffffffffffffffffffffbbbffg aaa gfffffffffffffffffffffffffffffffffffffffffffffffffffffffffbbbfffg caae gfffffffffffffffffffffffffffffffffffffffffffffffffffffffffbbbfffg aaa gffffffffffffffffffffffffffffffffffffffffffffffffffffffffbbbffffg aaa gffffffffffffffffffffffffffffffffffffffffffffffffffffffffbbbffffg eaac gfffffffffffffffffffffffffffffffffffffffffffffffffffffffbbbfffffg aaa gffffffffffffffffffffffffffffffffffffffffffffffffffffffdbbbfffffg caaa gffffffffffffffffffffffffffffffffffffffffffffffffffffffbbbffffffg aaa gfffffffffffffffffffffffffffffffffffffffffffffffffffffdbbdfcacffg aaa gfffffffffffffffffffffffffffffffffffffffffffffffffffffbbbffaaaffg eaac gffffffffffffffffffffffffffffffffffffffffffffffffffffdbbdfcaaaffg aaa gffffffffffffffffffffffffffffffffffffffffffffffffffffbbbffaaafffg caaa gfffffffffffffffffffffffffffffffffffffffffffffffffffdbbdfcaaefffg aaaf gfffffffffffffffffffffffffffffffffffffffffffffffffffbbbffaaaffffg aaa gffffffffffffffffffffffffffffffffffffffffffffffffffdbbdfcaaeffffg eaae gffffffffffffffffffffffffffffffffffffffffffffffffffbbbffaaafffffg aaa gfffffffffffffffffffffffffffffffffffffffffffffffffdbbdfeaaefffffg aaa gfffffffffffffffffffffffffffffffffffffffffffffffffbbbffaaaffffffg aaacgffffffffffffffffffffffffffffffffffffffffffffffffdbbdfeaaeffffffg aaagffffffffffffffffffffffffffffffffffffffffffffffffbbbffaaafffffffg caaafffffffffffffffffffffffffffffffffffffffffffffffdbbdfeaacfffffffg aaafffffffffffffffffffffffffffffffffffffffffffffffbbbffaaaffffffffg aaafffffffffffffffffffffffffffffffffffffffffffffbbbdfeaacffffffffg eaaeffffffffffffffffffffffffffffffffffffffffffffbbbffaaafffffffffg aaafffffffffffffffffffffffffffffffffffffffffffbbbffaaacfffffffffg caaaffffffffffffffffffffffffffffffffffffffffffbbbffaaaffffffffffg gaaacffffffffffffffffffffffffffffffffffffffffbbbffaaacffffffffffg gfaaaffffffffffffffffffffffffffffffffffffffffbbbffaaafffffffffffg gfeaaeffffffffffffffffffffffffffffffffffffffbbbffaaaffffffffffffg gffaaaffffffffffffffffffffffffffffffffffffffbbbffaaaffffffffffffg gffcaaafffffbbfffffffffffffffffffffffffffffbbbffaaafffffffffffffg gfffaaacfffdbbbffffffffffffffffffffffffffffbbbfcaaafffffffffffffg gffffaaafffdbbbdffffffffffffffffffffffffffbbbffaaaffffffffffffffg gffffeaaeffbbbbbffffffffffffffffffffffffffbbbfcaaaffffffffffffffg gfffffaaaffbbbbbbffffffffffffffffffffffffbbbffaaafffffffffffffffg gffffffaaafbbbbbbffffffffffffffffffffffffbbbfcaaefffffffffffffffg gffffffaaacbbbfbbbffffffffffffffffffffffbbbffaaaffffffffffffffffg gfffffffaaabbdfbbbdfffffffffffffffffffffbbbfcaaeffffffffffffffffg gfffffffcaaabdffbbbffffffffffffffffffffbbbffaaafffffffffffffffffg gffffffffaaadfffdbbdffffffffffffffffffdbbbfeaaefffffffffffffffffg gfffffffffaaaffffbbbffffffffffffffffffbbbffaaaffffffffffffffffffg gfffffffffeaaefffdbbbffffffffffffffffdbbbfeaaeffffffffffffffffffg gfffffffffbaaaffffbbbffffffffffffffffbbbffaaafffffffffffffffffffg gfffffffffbgaaaffffbbbffffffffffffffdbbdfeaacfffffffffffffffffffg gfffffffffbbaaacfffbbbdfffffffffffffbbbffaaaffffffffffffffffffffg gfffffffffbbdaaaffffbbbffffffffffffdbbdfeaacffffffffffffffffffffg gffffffffdbbfeaaefffdbbdfffffffffffbbbffaaafffffffffffffffffffffg gffffffffdbbffaaaffffbbbffffffffffdbbdfaaacfffffffffffffffffffffg gffffffffbbbffcaaafffdbbdfffffffffbbbffaaaffffffffffffffffffffffg gffffffffbbbfffaaacfffbbbffffffffdbbdfaaacffffffffffffffffffffffg gffffffffbbbffffaaafffdbbdfffffffbbbffaaafffffffffffffffffffffffg gfffffffbbbbffffeaaafffbbbffffffdbbdfaaaffffffffffffffffffffffffg gfffffdbbbbffffffaaafffdbbffffffbbbffaaaffffffffffffffffffffffffg gffffbbbbbffffffffaaafffbbbffffdbbdfaaafffffffffffffffffffffffffg gffdbbbbffffffffffeaaeffbbbffffbbbffaaafffffffffffffffffffffffffg gfbbbbbffffffffffffaaafffbbbffdbbdfaaaffffffffffffffffffffffffffg bbbbbffffffffffffffcaaaffbbbffbbbfcaaaffffffffffffffffffffffffffg bbbbbffffffffffffffffaaacffbbdbbbdfaaafffffffffffffffffffffffffffg dbbbbfffffffffffffffffffaaaffbbbbbbfcaaafffffffffffffffffffffffffffg bbbbbffffffffffffffffffffeaaefdbbbbffaaaffffffffffffffffffffffffffffg dbbbb gfffffffffffffffffffffaaaffbbbbfcaaeffffffffffffffffffffffffffffg bbbbd gfffffffffffffffffffffcaaafdbbffaaafffffffffffffffffffffffffffffg dbbbb gffffffffffffffffffffffaaacfddfcaaefffffffffffffffffffffffffffffg bbbbd gfffffffffffffffffffffffaaaffffaaaffffffffffffffffffffffffffffffg dbbbb gfffffffffffffffffffffffeaaeffeaaeffffffffffffffffffffffffffffffg bbbbd gffffffffffffffffffffffffaaaffaaafffffffffffffffffffffffffffffffg dbbbb gfffffffffffffffffffffffffaaaeaaefffffffffffffffffffffffffffffffg bbbbd gfffffffffffffffffffffffffaaaaaaffffffffffffffffffffffffffffffffg dbbbb gffffffffffffffffffffffffffaaaacffffffffffffffffffffffffffffffffg bbbbd caaa bbbb aa bd ``` <!-- end of image --> I wonder what we'll find inside area A? <!-- image --> ```palette Key,Color ,#fefefeff a,#f28f06ff b,#54c6bbff c,#f7c783ff d,#85d6ceff e,#f0a83fff f,#fbe4c4ff g,#c3eae7ff ``` ```image bbd bbbd bbbb bbbb dbbbb bbbbb gbbbb dbbbg dbbbg gbbbb dbbbb bbbbg gbbbd dbbbg bbbbb cc gbbbbd aaa bbbbd faaae bbbbg eaaac gbbbd faaaa gbbbb aaaae bbbbb aaaaf bbbbd faaae gbbbd caaae bbbb aaaaf bbbb aaaaa dbbbb aaaae bbbbb aaaaf bbbb aaaa dbbbg caaaa bbbb faaaaa gbbbbb aaaaa e dbbbbg aaaac a bbbbg eaaac ac gbbbb faaaa aaf dbbbg eaaaa aaaf dbbbb aaaaf aaaa gbbbbd faaae aaaa dbbbbg eaaaf caaae bbbbg eaaaf aaaac gbbbd caaaa eaaaac gbbbb aaaae faaaaa bbbbb aaaaf caaaa bbbbd caaae faaaa gbbbd caaaa aaaae bbbb aaaaa aaaaa gbbbd caaaac eaaac gbbg gbbbb aaaac faaaaf bbbbg bbbbb faaaa aaaaf bbbbbg bbbb faaaa aaaaa bbbbbb dbbbd eaaaa eaaaa bbbbbb bbbb faaaaa caaae bbbbbbd bbbbb aaaae aaaac bbbbbbbg dbbbbg aaaaf aaaaa bbbbbbbd bbbbb faaae faaaaa gbbbgbbbbb bbbb faaaa caaaa gbbb dbbbb dbbbg eaaaa faaaadbbb dbbbd dbbbb aaaaf aaaaebbb bbbbg bbbbb caaae aaaaabbb bbbbd bbbbg aaaaf eaaaebb gbbbb dbbbg aaaaf faaaabb dbbbd gbbbd caaaa caaaeb bbbbg dbbbg aaaaa aaaaa bbbbg dbbbb aaaa eaaaa bbbbb bbbbd caaac beaaae gbbbb gbbbd caaaa bbaaaac dbbbd bbbbg faaaaa bbaaaaa bbbbg gbbbb eaaaac bbbaaaaa bbbbbg gbbbbd aaaac bbbcaaaa gbbbbb bbbbbg faaae bbbgeaaac dbbbb bbbbd eaaac gbbbg aaaae dbbbd gbbbd eaaaa gbbb aaaaaf bbbbg bbbb aaaae dbbd eaaaa bbbbb bbbbb faaae dbbd faaaaf gbbbb bbbbd eaaaf bbbd caaae bbbb bbbb caaae gbbbg aaaaa bbbb bbbb caaaa gbbb eaaaa dbbbg dbbbg aaaaa gbbbb faaaaf bbbb bbbb aaaae gbbbbbb eaaac bbbbd bbbbb caaac dbbbbbbd faaaaf dbbbb bbbbg aaaa dbbbbbbd aaaaa dbbb dbbbg aaaaa gbbbbbbg caaaa gbbbd gbbbb caaaac dbbbbbb eaaac bbbb dbbbb aaaaa dbbbbbd aaaae bbbbb dbbbbg faaaa gbbbbbbb aaaaac dbbbbg bbbbd eaaac bbbbbbd caaaaa bbbbd bbbbg faaaa bbbbbd faaaaf gbbbb dbbbg aaaae bbbbg caaae dbbbgbbbb aaaaf bbg aaaaa bbbbbbbd eaaaf b eaaaa bbbbbbbg faaae g faaaaf bbbbbbd eaaaf eaaac bbbbd eaaaa faaaaf dbbbg aaaae aaaae bbb aaaaf caaaa aaaaf eaaac caaaa aaaae caaaac aaaaac aaaaa faaaaa aaaac faaaafcaaac caaaaaaaa aaaaaaaa eaaaaaac ``` <!-- end of image --> The close-up clearly shows 1 intersection point in area A. Answer: A: 1; 1 = 1 I have found one intersection!

<!-- image --> ```palette Key,Color ,#fefefeff a,#f28f06ff b,#54c6bbff c,#f9cb8bff d,#89d7d0ff e,#f4ab45ff f,#fce7ccff g,#d1efecff ``` ```image ff aaa eaac aaa caaa aaaf aaa eaae aaa bg faaa bbb aaac gbbb aaa bbb caae gbbb aaa bbb faaa gbbd eaac bbb aaa gbbd caaa bbb aaaf gbbd fac aaa bbb aaa eaae gbbd faae aaa bbb aaa faaa dbbd caae aaaf bbb aaa aaa dbbd caae eaae bbb aaa aaa dbbd caac faaa bbb aaa aaac dbbg eaac aaa bbb aaa caae dbbg eaac aaaf bbb aaa faaa dbbg eaac eaac bbb aaa aaa dbbg eaaf caaa bbb aaa aaaf bbbg aaaf aaa bbb aaa eaae bbbg aaaf aaa bbb faaa faaa bbg bbb aaa aaac gbbb bbb faaa aaa dbbbd bbb aaa caae bbbbb bbb faae aaa bbbbbd bbb aaa faaa bbbbbb gbbb faae eaacbbdgbbb bbb aaa aaabbd bbbg gbbb caae caaabg bbb bbb aaa aaab dbbd gbbd caae aaa bbb bbb aaa eaae gbbb gbbd caac baaa bbb bbb aaa bbaaa bbb gbbd eaac bbaaaf bbbg bbb aaa bbgaaa bbb gbbd eaac gbbgeaae dbbd bbb aaa dbb aaa bbb dbbd eaaf dbb faaa gbbd bbb aaa bbb aaac bbb dbbd aaaf bbb aaa dbbg bbb aaa bbbb caae bbb dbbd aaaf dbbbb aaaf dbbg bbb aaa bbbbd faaa bbb dbbg aaa dbbbbg eaac bbb bbb faaa bbbbd aaa bbb dbbg aaa dbbbbg caaa bbb bbb faaa gbbbbd aaaf gbbddbbg aaa dbbbbg aaa bbbbbb faae gbbbbd eaae gbbbbg aaa dbbbbg aaa bbbb caae gbbbbd faaa dbbg aaa dbbbbg aaac dd caae gbbbbd aaa aaa dbbbb caae caac gbbbbd aaa aaa dbbbb faaaeaac gbbbbd eaaaaa dbbbb aaaac gbbbbd caaa bbbb aaf bd ``` <!-- end of image -->

Let's examine this image for potential line intersections. These zones are intriguing. I bet there's something interesting happening within them. <!-- image --> ```palette Key,Color ,#fefefeff a,#8d7664ff b,#7bcc71ff c,#d5ddccff d,#b1d7b1ff e,#95cc94ff f,#a89f8eff g,#eef4edff ``` ```image cd aaf aaaa acdaa ca caa fa gaag dad aa aac gaaaa aa aad faaccac af aaf caaf aa ac faf gaaag dag ca faa faac aa fa caa caaf fa aa gaa aaag af af gaag faac aa ad aac caaf gad aaf aaag aa aaf faad cac faa caaa aa daaaaag cag caaf aa fa af aa af aa gac aa cag ebeg aa bbbbbeg fa be cbbbbbc gggggggafggggggggggggggggggggggggg bc gebbbbc eddddddaadddddddddddddddddddddddde gbg gebbbbd edddddddafddddddddddddddddddddddde cb dbbbbd edddddddaaddddddddddddddddddddddde eb dbbbbeg eddddddddafdddddddddddddddddddddde bb cbbbbbc eddddddddaadddddddddddddddddddddde bb gebbbbc eddddddddfadddddddddddddddddddddde bd gebbbbd edddddddddaaddddddddddddddddddddde bc dbbbbd edddddddddfaddddddddddddddddddddde gb dbbbbeg eddddddddddaadddddddddddddddddddde db cbbbbeg eddddddddddaadddddddddddddddddddde eb cbbbbbeddddddddddafddddddddddddddddddde bb gebbbbedddddddaaddddddddddddddddddde be edebbbbedddddafdddddddddddddddddde bd eddddebbbbeddaadddddddddddddddddde bc edddddddebbbbbadddddddddddddddddde cb eddddddddddebbaaddddddddddddddddde db edddddddddddddaaddddddddddddddddde bb eddddddddddddddaadddddddddddddddde bb eddddddddddddddaadddddddddddddddde be edddddddddddddddaaddddddddddddddde bd edddddddddddddddaaddddddddddddddde gbg eddddddddddddddddabdddddddddddddde cb eddddddddddddddddaadddddddddddddde db eddddddddddddddddfabddddddddddddde bb edddddddddddddddddaaddddddddddddde bb edddddddddddddddddfabdddddddddddde be eddddddddddddddddddaadddddddddddde bc eddddddddddddddddddaabddddddddddde gbg edddddddddddddddddddaaddddddddddde cb edddddddddddddddddddaaedddddddddde eb eddddddddddddddddddddabdddddddddde bb eddddddddddddddddddddaaeddddddddde bb eddddddddddddddddddddfabddddddddde bd edddddddddddddddddddddaaedddddddde bc edddddddddddddddddddddfabdddddddde gb eddddddddddddddddddddddaaeddddddde db eddddddddddddddddddddddaabddddddde eb edddddddddddddddddddddddaaedddddde bb edddddddddddddddddddddddaabdddddde be eddddddddddddddddddddddddabeddddde bd eddddddddddddddddddddddddaabddddde bc eddddddddddddddddddddddddeabedddde cb edddddddddddddddddddddddddaabdddde db edddddddddddddddddddddddddfabeddde bb eddddddddddddddddddddddddddaabddde bb eddddddddddddddddddddddddddaabedde be edddddddddddddddddddddddddddaaddde bd edddddddddddddddddddddddddddaaddde eddddddddddddddddddddddddddddafdde eddddddddddddddddddddddddddddfddde edddddddddddddddddddddddddddddddde deeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeed ``` <!-- end of image --> Here's a close-up of the area A. <!-- image --> ```palette Key,Color ,#fefefeff a,#8d7563ff b,#7ccb72ff c,#cbd3bfff d,#b3a599ff e,#a6dc9fff f,#909171ff g,#e4ebdfff ``` ```image daaf caaag faad caaag aaad caaa aaac daaf gaaac daaf gaaag faad caaag aaad caaa aaac daaf gaaac daaf gaaag faad caaag beg faad bbbbec caaa bbbbbbbecg aaac cebbbbbbbbecg daaf cebbbbbbbbbeg gaaac gebbbbbbbbbeg daaf gebbbbbbbbbeg gaaag gcbbbbbbbbbec faad gcebbbbbbbbbaaag cebbbbbbaaad gebbbfaaag gebaaad faaa gaaad faaa caaae faaf caaac aaaf daaac aaaf daaac gaaaf daaag gaaab faafg caaab faafg caaae aaafg daaae gaaafg daaae gaaabg faafe caaabg faafe caaabg aaafe daaabg gaaafe daaabg gaaabe daafbg caaabe faafbg caaabe aaafbg daaabe gaaafbg daaabe gaaabb daafbe caaabb faafbe caaabb aaafbc daaabb gaaafbc daaabb gaaabbc daafbb caaabbc faafbb caaabbc aaafbb daaabbc gaaafbb daaabbc gaaabbb daaabbc caaabbe faafg caaag aaad daaa gaaac dafc gc ``` <!-- end of image --> The evidence is clear: there's 1 intersection in area A. Answer: A: 1; 1 = 1 The final count is: one intersection.

<!-- image --> ```palette Key,Color ,#fefefeff a,#8d7564ff b,#7bcd72ff c,#cedec6ff d,#c1b3aaff e,#a3dc9dff f,#a19381ff g,#eaeee6ff ``` ```image cd aaf aaaa acdaa ca caa da gaag dad aa aag gaaaa aa aad faacgac ad aaf caaf aa ag faf aaa dag ca daa faac aa fa caa caaf fa aa gaa aaag af af gaag faad fa ad aac caaf ad aad aaag aa faf daad gac faa gaaf aa daaaaag dag caad aa da af fa ad aa gac aa cag bbeg aa bbbbbeg da be cbbbbbc af bc gebbbbc fa gbg ebbbbe ad cb ebbbbe aa eb cbbbbeg gac bb cbbbbbg aa bb gbbbbbc cag be gebbbbc aa bc ebbbbe da gb cbbbbeg af cb cbbbbeg fa eb cbbbbbc ad bb gebbbbc aa bb ebbbbe gac be ebbbbe aa bg cbbbbfag cb cbbaa eb fa bb aa bb aa be af bc aa bg gaf cb aa eb cab bb aa bb dae be aa bc fae gbg aa cb aae eb gab bb aae bb cab be aae bc dab gb aae cb fab eb aae bb aab bb gabc be aab bg cabc cb aab eb dabc bb aab bb fabc be af bc aa gad c ``` <!-- end of image -->

The hunt for intersections begins! Let's analyze this image closely. I wonder what's going on inside those areas? Perhaps intersections are hiding there. <!-- image --> ```palette Key,Color ,#fefefeff a,#f03007ff b,#e1a381ff c,#b36c0dff d,#b1d7b1ff e,#9ec693ff f,#d87848ff g,#f5d6c7ff ``` ```image baa faa aaf aab aag aa aa gaa baa faa aaf aab aag aa aa gaa baa faa aaf aab aag aa eeeeeeeeeeeeeeaaeeeeee dddddddddddddeaadddddd dddddddddddddbaadddddd dddddddddddddfaadddddd gb gccgdddddddddddddaafdddddd bcc cccccdddddddddddddaafdddddd eeccddddddddddde fcccccccddddddddddddaabdddddd edccdddddddddddd bccccg gccfdddddddddddaaddddddd edccdddddddddddd gccccb bcceddddddddddaaddddddd edcceddddddddddd ccccf cccdddddddddeaaddddddd edcceddddddddddd bcccc dcccddddddddbaaddddddd edccfddddddddddd gccccg deccfdddddddfaaddddddd ebaacddddddddddd ccccb ddfcceddddddaaaddddddd efaacddddddddddd fcccf dddcccddddddaafddddddd eeaacddddddddddd bcccc ddddcccdddddaabddddddd edaacddddddddddd gccccg ddddeccfddddaadddddddd edaacddddddddddd ccccb dddddfccedddaadddddddd edaacedddddddddd fcccc ddddddcccdddaadddddddd edaaaedddddddddd bccccg dddddddcccdbaadddddddd edfaafdddddddddd gccccb dddddddeccffaadddddddd edfaacdddddddddd ccccf ddddddddfccaaadddddddd edeaacdddddddddd fcccc dddddddddccaafdddddddd eddaacdddddddddd bccccg ddddddddddcaabdddddddd eddaacdddddddddd gccccb ddddddddddeaafdddddddd eddaacdddddddddd ccccf dddddddddddaaceddddddd eddaaadddddddddd bcccc dddddddddddaaccddddddd eddfaaeddddddddd gccccg ddddddddddbaacccdddddd eddfaafddddddddd ccccb ddddddddddfaaeccfddddd eddeaacddddddddd fcccc ddddddddddaaadfccedddd edddaacddddddddd bcccc ddddddddddaafddcccdddd edddaacddddddddeccccg ddddddddddaabdddcccddd edddaacdddddddccccb ddddddddddaaedddecfddd edddaaadddddccccc ddddddddddaadddddedddd edddfaadddbcccce ddddddddddaadddddddddd edddfaaeeccccbdd dddddddddbaadddddddddd edddeaaccccfdddd dddddddddfaadddddddddd eddddaacccdddddd dddddddddaaadddddddddd deeeeaaceeeeeeee dddddddddaafdddddddddd aab dddddddddaabdddddddddd aaf dddddddddaaedddddddddd faa dddddddddaaddddddddddd baa dddddddddaaddddddddddd gaa ddddddddbaaddddddddddd aa ddddddddfaaddddddddddd aag ddddddddfaaddddddddddd aab ddddddddaafddddddddddd aaf ddddddddaabddddddddddd faa eeeeeeeeaaeeeeeeeeeeee baa aa gaa aa aaaafbgg gaa aaaaaaaaaaaaaafbgg baa bbfaaaaaaaaaaaaaaaaaaaafbbg faa ggbfaaaaaaaaaaaaaaaaaaaaffbg aaf ggbfaaaaaaaaaaaaaaaaaaaaafbg aab gbfaaaaaaaaaaaaaaaaaaaaafbg aag gbfaaaaaaaaaaaaaaaaaaaaaa gbffaaaaaaaaaaa gbbfb ``` <!-- end of image --> Let's see if area A yields any clues. <!-- image --> ```palette Key,Color ,#fefefeff a,#f03007ff b,#e8b696ff c,#b46c0eff d,#d34c09ff e,#c99855ff f,#f57256ff g,#f1ddcbff ``` ```image bccccg gccccb gccccb cccce cccce ecccc ecccc bccccg bccccg gccccb gccccb cccce cccce gbddacc faaaacc baaaaccg baaaadcg gaaaadcb aaaadcb aaaaace faaaace faaaacc baaaacc baaaadcg gaaaadcg aaaadcb aaaaacb faaaace faaaace baaaacc baaaadc gaaaadcg aaaadcg aaaaacb faaaacb faaaace baaaace baaaadc gaaaadc aaaadc aaaaacg faaaacb faaaacb baaaace baaaade gaaaade aaaadc aaaaac faaaacg faaaacb baaaacb ge baaaade bcc gaaaade bcccc aaaade geccccc aaaaac eccccccc faaaac bcccccccce faaaacg gcccccccceg baaaacg geccccccccb baaaadbecccccccce gaaaadcccccccceg aaaadcccccccg aaaaacccccb ``` <!-- end of image --> There is no intersection present within area A. Let's move forward and inspect another region. I'm analyzing this close-up of area B with precision. <!-- image --> ```palette Key,Color ,#fefefeff a,#f02f06ff b,#f6856dff c,#b46d0eff d,#efb9a1ff e,#ca9857ff f,#f25837ff g,#f6ded2ff ``` ```image faaaf aaaaf aaaab gaaaab daaaad daaaad baaaag baaaa faaaa faaaf aaaab e gaaaab cd daaaad ccg daaaad ccc baaaag ccce baaaa ccccd faaaa cccccg faaaf eccccc aaaab gccccce gaaaab dcccccd gaaaad ecccccg daaaad eccccc baaaag gccccce baaaa dcccccd faaaa ecccccg faaaf cccccc aaaab gccccce gaaaab dcccccd gaaaad ecccccg daaaad cccccc baaaag gccccce baaaa dcccccd faaaa ecccccg faaaf cccccc aaaaf gccccce gaaaab dcccccd gaaaad ecccccg daaaad cccccc baaaag gccccce baaaa dcccccdfaaaa ecccccfaaaf cccccaaaaf gccccaaaab dcccaaaad eccaaaad ccaaaag gaaaaae faaaacd faaaaccg aaaaacce aaaaaccce gaaaacccccd daaaafcccccg daaaadccccce baaaaggccccce faaaa dcccccd faaaf ecccccg aaaaf ccccce aaaab gccccce gaaaab dcccccd daaaad ecccccg daaaag ccccce baaaag gccceg baaaa dcd faaaf g aaaaf aaaab gaaaab daaaad daaaag baaaag baaaa faaaf aaaaf aaaab gaaaab daaaad daaaad baaaag baaaa faaaa aaaaf aaaab gaaaab daaaad daaaad baaaag baaaa faaaa faaaf aaaab gaaaab gaaaad ``` <!-- end of image --> I am surprised, so clear, 1 intersection has appeared in area B. Answer: A: 0; B: 1; 0 + 1 = 1 I've found a single intersection point in the image.

<!-- image --> ```palette Key,Color ,#fefefeff a,#f02f06ff b,#f7917bff c,#b46d0eff d,#efb9a1ff e,#cc9c5dff f,#f36142ff g,#f5ded1ff ``` ```image baa faa aaf aab aag aa aa gaa baa faa aaf aab aag aa aa gaa daa faa aaf aab aag aa aa gaa daa faa gd gccg aaf dcc ccccc aab gcc eccccccc aad cc dccccg gcce aa cc gccccd eccg aa ccg cccce ccc gaa ccd ecccc ccc daa cce dccccg gcce baa gfac cccce eccg faf baac ccccc ccc aab gaac ecccc ccc aad aac gccccd gcce aa aac cccce eccg aa aacg ecccc ccc gaa aaad dccccg ccc daa faae gccccd gccebaa baac cccce eccfaf gaac ecccc ccaab aac dccccg caad aac gccccd gaae aac cccce aacg aaag ecccc aacc faad dccccg daaccc baae cccce baagcce gaac ccccc faf eccg aac ecccc aab ccc aac gccccd aad ccc aac cccce aag gce aaa ecccc aa g faa dccccg aa baadgccccd daa gaacccce baa aaccc faa aacg aaf aad aad aaf aag faa aa daa aa gaa daa aa baa aag faa aad aaf aaf aad faa aag daa aa gaa aa aaaafbdg gaa aaaaaaaaaaaaaafbdg baa dbfaaaaaaaaaaaaaaaaaaaafbdg faa gdbfaaaaaaaaaaaaaaaaaaaafbdg aaf gdbfaaaaaaaaaaaaaaaaaaaafbbg aab dbffaaaaaaaaaaaaaaaaaaaffbd aag gbbfaaaaaaaaaaaaaaaaaaaaa gdbfaaaaaaaaaaa gdbfb ``` <!-- end of image -->

This is the image I'm working with. The goal is to count the intersections. These areas seem to enclose narrow spaces where lines might be close. <!-- image --> ```palette Key,Color ,#fefefeff a,#a6e11aff b,#dbf6aeff c,#82f219ff d,#bdeb79ff e,#a9e94bff f,#f0f8eaff g,#afd6aeff ``` ```image fb baae aaaa aaaaad baaaaaa aaaaaaad aaaa daaa baaab aaab aaae daaa aaaa aaab daaaf eaaa aaae aaaf aaaa eaaa daaaf aaaf faaae aaaa aaaa faaaf eaaaf aaaa faaad faaa aaaa aaae eaaa baaa faaad aaae aaaa baaa eaaa aaad baaab baaa aaaa aaad aaaa daaa baaab aaab aaaa daaa aaaa aaad baaab daaa aaae aaaa aaaa faaab daaaf eaaa faaae aaae aaaa baaaf daaaf aaaa faaad aaad aaaa daaaf eaaaf aaaa faaad faaab aaaa eaaafffffffffffffffffff eaaa fgaaaaggggggggggggggggggf baaad fgdaaadgggggggggggggggggf aaaa fggaaaagggggggggggggggggf aaaa fgggaaaeggggggggggggggggf baaab fgggeaaaggggggggggggggggf aaaa fggggaaaagggggggggggggggf aaaa fgggggaaaeggggggggggggccf baaab fgggggeaaaggggggggggccccf aaae fggggggaaaagggggggcccccce aaaa fggggggdaaadggggeccccccgf daaaf fgggggggaaaaggdccccccgggf aaae fggggggggaaaeccccccdggggf aaaa fggggggggdaaacccceggggggf daaaf fggggggggeaaaaccggggggggf faaae fggggggecccaaaegggggggggf aaaa fggggdcccccaaaagggggggggf eaaaf fgggccccccegaaaaggggggggf faaad fgcccccceggggaaadgggggggf aaaa eccccccggggggaaaagggggggf faaa bccccccgggggggggaaaaggggggf ed fccccccdggggggggggdaaaggggggf ccccccegggggggggggggaaaagggggf ecccccefgggggggggggggggaaaeggggf dcccccc fgggggggggggggggeaaaggggf bccccccf fggggggggggggggggaaaagggf fccccccb fgggggggggggggggggaaadggf ccccccd fgggggggggggggggggaaaaggf eccccce fggggggggggggggggggaaaagf dccccccf baaaf fd bccccccb aaaa ccccb fccccccd aaad ccccccef eccccce dae dccccccccd dcccccc f eccccccccb bccccccf fcccccccccb fccccccb bccccccccef ccccccd dccccccccd eccccce feccccccccbdcccccc bccccccccccccf dcccccccb eccd ``` <!-- end of image --> Let's put area A under the microscope. <!-- image --> ```palette Key,Color ,#fefefeff a,#a6e11aff b,#e1f8beff c,#82f218ff d,#baf16cff e,#a9ec43ff f,#f1fbe0ff g,#cff496ff ``` ```image faaaaaaab gaaaaaaaf eaaaaaad baaaaaaab daaaaaae faaaaaaag gaaaaaaaf eaaaaaae faaaaaaag gaaaaaaaf eaaaaaad baaaaaaab daaaaaae beb faaaaaaag fecce gaaaaaaaf fdccccc eaaaaaae gccccccc faaaaaaag gccccccccc gaaaaaaaf becccccccccc eaaaaaad fdccccccccccce baaaaaaab fdccccccccccccg daaaaaae gccccccccccccdf faaaaaaag becccccccccccdf baaaaaaaf beccccccccccceb daaaaaaedccccccccccccg faaaaaaacccccccccccg gaaaaaaaccccccccdf eaaaaaaacccccef fecaaaaaaaccceb fdcccaaaaaaaacg gccccccaaaaaaad gcccccccccaaaaaaaf beccccccccccaaaaaaae fdcccccccccccegaaaaaaag fdccccccccccccg gaaaaaaaf gccccccccccccdf eaaaaaad becccccccccccdf faaaaaaab beccccccccccceb daaaaaae dccccccccccccg eaaaaaad cccccccccccg baaaaaaab cccccccccdf daaaaaae cccccccef faaaaaaag ccccceb gaaaaaaaf ccccg eaaaaaad ccdf faaaaaaab df gaaaaaaaf eaaaaaad baaaaaaab daaaaaae faaaaaaag gaaaaaaaf eaaaaaae faaaaaaag gaaaaaaaf eaaaaaad baaaaaaab ``` <!-- end of image --> The close-up clearly shows 1 intersection point in area A. Answer: A: 1; 1 = 1 My investigation reveals that there is exactly one intersection in this image.

<!-- image --> ```palette Key,Color ,#fefefeff a,#a6e11aff b,#daf6adff c,#82f218ff d,#bbed64ff e,#aaeb41ff f,#edfad6ff g,#c8f286ff ``` ```image fb faad aaaa eaaaad baaaaaa aaaaaaag aaaa gaaa baaab aaab aaae daaa aaaa aaab gaaaf eaaa aaae aaaf aaaa eaaa daaaf aaaf aaad aaaa aaaa aaa daaa aaaa faaad faaa aaaa aaae eaaa faaa faaag aaad aaaa baaa eaaa aaad baaab gaaa aaaa aaag aaaa gaaa baaab aaab aaae daaa aaaa aaad gaaaf daaa aaae aaaa aaaa faaab gaaaf eaaa aaae aaae aaaa baaaf daaaf aaaa faaad aaad aaaa gaaa daaa aaaa faaag faaag aaaa eaaa eaaa aaaa faaag baaaf aaaa aaaa eaaa aaad baaab gaaa aaaa aaaa aaaa aaag fce baaab daaa cccc aaae aaaa eccccce aaaa faaab gcccccc gaaaf aaaa bccccccf aaae aaaeccccccb aaaa gaaaccccd daaaf eaaaace aaad gcccaaag aaaa fcccccaaaa daaa ccccccg aaaa faaad ecccccd faaab aaaa dcccccc eaaa faaa bccccccf aaae eg fccccccb baaaf ccccccg aaaa eccccce aaad gcccccc daaa bccccccf aaaa fccccccb faaab ccccccd eaaa dccccce aaae gcccccc baaaf fg fccccccf aaaa ccccb ccccccg aaad ccccccef ecccccd gae gccccccccd dcccccc f eccccccccg bccccccf fcccccccccf fccccccb bcccccccce ccccccg dccccccccg eccccce feccccccccbgcccccc bccccccccccccf gcccccccb dccd ``` <!-- end of image -->

I have a feeling there might be some intersections in this image. There are 2 areas where the lines seem to converge. We should take a closer look at area A,, and B. <!-- image --> ```palette Key,Color ,#fefefeff a,#b5933aff b,#b92726ff c,#e5d4bbff d,#c2ac7cff e,#bc6054ff f,#9bc896ff g,#b1d7b0ff ``` ```image cad aaa aaaac aaaaa aaacaa caac aad aaa aaa aaa caa caad aad aaa daa daa aac aaa aaa aaa caa caac aac aaa aaa cac daa caa daaaa aad aad caaaaaaa aaa daa caaaaad aa caaceb aa daaaaac aac gffaaafbbbfffffffffffaaafffffffffffffffffff caaa aad fgaaaggbbbbfgggggggggdaaggggggggggggggggggg d aaa fgaaagebbbbbfgggggggggaadgggggggggggggggggg daa faaaggbbbgbbbdggggggggaaagggggggggggggggggg caa daafggbbeggbbbdgggggggdaagggggggggggggggggg aa aaagggbbggggbbbdgggggggaadggggggggggggggggg aac daagggdbbgggggbbbdggggggaaaggggggggggggggggg aad aaagggbbbggggggbbbeggggggaaggggggggggggggggg aaa aaaggggbbegggggggbbbegggggaaagggggggggggggggg daa aadggggbbdggggggggbbbeggggdaagggggggggggggggg caa aaafgggdbbggggggggggbbbeggggaafggggggggggggggg aa caacfgggebbgggggggggggbbbegggaaaggggggggggggggg aac aaa fgggbbeggggggggggggbbbbggdaaggggggggggggggg aad daa fgggbbdgggggggggggggbbbbggaadgggggggggggggg aaa aaa fggfbbgggggggggggggggebbbgaaagggggggggggggg caa aaa fggebbggggggggggggggggebbbfaagggggggggggggg aa aad fggbbbgggggggggggggggggebbbaaaggggggggggggg aa aaa fggbbeggggggggggggggggggebbaaaggggggggggggg aac caac fggbbggggggggggggggggggggebbaafgggggggggggg aaa aaa fgebbgggggggggggggggggggggdbaaagggggggggggg daa daa fgbbbggggggggggggggggggggggdeaagggggggggggg caa aaa fgbbegggggggggggggggggggggggdaaeggggggggggg aa aaa fgbbfggggggggggggggggggggggggaaabgggggggggg aac aad fdbbgggggggggggggggggggggggggfaabbfgggggggg aad aaa febbggggggggggggggggggggggggggaaebbfggggggg aaa caac fbbeggggggggggggggggggggggggggaaabbbdgggggg daa aaa fbbdgggggggggggggggggggggggggggaafbbbdggggg caa daa dbbggggggggggggggggggggggggggggaaagbbbdgggg aa aaa ebbggggggggggggggggggggggggggggdaaggbbbeggg aac daa bbbgggggggggggggggggggggggggggggaadggbbbegg aad aad bbdgggggggggggggggggggggggggggggaaagggbbbeg aaa aaa bbggggggggggggggggggggggggggggggdaaggggbbbe daa caac dbbgggggggggggggggggggggggggggggggaadggggbbbe caa aaa bbbgggggggggggggggggggggggggggggggaaagggggbbbe aa daac bbd caa bbbb fggggggaadaaaggf bb aad ebb fggggggaaaaagggg dbb daa e fggggggaaaaagggg bbb aac fggggggdaaaggggg bbd aaa fggggggfaadggggg bb caa fgggggfbaagggggg dbb aac fgggebbbbbbggggg bbb aaa fdbbbbbbebbbgggg bbe caa ebbbbbbgggfbbbfgg bbc aad cbbbbbbdgggggggbbbfg cbb daa ebbbbbegggggggggggbbbd ebb aac dbbbbbbc fggggggggggggbbbc bbe aaa ebbbe fgggggggggggggbbbc bbc daa bc fggggggggggggggbbbc cbb aac fgggggggggggggggbbbc ebb aaa fggggggggggggggg bbbd bbe caa fggggggggggggggf bbbdbbc aad bbbbb daa bbbb aa bbe aaa c daa aac aaa caa aad aaa ac ``` <!-- end of image --> Let's see what secrets area A holds. <!-- image --> ```palette Key,Color ,#fefefeff a,#b5933aff b,#ba2626ff c,#e7ccbbff d,#d4ac89ff e,#c34845ff f,#f6e9e6ff g,#d06e6eff ``` ```image daaaaffaaaaad daaaacdaaaaaf caaaadaaaaac faaaaaaaaaa aaaaaaaaac aaaaaaaad daaaaaaaf daaaaaad caaaaaaf faaaaac faaaaa fgbeaaaef fdebbbbbebbef cgbbbbbbbbbbbbef fdebbbbbbbbbbbbbbbef cgbbbbbbbbbbbedebbbbbef debbbbbbbbbbbgc febbbbbef bbbbbbbbbbedf febbbbbef bbbbbbbbgc febbbbbef bbbbbedf febbbbbef bbbgc febbbbbbf ec febbbbbbc febbbbbb febbbbb fgbbbb gbbb gbb gb g ``` <!-- end of image --> This close-up reveals that there are no intersections in area A. I'm ready to analyze the next area. This close-up might reveal an intersection in area B. <!-- image --> ```palette Key,Color ,#fefefeff a,#b5933aff b,#ba2726ff c,#e4c0b3ff d,#ccb478ff e,#c75652ff f,#f2e2dbff g,#d88888ff ``` ```image daaaaaf gbbbbbef faaaaa faaaaad ebbbbbbef aaaaaf daaaaa fbbbbbbbbef daaaad caaaaac cbbbbbbbbbef faaaaa aaaaad gbbbbbbbbbbbf daaaac daaaaaf ebbbbcebbbbbbf caaaad faaaaac bbbbb febbbbbbf faaaaaf daaaaa cbbbbe febbbbbbc daaaac caaaaaf gbbbbg ebbbbbbc caaaaa aaaaad ebbbbc ebbbbbbc aaaaaf aaaaaf bbbbbf ebbbbbbc daaaad aaaac fbbbbe ebbbbbbc faaaaa aaaa cbbbbg gbbbbbbg aaaaac aaac gbbbbc gbbbbbbg caaaad aad ebbbbf gbbbbbbg faaaaaf aaf fbbbbb gbbbbbbg daaaac ad cbbbbe gbbbbbbg caaaad af gbbbbg cbbbbbbg aaaaaf d ebbbbf cbbbbbbe daaaad bbbbb cbbbbbbe faaaaa cbbbbe cbbbbbbe aaaaaf gbbbbg cbbbbbbe daaaad ebbbbc cbbbbbbef faaaaa bbbbb fbbbbbbef daaaac fbbbbe fbbbbbbef caaaad gbbbbg fbbbbbbef aaaaaf ebbbbc febbbbbbf daaaac bbbbbf febbbbbbf caaaaa fbbbbe febbbbbbc aaaaaf cbbbbg ebbbbbbc daaaad gbbbbc ebbbbbbcfaaaaa ebbbbf ebbbbbbcaaaaac fbbbbb ebbbbbbdaaaad cbbbbe gbbbbbbaaaaaf gbbbbg gbbbbbaaaaac ebbbbc gbbbbbaaaaa bbbbb gbbbbaaaaaf cbbbbe gbbbeaaaad gbbbbg gbbbaaaaa ebbbbc cbbaaaaac bbbbbf cbeaaaaa fbbbbe cbaaaaae cbbbbg caaaaaee gbbbbc daaaaabef bbbbbf aaaaabbef fbbbbb daaaaebbef cbbbbe faaaaabbbef gbbbbg aaaaabbbbbf ebbbbf daaaaabbbbbf bbbbb faaaaabbbbbbf cbbbbe daaaaebbbbbbc gbbbbg caaaadebbbbbbc ebbbbc aaaaafebbbbbbc bbbbb daaaac ebbbbbbc fbbbbe caaaaa ebbbbbbc gbbbbg aaaaaf gbbbbbbg ebbbbc daaaad gbbbbbbg bbbbbf faaaaa gbbbbbbg bbbbe aaaaac gbbbbbbg bbbbg caaaad gbbbbbbg bbbbc faaaaaf gbbbbbbg bbbbf daaaac cbbbbbbe bbbb caaaaa cbbbbbbe bbbe aaaaaf cbbbbbb bbbg daaaad cbbbbb bbbf faaaaa cbbbb bbb aaaaac fbbb ``` <!-- end of image --> Yes! I knew it! There's 1 intersection right here in area B! Answer: A: 0; B: 1; 0 + 1 = 1 It was tricky, but I finally found one single intersection in the image.

<!-- image --> ```palette Key,Color ,#fefefeff a,#b5933aff b,#ba2626ff c,#e2c9afff d,#cbb375ff e,#c75653ff f,#f2e5dbff g,#d98b8bff ``` ```image cad aaa aaaac faaaaa aaacaa caaf aac aaa aaa aaa faa faad aad aaa daa daaf aaf aaa aaa aaa caa faac aac aaa aaa cac daaf faa daaaa aad aad faaaaaaa aaa daa caaaaad aa caaceb aaf daaaaac aaf aaa bbbf aaa caaaf aad daa fbbbbf daa d aaa aad gbbbbbf aac daa aaa bbbfbbbf aaa caa caaf bbg bbbc caa aa aaa bbf bbbc aad aac daa gbb bbbg aaa aad aad ebb bbbg faaf aaa aaa bbe bbbg aad daa faac bbf bbbe daa faa aaa cbb bbbe aac aa caaf ebb bbbe aaa aac aaa bbe bbbe caa aad daa bbc ebbb aac aaa aaa fbb ebbb aaa caa aaa gbb ebbbfaa faa faad bbb ebbbaad aaf aaa bbg gbbaaa aac caac bb gbbaaf aaa aaa gbb gbaaa daa daaf bbb ceaa caa aaa bbg caae aa aaa bbf aaabf aaf aad cbb faabbf aad aaa ebb aaabbf aaa faac bbe daabbbc daa aaa bbc aafbbbc caa caaf fbb aaa bbbc aa aaa ebb daa bbbg aac daa bbe aac bbbg aad aad bbc aaa bbbg aaa aaa fbb caa bbbe daa faac gbb aad bbbe faa aaa bbb aaa bbbe aa caaf bbg faa bbbb aacaaa bb aad ebb aaaaa gbb daa e aaaad bbb aaf caaa bbg aaa faac bbf caa fbaa gbb aac gbbbbbbf bbb aaa cbbbbbbgbbbf bbg faa ebbbbbef fbbbf bbf aad cbbbbbbg fbbbf cbb daa ebbbbbe fbbbf ebb aaf gbbbbbbc bbbc bbe aaa gbbbe bbbc bbf caa bc bbbc cbb aac bbbc ebb aaa bbbg bbe caa bbbgbbc aad bbbbb daa bbbb faaf bbe aaa f daa aac aaa caa aad aaa fac ``` <!-- end of image -->

I'm examining this image closely. My goal: find any and all intersections. Could these regions be concealing intersection points? Let's find out. <!-- image --> ```palette Key,Color ,#fefefeff a,#985071ff b,#e1c1dbff c,#c9a3b6ff d,#efe3ecff e,#b2d7b2ff f,#97c896ff g,#aa7e8fff ``` ```image cbd aaa aaa aaa aaa aaa daag caac caab gaad aaa aaa aaa aaa aaa daaa baag caac gaab aaa aaa aaa aaa aaa bbb aaa bbbbbbd daag dbbbbbbbbb caac dbbbbbbbbdbbbd caab dbbbbbbbbd bbb gaad bbbbbbbbd bbbb aaa bbbbbbbbb bbb aaa dbbbbbbbbd bbbb aaa dbbbbbbbbd bbb aaa dbbbbbbbd dbbb aaa bbbbbbd bbb daaa dbbbbb dbbb baag bbbbbd bbbd caac bbbbbb dbbb gaab bbbbb bbbd aaa bbbbbb bbb aaa bbbbb bbbbffffffffffffaaafffffff bbbbbd bbbeeeeeeeeeeeeaaaeeeeeee dbbbbb bbbbeeeeeeeeeeeaaaeeeeeee bbbbbd bbbeeeeeeeeeeeaaaebbbeee dbbbbb bbbbeeeeeeeeefaagebbbeee bbbbbd bbbeeeeeeeeegaagebbbeee bbbbb ebbbeeeeeeeegaafebbbeee bbbd fbbbeeeeeeeeaaaeebbbeee dbbd febbbeeeeeeeaaaeebbbeee bbb febbbeeeeeeeaaaeebbbeee bbb feebbbeeeeeeaaaeebbbeee bbb feebbbbeeeeeaaaeebbbeee bbb feeebbbeeeeeaaaeebbbeee dbbd feeebbbbeeeeaaaeebbbeee bbb feeeebbbeeefaageebbbeee bbb feeeebbbbeegaageebbbeee bbb feeeeebbbeegaafebbbeeee dbbb feeeeebbbbeaaaeebbbeeee dbbd feeeeeebbbeaaaeebbbeeee bbb feeeeeebbbbaaaeebbbeeee bbb feeeeeeebbbaaaeebbbeeee bbb feeeeeeeebbaaaeebbbeeee dbbb feeeeeeeebbaaaeebbbeeee dbbd feeeeeeeeecaageebbbeeee bbb feeeeeeeeecaageebbbeeee bbb feeeeeeeeegaaceebbbeeee bbb feeeeeeeeeaaacbebbbeeee dddddbbbdddd feeeeeeeeeaaabbebbbeeee eeeebbbeeeeef feeeeeeeeeaaabbbbbbeeee eeeebbbeeeeef feeeeeeeeeaaabbbbbbeeee eeeebbbeeeeef feeeeeeeeeaaabbbbbbeeee eeeebbbeeeeef feeeeeeeeeaaaebbbbbeeee eeeebbbeeeeef feeeeeeeeeaaaeebbbbeeee eeebbbeeeeeef feeeeeeeefaageebbbbeeee eeebbbeeeeeef feeeeeeeegaageeebbeeeee eeebbbeeeeeef feeeeeeeegaafeeeeeeeeee eeebbbeeeeeef feeeeeeeeaaaeeeeeeeeeee eeebbbeeeeeef feeeeeeeeaaaeeeeeeeeeee eebbbeeeeeeef ddddbbbbbcccccccgggggggaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaafffffffffff eeaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa eeaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaad eeaaaaaaaaaaaaaaaaaaaagggggggcccccccbbbbbddddd eeeeeeeeeeeef eeeeeeeeeeeef ``` <!-- end of image --> I'm analyzing this close-up of area A with precision. <!-- image --> ```palette Key,Color ,#fefefeff a,#985071ff b,#e2c0dbff c,#bc8ba4ff d,#ebd7e7ff e,#c8a2b4ff f,#f6eef4ff g,#d6b9c6ff ``` ```image dbbbbbd dbbbbbf bbbbbbf fbbbbbb fbbbbbd dbbbbbd dbbbbbf bbbbbb fbbbbbb fbbbbbd dbbbbbd dbbbbbf bbbbbb fbbbbbb fbbbbbd dbbbbbd dbbbbbf bbbbbb fbbbbbb fbbbbbd dbbbbbd bbbbbbf fcccccceeeeccccccccc daaaaaaaaaaaaaaaaaaa daaaaaaaaaaaaaaaaaaa daaaaaaaaaaaaaaaaaaa faaaaaaaaaaaaaaaaaaa faaaaaaaaaaaaaaaaaaa eeeeeggggggggbbbbdd ``` <!-- end of image --> Area A is clear of intersections, but the search continues. Okay, let's proceed to the next area. Let's get to the bottom of what's happening inside area B. <!-- image --> ```palette Key,Color ,#fefefeff a,#985071ff b,#e2c0dbff c,#be8fa6ff d,#ead4e5ff e,#ceabbdff f,#f4e8f1ff g,#aa6f8bff ``` ```image d baaaaac bf eaaaaae bd caaaaae bbf caaaaab bbb gaaaaad bbbf gaaaaaf bbbddd bbbb aaaaaa fbbbbbd bbbbf faaaaag fbbbbbd bbbbb daaaaag fbbbbbd bbbbbd baaaaac fbbbbbd bbbbbb eaaaaac fbbbbbd bbbbbbd eaaaaae fbbbbbf dbbbbbbf caaaaab fbbbbbf bbbbbbd gaaaaad dbbbbbf fbbbbbbf gaaaaaf dbbbbbf bbbbbbd aaaaaa dbbbbbf fbbbbbbf aaaaaa dbbbbbf bbbbbbb faaaaag dbbbbbf fbbbbbbf daaaaag dbbbbb dbbbbbb baaaaac bbbbbb fbbbbbbf eaaaaae bbbbbb dbbbbbb caaaaae bbbbbb fbbbbbbd caaaaab bbbbbb dbbbbbb gaaaaad bbbbbb bbbbbbd gaaaaaf bbbbbb dbbbbbbf aaaaaa fbbbbbd bbbbbbd faaaaag fbbbbbd fbbbbbbf daaaaag fbbbbbd bbbbbbd baaaaac fbbbbbd fbbbbbbf eaaaaac fbbbbbd bbbbbbb eaaaaae fbbbbbd fbbbbbbf caaaaab fbbbbbf dbbbbbb gaaaaad dbbbbbf fbbbbbbd gaaaaaf dbbbbbf dbbbbbb aaaaaa dbbbbbf fbbbbbbd aaaaaa dbbbbbf dbbbbbb faaaaag dbbbbbf bbbbbbddaaaaag dbbbbb dbbbbbbeaaaaac bbbbbb bbbbbbcaaaaae bbbbbb fbbbbbcaaaaae bbbbbb bbbbbgaaaaab bbbbbb fbbbbgaaaaad bbbbbb dbbbaaaaaaf bbbbbb fbbbaaaaaa bbbbbd dbbaaaaag fbbbbbd fbeaaaaag fbbbbbd deaaaaac fbbbbbd caaaaac fbbbbbd caaaaacf fbbbbbd caaaaacd fbbbbbf gaaaaaebf dbbbbbf gaaaaaebd dbbbbbf aaaaaabbbf dbbbbbf aaaaaabbbb dbbbbbf faaaaagbbbbfdbbbbbf daaaaagbbbbbbbbbbbf baaaaagbbbbbbbbbbb eaaaaacbbbbbbbbbbb caaaaaebbbbbbbbbbb caaaaabdbbbbbbbbbb gaaaaad bbbbbbbbbb gaaaaaf dbbbbbbbbb aaaaaa bbbbbbbbd faaaaag fbbbbbbbd daaaaag bbbbbbbd baaaaac fbbbbbbd eaaaaac bbbbbbd eaaaaae fbbbbbf caaaaab dbbbd gaaaaad fdf gaaaaaf aaaaaa aaaaaa faaaaag ``` <!-- end of image --> Wow! I can see 1 intersection so clearly in area B! Answer: A: 0; B: 1; 0 + 1 = 1 It was tricky, but I finally found one single intersection in the image.

<!-- image --> ```palette Key,Color ,#fefefeff a,#985071ff b,#e1c0dbff c,#bd8ea4ff d,#ead4e5ff e,#cdaabbff f,#f4e9f1ff g,#aa6f8aff ``` ```image ebf aaa aaa aaa aaa aaa daag eaac caab gaaf aaa aaa aaa aaa aaa faag baac eaae gaad aaa aaa aaa aaa aaa fbbb aaa dbbbbbf daag dbbbbbbbbb eaac fbbbbbbbbfbbbd caab fbbbbbbbbd bbb gaaf fbbbbbbbbd bbbd aaa dbbbbbbbb bbb aaa dbbbbbbbbf dbbb aaa fbbbbbbbbf bbb aaa dbbbbbbbd dbbb aaa bbbbbbd bbbf faag dbbbbb fbbb baac bbbbbf bbbf eaae dbbbbb fbbb gaad bbbbbf bbbd aaa dbbbbd fbbb aaa fbbbbb bbbd aaa bbbbbd bbb aaa fbbbbb bbbb aaa bbbbbd bbb aaa bbb fbbbbb dbbb daag bbb bbbbbd bbb eaac bbb bbbbb dbbb caab bbb bbbf bbbf gaaf bbb dbbd fbbb aaa bbb bbb bbbf aaa bbb bbb fbbb aaa bbb bbb bbbd aaa bbb fbbb bbb aaa bbb dbbf bbbd faag fbbd bbb bbb baac fbbd bbb bbbb eaae fbbd bbb bbb gaad dbbf fbbb dbbb aaa dbbf dbbf bbb aaa dbbf bbb dbbbaaa bbb bbb bbbaaa bbb bbb fbbaaa bbb fbbd bbaaa bbb dbbf feaag bbb bbb caac bbb bbb caac bbb bbb gaaed bbb fbbd aaabb bbb dbbf aaabbbbbb bbb aaabbbbbb bbb aaadbbbbb bbb aaa bbbbb fbbd faag fbbbd dbbf baac bbbd bbb eaae fbbf bbb gaad ff bbb aaa fbbd aaa dbbf fffdddbbbbeeeeecccccgggggaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaad aaaaaaaaaaaaaaaaaaagggggccccceeeeebbbbdddfff ``` <!-- end of image -->

This image looks interesting. I wonder if there are any intersections hidden in there? These zones are intriguing. I bet there's something interesting happening within them. <!-- image --> ```palette Key,Color ,#fefefeff a,#175e33ff b,#3d1471ff c,#94b69dff d,#b1d6b2ff e,#538966ff f,#715696ff g,#dadbe1ff ``` ```image fd bbbg bbfbb gbbg bb dbb bb fbb gbb bbf dbf bbc fbf gbbg fbd dbb bbg ac fbb bb cccaeccccccccccd bbf bb dddaeddddddddddc bbc bb dddaeddddddddddc gbbg gbb dddaeddddddddddc cbb cbf dddaeddddddddddc fbb fbc dddaeddddddddddc bbf bbg dddaeddddddddddc bbc bbg dddaeddddddddddc gbbg bb dddaeddddddddddc cbb bb dddaeddddddddddc fbb gbb dddaeddddddddddc bbf dbb dddaeddddddddddc bbc fbf dddbaddddddddddc gbbg fbc dddbbddddddddddc cbb bbg dddbbddddddddddc fbb bb dddabcdddddddddc bbf bb dddabbdddddddddcbbd bb dddabbddddddddcbbg gbb dddaabcddddddfbb cbf dddaabbdddddbbbc fbf dddaafbddddbbfdc bbg dddaadbcddbbcddc bbg dddaadbbcbbddddc bb dddaadfbbbdddddc bb dddaaddbbddddddc gbb dddaaddddddddddc gbb dddaaddddddddddc cbf dddaaddddddddddc fbc dddaaddddddddddc bbg dddaaddddddddddc b dddaaddddddddddc dddaadddddddddca aa aa aa aae aa daaa aa aaca aa ae ad aa dag aa ea aa aa ea ae da ea dag ac ea aa aa ea ae eaaaaaeeeecccddgg ea dag aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaeeeecccddggg ea aa ggddccceeeeaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaeed ea ae ggddccceeeeaaaaaaaaad ea ad ea ea ea aa ea ae ca da ca ea ca aa ca ac ca ca ca aa ca ae ca gag ca ea da aa da ac dada daaa daaa daad gaa gaa gae gag ``` <!-- end of image --> I'm now examining the contents of area A in detail. <!-- image --> ```palette Key,Color ,#fefefeff a,#165c32ff b,#3d1471ff c,#87a397ff d,#b9bcc7ff e,#608f73ff f,#745999ff g,#dfe4e4ff ``` ```image eaac eaac eaac eaac eaac eaac eaac eaac eaae eaae caae caae caae caae caae caae caae caae caae caae caae caae caae caae fbbe bbbb fbbb cbbbd dbbbf dabbb dabbbd dabbbf daabbb daabbbd g daabbbf gb daaabbb dbb daaabbbd cbbb daaafbbf fbbbb daaadbbb gfbbbbg daaagbbbd gbbbbfg daaa fbbf dbbbbf daaa dbbb cbbbbc gaaa gbbbd fbbbbd gaaa fbbf gfbbbbg gaaa dbbb dbbbbfg gaaa gbbbfbbbbf gaaa fbbbbbbc gaaa dbbbbbd gaaa bbbbg gaaa dbfg gaaag gaaag gaaag gaaag gaaag gaaag gaaag aaag aaag aaag aaag aaag ``` <!-- end of image --> Wow! I can see 1 intersection so clearly in area A! Answer: A: 1; 1 = 1 There's only one, but is an intersection after all.

<!-- image --> ```palette Key,Color ,#fefefeff a,#175e32ff b,#3d1471ff c,#8a9f9dff d,#b6bec3ff e,#548869ff f,#6d4e95ff g,#dedee4ff ``` ```image cd bbbg bbcbbg gbbg bb dbb bb fbb gbb bbf dbf bbc fbf gbbg fbd dbb bbg ac fbb bb ac bbf bb ac bbc gbb ac gbbg gbb ac dbb cbf ac fbb fbc ae bbf bbd ae bbd bbg ae gbbg bb ae dbb bb ae fbb gbb ae bbf dbf ae bbd cbf be gbbg fbd bb cbb bbg bb fbb bb abd bbf bb abb bbd bb abb gbbg gbb aabd cbb dbf aabb fbb fbc aafb bbf bbd aagbd bbd bbg aa bbgbbg bb aa fbbb bb aa bb gbb aa dbb aa cbf aa fbc aa bbg aa b aa aa ga aa aag aa aae aa daaa aa aaca aa ae ad aa dag aa ea aa aa ea ae da ea dag ac ea aa aa ea ae eaaaaaeeeecccddggg ea dag aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaeeeecccddggg ea aa ggdddcceeeeaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaeed ea ae ggdddccceeeaaaaaaaaad ea ad ea ea ea aa ca ae ca da ca ea ca aa ca ad ca ca ca aa ca ae ca gag da ea da aa da ac dada daaa daaa daad daa gaa gae gag ``` <!-- end of image -->

Let's examine this image for potential line intersections. These spots are like clues. Let's see what they reveal about potential intersections. <!-- image --> ```palette Key,Color ,#fefefeff a,#af9b81ff b,#a23e17ff c,#d5c3b5ff d,#b1d7b1ff e,#9bc796ff f,#a9633fff g,#eff4edff ``` ```image c ga a ac ca ga a ac ca a ag ac ga a ag cc ga a ag cc ga ga ca ca ca aa ac ac ag deeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeag edddddddddddddddddddddddddddddddddddddddaeg eddddddddddddddddddddddddddddddddddddddaddg eddddddddddddddddddddddddddddddddddddeadddg edddddddddddddddddddddddddddddddddddeaddddg eddddddddddddddddddddddddddddddddddaadddddg edddddddddddddddddddddddddddddddddaaddddddg eddddddddddddddddddddddddddddddddaadddddddg edddddddddddddddddddddddddddddddaeddddddddg eddddddddddddddddddddddddddddddaedddddddddg c edddddddddddddddddddddddddddddadddddddddddg cfbbba eddddddddddddddddddddddddddddaddddddddddddg gafbbbag edddddddddddddddddddddddddddadddddddddddddg cabbbfcg edddddddddddddddddddddddddeaddddddddddddddg cfbbbfc eddddddddddddddddddddddddeaddddddddddddafbbbac edddddddddddddddddddddddaadddddddeabbbbaedg eddddddddddddddddddddddaadddefbbbfadddddddg edddddddddddddddddddddaaefbbfaddddddddddddg edddddddddddddddddddeafbfaddddddddddddddddg edddddddddddddddefbbaaddddddddddddddddddddg edddddddddddafbbfadaddddddddddddddddddddddg edddddddafbbfaddddadddddddddddddddddddddddg edddafbbfedddddddaddddddddddddddddddddddddg afbbfeddddddddddadddddddddddddddddddddddddg cfbbfeddddddddddddeaddddddddddddddddddddddddddg cfbbag eddddddddddddaadddddddddddddddddddddddddddg cfbbag edddddddddddaaddddddddddddddddddddddddddddg bbag eddddddddddaadddddddddddddddddddddddddddddg edddddddddaaddddddddddddddddddddddddddddddg eddddddddaedddddddddddddddddddddddddddddddg edddddddadddddddddddddddddddddddddddddddddg eddddddaddddddddddddddddddddddddddddddddddg edddddadddddddddddddddddddddddddddddddddddg eddddaddddddddddddddddddddddddddddddddddddg eddeadddddddddddddddddddddddddddddddddddddg edeaddddddddddddddddddddddddddddddddddddddg eaadddddddddddddddddddddddddddddddddddddddg aadddddddddddddddddddddddddddddddddddddddeg acggggggggggggggggggggggggggggggggggggggggg ac ag ag gag ga ca ca ca aa ac ac ac ``` <!-- end of image --> I'm focusing my attention on this specific region, area A. <!-- image --> ```palette Key,Color ,#fefefeff a,#b66c4eff b,#a34019ff c,#d1bdaeff d,#e3d5cbff e,#b0977fff f,#c3a894ff g,#f1ece7ff ``` ```image c fe gfef gfef geec geec deec deed ceed ceeg ceeg fefg gfefg gfef geec geec deec deed deed ceed ceeg feeg gfefg gfef geef geec deec deed deed dceab ceed gdfaabbbbbb ceeg gcfabbbbbbbafcg feeg dceabbbbbbbafcg fefg gceabbbbbbaefdg gfefg gceabbbbbaecd geef gcebbbbbaecg geeeabbbbbaecg dfeeabbbaecg dfabaeeaaecg dfabbbbaeefg dfabbbbbaefeed dfabbbbbafd ceeg dfabbbbbafd ceeg dfabbbbbafd fefg dfabbbbbafd gfefg gdfabbbbbafd gfef gceabbbbbafd geec gceabbbbbafd geec bbbbbafd deec bacd deed ceed ceeg ceeg fefg gfefg gfef geec geec deec deed ceed ceed ceeg feeg gfefg gfef geef geec deec deed deed ceed ceeg feeg fefg ``` <!-- end of image --> Bingo! This close-up reveals 1 intersection in area A! Answer: A: 1; 1 = 1 It was tricky, but I finally found one single intersection in the image.

<!-- image --> ```palette Key,Color ,#fefefeff a,#c17f66ff b,#a23e17ff c,#cab4a3ff d,#decfc4ff e,#b09a82ff f,#b16040ff g,#efe9e4ff ``` ```image d ge e ed de e e ed de e eg cd ge e eg cc ge e eg cc ge ge de de ce ec ec ed ed eg geg ge de de ce ce ec ed ed d eg cfbbba eg gefbbbeg ge dabbbfcg ge dabbbac de cfbbbad ce gefbbbeg ce gabbbfcg ecgabbfc gefbfc dabbec dabbfd eg dfbbfd eg dfbbad ge dfbbad ge cfbbag de cfbbag ce cfbbag ce bbag ec ec ed eg eg ge ge de ce ce ec ec ed eg eg ge ge de de ce ec ec ed ed ``` <!-- end of image -->

I have an image in front of me. I need to determine if there are any intersection segments. It's crucial to examine these regions more closely. <!-- image --> ```palette Key,Color ,#fefefeff a,#a4d47dff b,#c43537ff c,#e7afb0ff d,#eff4eaff e,#c97871ff f,#b1d7b0ff g,#80c540ff ``` ```image f ggg aggga gggggf ggggggg dgggdgggg gggg dggga fggg fgggf ggga gggg aggg gggg gggf gggg gggg fgggf dgggd agggd gggg gggg dggg gggg ggga fgggf aggg agggd gggf gggg aggg gggg dgggd dgggf gggg agggd dggg gggg ggga gggg fggg dgggf gggf agggd d aggg gggg bbbc gggd gggg bbbd gggg dggga cbbb dgggd agggd bbbe ggga gggg bbb fggg gggg cbbb ggga dggga bbbc aggg agggd bbb gggd gggg ebbb gggg gggg bbbd dgggd dggga dbbb gggg agggd bbbe dggg gggg bbbd aa gggg cbbb dggga bbbe agggd ddddddddddddddddddbbbdd gggg dfffffffffffffffffebbbffd gggg dfffffffffffffffffbbbeffd dgggadfffffffffffffffffbbbfffd agggfffffffffffffffffebbbfffd ggggffffffffffffffffbbbffffd ggggfffffffffffffffbbbffffd dggggfffffffffffffbbbeffffd fgggaffffffffffffbbbfffffd ggggfffffffffffebbbfffffd dggggffffffffffbbbefffffd dfggggfffffffffbbbffffffd dfagggafffffffebbbffffffd dffggggfffffffbbbeffffffd dfffggggffffffbbbfffffffd dffffggggffffebbbfffffffd dffffagggafffbbbffffffffd dfffffggggfffbbbffffffffd dffffffggggfbbbeffffffffd dfffffffggggbbbfffffffffd dfffffffagggbbbfffffffffd dffffffffggggbefffffffffd dfffffffffggggffffffffffd dfffffffffeggggfffffffffd dfffffffffbbgggaffffffffd dfffffffffbbggggffffffffd dffffffffebbbggggfffffffd dffffffffbbbffggggffffffd dffffffffbbbffagggafffffd dfffffffbbbefffggggfffffd dfffffffbbbfffffggggffffd dffffffebbbffffffggggfffd dffffffbbbeffffffagggaffd dffffffbbbffffffffggggffd bbbbbbbbbbbbbbbbbeeeeccccddd dfffffebbbfffffffffggggfd bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbeeeeccccddddfffffbbbeffffffffffggggd bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbfffffffffffaggga dddcccceeeebbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbffffffffffffggggd dddcccceeeebbbbbbbbbbbbbffffffffffffffgggg dffffffffffffffffffffffgggg dffffffffffffffffffffffaggga dfffffffffffffffffffffffagg dfffffffffffffffffffffffda dfffffffffffffffffffffffd ``` <!-- end of image --> Let's put area A under the microscope. <!-- image --> ```palette Key,Color ,#fefefeff a,#9ed26dff b,#c53538ff c,#e3a1a2ff d,#e9e2d2ff e,#d36d6eff f,#c0e2a0ff g,#80c43fff ``` ```image dbbbbbbc cbbbbbbd bbbbbbe dbbbbbbc ebbbbbb bbbbbbe cbbbbbbd d ebbbbbb g bbbbbbc ga cbbbbbbd ggf ebbbbbe gggd dbbbbbbc gggg cbbbbbbd gggga bbbbbbe gggggf dbbbbbbc ggggggd ebbbbbb ggggggg bbbbbbe ggggggga cbbbbbbd dgggggggf ebbbbbb fgggggggd bbbbbbc agggggggd cbbbbbbd ggggggga ebbbbbe dgggggggf dbbbbbbc fgggggggd cbbbbbbd agggggggd bbbbbbe ggggggga dbbbbbbc dgggggggf ebbbbbb fgggggggd bbbbbbe agggggggd cbbbbbbd ggggggga ebbbbbb dgggggggf bbbbbbc fgggggggf cbbbbbbd agggggggd ebbbbbe agggggga dbbbbbbc dggggggga cbbbbbbd fgggggggf bbbbbbe agggggggddbbbbbbc aggggggaebbbbbb dggggggggbbbbbe fgggggggbbbbbd agggggggbbbb agggggggbbc dggggggggbd fggggggge agggggggd cggggggga bbggggggga dbbbgggggggf ebbbggggggggd bbbbbgggggggg cbbbbbbggggggga ebbbbbbfgggggggf bbbbbbc fgggggggd cbbbbbbd aggggggg ebbbbbe dggggggga dbbbbbbc dgggggggf cbbbbbbd fgggggggd bbbbbbe aggggggg dbbbbbbc dggggggga ebbbbbb dgggggggf bbbbbbe fgggggggd cbbbbbbd aggggggg ebbbbbb ggggggga bbbbbbc dgggggggf cbbbbbbd fgggggggd ebbbbbe aggggggg dbbbbbbc ggggggga cbbbbbbd dgggggggf bbbbbbe fgggggggd dbbbbbbc aggggggg bbbbeeeeeeeebbbbbb ggggggg bbbbbbbbbbbbbbbbbe dgggggg bbbbbbbbbbbbbbbbbd fggggg bbbbbbbbbbbbbbbbb agggg bbbbbbbbbbbbbbbbc gggg bbbbbbbbbbbbbbbb dggg dddccccccceeeec fgg ag g d ``` <!-- end of image --> Aha! I've found 1 intersection inside area A! Answer: A: 1; 1 = 1 The final count is: one intersection.

<!-- image --> ```palette Key,Color ,#fefefeff a,#9bd068ff b,#c53538ff c,#e6abacff d,#e7e9d5ff e,#d77476ff f,#bde09bff g,#80c53fff ``` ```image d ggg aggga gggggd ggggggg dgggdgggg gggg ggga dggg fgggf ggga aggg fggg gggg gggf ggga aggg fgggf gggd aggg gggg gggg dggg ggga ggga dgggf fggg aggg gggf gggg aggg gggg gggd dgggf gggg aggg dggg gggg ggga gggg fggg dgggf gggf agggd d aggg gggg bbbc gggd gggg bbb gggg dgggf cbbb dggg agggd bbbe ggga gggg bbb fggg gggg cbbb gggf dgggf bbbc aggg agggd bbb gggd gggg ebbb gggg gggg bbbd dggg dggga dbbb ggga fgggd bbbe dggg gggg bbb ff gggg cbbb dggga bbbe fgggd bbb gggg cbbb gggg bbbc dggga bbb fgggd ebbb gggg bbbd gggg dbbb dggga bbbe fgggd bbb gggg cbbb gggg bbbe ggga bbb fgggd cbbb gggg bbbc gggg bbb ggga ebbb fgggd bbbd aggg dbbb gggg bbbe gggabbb fgggbbb agggbe gggg cggga bbgggf bbgggg ebbbgggg bbbd gggg dbbb dgggf bbbe aggg bbb gggg cbbb gggg bbbe dgggf bbb agggd bbbbbbbbbbbbbbbbbeeeecccddd cbbb gggg bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbeeeeccccdd bbbc gggg bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb dgggf ddcccceeeebbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb agggd ddcccceeeebbbbbbbbbbbbb gggg gggg dgggf agg f ``` <!-- end of image -->

I'm on the case! Let's uncover any intersections hidden in this image. These zones are intriguing. I bet there's something interesting happening within them. <!-- image --> ```palette Key,Color ,#fefefeff a,#7e5afeff b,#2cba27ff c,#92ce91ff d,#ac9ef2ff e,#ebf1f1ff f,#5dc35eff g,#b0d7b1ff ``` ```image eggggggggggggggggggggg eggggggggggggggggggggg egggggggggggggggfffggg egggggggggggggggbbbcgg egggggggggggggggbbbggg egggggggggggggggbbbggg egggggggggggggggbbbggg egggggggggggggggbbbggg eggggggggggggggcbbbggg eggggggggggggggcbbbggg eggggggggggggggfbbbggg e eggggggggggggggfbbbdgg aaadde aaa eggggggggggggggfbbbggg aaaaaaaaaaaadde eaaaa eggggggggggggggbbbbggg aaaaaaaaaaaaaaaaaaaaadde eaaaaae eggggggggggggggbbbfggg ddaaaaaaaaaaaaaaaaaaaaaaaa eaaaaaae eggggggggggggggbbbfggg eddaaaaaaaaaaaaaaad daaaaaaad eggggggggggggggbbbfggg eddaaaaaaa daaadaaaad egggggggggggggdbbbcggg eaaa daaa eaaaaa egggggggggggggabbbcggg aaae daaa eaaaaa egggggggggggggabbbgggg aaad daaa aaaaa egggggggggggggabbbgggg aaaa daaa aaaaa eggggggggggggaabbbgggg daaa aaaa aaaaa eggggggggggggaabbbgggg aaa aaad aaaaae eggggggggggggaabbbgggg aaad aaad daaaae egggggggggggdaabbbgggg aaaa aaad daaaad egggggggggggaaabbbgggg daaa aaad daaaad egggggggggggaafbbbgggg aaa aaad eaaaaa egggggggggggaafbbbgggg aaae aaad eaaaaa eggggggggggdaafbbbgggg aaad aaae aaaaa eggggggggggaaabbbbgggg daaa aaae aaaaa eggggggggggaaabbbfgggg eaaa aaae aaaaa eggggggggggaaabbbfgggg aaae aaae aaaaae egggggggggdaaabbbcgggg aaad aaa daaaae egggggggggaaaabbbcgggg aaaa aaa daaaad egggggggggaaadbbbcgggg daaa aaa eaaaadegggggggggaaagbbbggggg aaa aaa eaaaaaggggggggdaaagbbbggggg aaad aaa aaaaagggggggaaaagbbbggggg eeaaaaeaaaeeeee aaaaaggggggaaaggbbbggggg cggdaaagaaaggggce aaaaagggggaaagcbbbggggg cgggaaagaaaggggge aaaaagggaaaagcbbbggggg cgggaaadaaaggggge eaaaaaggaaadgfbbbggggg cgggaaaaaaaggggge egdaaaadaaaggfbbbggggg cgggdaaaaaaggggge eggdaaaaaaaggfbbbggggg cggggaaaaaaggggge egggdaaaaaaggbbbbggggg ebe cggggaaaaaaggggge egggggaaaadggbbbfggggg bbbbe cggggaaaaaaggggge eggggggaaagggbbbfggggg ebbbbbbe cggggaaaaaaggggge egggggggdggggbbbfggggg cbbbbbbbg cggggdaaaaaggggge eggggggggggggbbbcggggg gbbbbbbbg cgggggaaaaaggggge eggggggggggggbbbcggggg gbbbbbbbg cgggggaaaaaggggge eggggggggggggbbbgggggg gbbbbbbbc cgggggaaaaaggggge eggggggggggggbbbgggggg ebbbbbbbc cgggggdaaadggggge ccccccccccccbbbcccccc ebbbbbbbf cggggggaaadggggge bbb ebbbbbbbf cggggggaaadggggge ebbb fbbbbbbf cggggggaaagggggge gbbb fbbbbbbbcgggggggadgggggge gbbb fbbbbbbbcggggggggggggge cbbb cbbbbbbbcggggggggggge cbbb cbbbbbbbcggggggggge fbbb fbbbbbbbcggggggge bbbf cgcbbbbbbbfggggge bbbf cgggcbbbbbbbfggge bbbc cgggggcbbbbbbbfge bbbg cgggggggcbbbbbbbf bbbg eeeeeeeeeebbbbbbbf bbbe fbbbbbbb bbbe fbbbbbbbe bbb fbbbbbbbe bbb cbbbbbbbe bbb cbbbbbbbg ebbb gbbbbbbbg gbbb gbbbbbbbc gbbb ebbbbbbbc cbbb ebbbbbbbf fbbb ebbbbbbbf fbbb fbbbbbbf bbbf fbbbbbbbe bbbf fbbbbbbbe bbbc cbbbbbbbebbbg cbbbbbbbbbg gbbbbbbbe gbbbbb gbbb ``` <!-- end of image --> I'm focusing my attention on this specific region, area A. <!-- image --> ```palette Key,Color ,#fefefeff a,#7e59ffff b,#2dba28ff c,#75d172ff d,#beabffff e,#e4e6f5ff f,#9c80ffff g,#bae8b8ff ``` ```image aaaaaaa aaaaaaf faaaaaae aaaaaaf daaaaaadeaaaaaad eaaaaaadeaaaaaad aaaaaafeaaaaaad faaaaaaeaaaaaad daaaaaadaaaaaad daaaaaafaaaaaad eaaaaaaaaaaaaad aaaaaaaaaaaaad faaaaaaaaaaaae daaaaaaaaaaaae eaaaaaaaaaaaae aaaaaaaaaaaae faaaaaaaaaaae daaaaaaaaaaae eaaaaaaaaaaa aaaaaaaaaaa faaaaaaaaaa daaaaaaaaaa daaaaaaaaaa eaaaaaaaaaa aaaaaaaaaf faaaaaaaaf daaaaaaaaf eaaaaaaaaf aaaaaaaaf faaaaaaaf daaaaaaaf eaaaaaaad aaaaaaad faaaaaad daaaaaad daaaaaad eaaaaaae daaaaf dfad bce bbbce bbbbbce bbbbbbbcg bbbbbbbbbcg bbbbbbbbbbbcg bbbbbbbbbbbbbcg gbbbbbbbbbbbbbbbg gbbbbbbbbbbbbbbbg gcbbbbbbbbbbbbbbg gcbbbbbbbbbbbbbbce gcbbbbbbbbbbbbbbce ecbbbbbbbbbbbbbbce ecbbbbbbbbbbbbbbce ecbbbbbbbbbbbbbbc ecbbbbbbbbbbbbb ``` <!-- end of image --> Area A does not contain any intersection points. Hmm, interesting. Let's check out another area. This close-up might reveal an intersection in area B. <!-- image --> ```palette Key,Color ,#fefefeff a,#7e5afeff b,#2cba27ff c,#96db95ff d,#ac96fdff e,#d7ccfeff f,#5fc264ff g,#c7ebc7ff ``` ```image gfffccc cbbbbbbg cbbbbbbg fbbbbbb fbbbbbb fbbbbbb bbbbbbf bbbbbbf bbbbbbf bbbbbbf gbbbbbbc gbbbbbbc gbbbbbbc gbbbbbbg cbbbbbbg cbbbbbbg cbbbbbbad cbbbbbbae fbbbbbba fbbbbbba fbbbbbbd bbbbbbbe bbbbbbf bbbbbbf ebbbbbbf dbbbbbbf abbbbbbc abbbbbbc abbbbbbc abbbbbbg fbbbbbbg efbbbbbbg efbbbbbbg dfbbbbbb afbbbbbb eafbbbbbb dabbbbbbb dabbbbbbf aabbbbbbf eaabbbbbbf daabbbbbbf aaabbbbbbc eaaabbbbbbc daaabbbbbbc aaaabbbbbbg aaaabbbbbbg eaaaabbbbbbg daaaabbbbbb aaaaabbbbbb eaaaaabbbbbb eaaaaabbbbbb daaaaabbbbbb aaaaaabbbbbf eaaaaaabbbbbf daaaaaabbbbbf daaaaaabbbbbc aaaaaaabbbbbc eaaaaaadbbbbbc daaaaaacbbbbbc daaaaaacbbbbbg aaaaaaacbbbbbg eaaaaaadcbbbbbg daaaaaaecbbbbbg aaaaaaa cbbbbb aaaaaaa fbbbbb eaaaaaad fbbbbb daaaaaae fbbbbb ae aaaaaaa fbbbbf aae aaaaaad bbbbbf aaae eaaaaaad bbbbbf aaaae daaaaaae bbbbbf aaaaad aaaaaaa bbbbbc aaaaaad eaaaaaad gbbbbbc aaaaaaad eaaaaaad gbbbbbc aaaaaaaad daaaaaae gbbbbbc aaaaaaaaaa aaaaaaa cbbbbbg aaaaaaaaaae eaaaaaad cbbbbbg daaaaaaaaae daaaaaae cbbbbbg daaaaaaaaaaaaaaaa fbbbbb daaaaaaaaaaaaaad fbbbbb eaaaaaaaaaaaaae fbbbbb eaaaaaaaaaaaa fbbbbb eaaaaaaaaaaa bbbbbf eaaaaaaaaad bbbbbf aaaaaaaae bbbbbf daaaaaa bbbbbf daaaae gbbbbbc edde gbbbbbc gbbbbbc gbbbbbg cbbbbbg cbbbbbg cbbbbbg cbbbbb fbbbbb fbbbbb fbbbbb ``` <!-- end of image --> The lines cross each other within area B, forming 1 intersection. Answer: A: 0; B: 1; 0 + 1 = 1 I've found a single intersection point in the image.

<!-- image --> ```palette Key,Color ,#fefefeff a,#7e5afeff b,#2cba27ff c,#97dc95ff d,#ad96ffff e,#d9cfffff f,#5fc660ff g,#cdeeccff ``` ```image ffc bbbg bbb bbb bbb bbb gbbb gbbb cbbb e cbbbe aaadee aaa fbbb aaaaaaaaaaaadee eaaaa bbbb aaaaaaaaaaaaaaaaaaaaadee eaaaaa bbbf edaaaaaaaaaaaaaaaaaaaaaaaa eaaaaaae bbbf eedaaaaaaaaaaaaaaad eaaaaaaae bbbc eddaaaaaaa daaaeaaaad dbbbg eaaa daaa eaaaad abbbg aaa daaa aaaaa abbb aaad daaa aaaaa eabbb aaaa daaa aaaaa dabbb eaaa aaaa aaaaa aabbb aaa aaad aaaaae aabbb aaae aaad daaaae eaabbb aaaa aaad daaaad aaabbb daaa aaad eaaaad aafbbb aaa aaad eaaaaa aafbbb aaae aaae aaaaa eaafbbb aaad aaae aaaaa aaabbbf daaa aaae aaaaa aaabbbf eaaa aaae aaaaa aaabbbc aaa aaa aaaaae daaabbbc aaad aaa daaaae aaaabbbg aaaa aaa daaaad aaaebbbg eaaa aaa eaaaad aaa bbb aaa aaa eaaaaa daaa bbb aaae aaa aaaaa aaad bbb aaaa aaa aaaaa aaae bbb daaa aaa aaaaa eaaa gbbb aaaeaaa aaaaa daaa gbbb aaadaaa aaaaae aaad cbbb aaaaaaa daaaaeaaae cbbb daaaaaa daaaaaaa fbbb eaaaaaa eaaaaaa fbbb gb aaaaaa eaaaad bbbf bbbb aaaaaa aaa bbbf bbbbbbg aaaaaa de bbbc cbbbbbbbg eaaaaa bbbc cbbbbbbbg aaaaa bbbg gbbbbbbbc aaaad bbb gbbbbbbbc aaaad bbb gbbbbbbbc daaad bbb bbbbbbbf aaad bbb bbbbbbbf aaad bbb fbbbbbbf aaae gbbb fbbbbbbb ad cbbb fbbbbbbbg cbbb cbbbbbbbg fbbb cbbbbbbbg fbbb cbbbbbbbc bbbf gbbbbbbbc bbbf gbbbbbbbc bbbc gbbbbbbbf bbbc bbbbbbbf bbbg bbbbbbbf bbbg fbbbbbbb bbb fbbbbbbb bbb fbbbbbbbg bbb cbbbbbbbg bbb cbbbbbbbg gbbb cbbbbbbbc gbbb gbbbbbbbc cbbb gbbbbbbbc cbbb gbbbbbbbf fbbb bbbbbbbf fbbb fbbbbbbf bbbf fbbbbbbb bbbf fbbbbbbb bbbc cbbbbbbbgbbbc cbbbbbbbbbg cbbbbbbbg gbbbbb gbbb ``` <!-- end of image -->

Hmm, I'm not sure what to expect from this image. Let's see if any lines cross. I wonder what's going on inside those areas? Perhaps intersections are hiding there. <!-- image --> ```palette Key,Color ,#fefefeff a,#a46d9cff b,#8bd6f2ff c,#d6bdd2ff d,#b397afff e,#eaeef0ff f,#b1d7b1ff g,#96c996ff ``` ```image bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbe bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbgggggggggggggggggggggggggg bbb effffbbbfffffffffffffffffffffffff bbe efffffbbbffffffffffffffffffffffff bbb effffffbbbfffffffffffffffffffffff ebb efffffffbbbffffffffffffffffffffff bbe effffffffbbbfffffffffffffffffffff bbb effffdafffbbbffffffffffffffffffff ebb efffaaaffffbbbfffffffffffffffffff bbe effaaaadffffbbbffffffffffffffffff bbb eaaaadaafffffbbbfffffffffffffffff ebb aaadfdaaffffffbbbffffffffffffffff bbe caaaffffaafffffffbbbfffffffffffffff bbb aaaafffffaaffffffffbbbffffffffffffff ebb eaaacefffffaafffffffffbbbfffffffffffff bbe daaa efffffaadfffffffffbbbfffffffaafff bbb aaad efffffdadffffffffffbbbfffffdaafff ebb caaae efffffdaafffffffffffbbbffffaadfff bbe aaaa effffffaaffffffffffffbbbfffaaffff bbb eaaac effffffaafffffffffffffbbbffaaffff ebb caaae effffffaaffffffffffffffbbbfaaffff bbb aaad effffffaadffffffffffffffbbbaaffff bbb eaaac effffffdadfffffffffffffffbdaaffff ebb daaa effffffdaaffffffffffffffffaadffff bbb aaad efffffffaaffffffffffffffffaabbfff bbb caaae efffffffaaffffffffffffffffaabffff ebb aaaa efffffffaaffffffffffffffffaafffff bbb eaaac efffffffaadffffffffffffffdaafffff eeeeeeeebbbe daaa efffffffaadffffffffffffffdadfffff ffffffffbbffg aaad efffffffdaaffffffffffffffaadfffff fffffffbbbffg caaae effffffffaaffffffffffffffaaffffff ffffffbbbfffg eaaaa effffffffaaffffffffffffffaaffffff ffffffbbffffg aaaac effffffffaaffffffffffffffaaffffff fffffbbbffffg daaad effffffffaafffffffffffffdaaffffff ffffbbbfffffg daaaa effffffffaadffffffffffffdadffffff ffffbbffffffg caaaae ggggggggdaaggggggggggggaaggggggg fffbbbffffffg eaaaae eaa aa ffbbbfffffffg aaaac aa aa fffbffffffffgaaaad aa eaa fffffffffffdaaad aae caa ffffffffffaaaa aac dad fffffffffdaag cad aae fffffffffaadg eaa aa fffffffffaafg aa aa fffffffffaafg aa eaa eeeeeeeeeaae aae caa caa aac dac aac cad aae aae eaa aa aa aa aa aa aa eaa caa aae cad dad aac aac aae dad aae aa caa aa aa aa aa caa aa eaa dad aae dad aac aac aac aa dad aae aa caa aa caa aa aa dad aa caa aac aa dad aa aac aac aa dad aa eaa caa aa dad aa aa aac aa caa aa aa dad aa aacaac eaa dadaa caa caaaa aac eaaaa aae aaaa aa aaad eaa aaae caa daa e caa eaa ce ``` <!-- end of image --> Let's see what secrets area A holds. <!-- image --> ```palette Key,Color ,#fefefeff a,#a46d9cff b,#8ad6f3ff c,#c6a4c1ff d,#a4def5ff e,#edf5faff f,#caecf9ff g,#e1cfdeff ``` ```image dbbbbf fbbbbd ebbbbbe dbbbbf fbbbbd ebbbbbe dbbbbf fbbbbd ebbbbbe dbbbbf fbbbbd ebbbbbe dbbbbf fbbbbd ebbbbbe dbbbbf fbbbbd ebbbbbe dbbbbf fbbbd edbe e ec ecaa aaaa gaaaa caaaa caaac aaaac eaaaag gaaaae caaaa ``` <!-- end of image --> I had hoped to find an intersection in area A, but there isn't one. Now, let's turn our attention to the next spot. My goal is to determine if there's an intersection inside area B. <!-- image --> ```palette Key,Color ,#fefefeff a,#a46c9cff b,#8bd6f2ff c,#cfb2cbff d,#b791b5ff e,#e9f0f7ff f,#b8e5f7ff g,#e3d2e0ff ``` ```image bbbbbbbbbbbbe bbbbbbbbbbbbbe bbbbbbbbbbbbbbe ebbbbbbe ebbbbbbe ebbbbbbe ebbbbbbe ebbbbbbe ebbbbbbe ebbbbbb ebbbbbb ebbbbbb ebbbbbb caag ebbbbbb edaaad ebbbbbb caaaaaae ebbbbbb edaaaaaaag ebbbbbb gaaaaaaaaac ebbbbbf caaaaaaaaaac ebbbbbf edaaaaaacdaaad ebbbbbf aaaaaaag caaaa ebbbbbf aaaaad gaaaae ebbbbbf aaaag eaaaag ebbbbbf aade aaaag ebbbbbf ac daaac ebbbbbf g daaad fbbbbbf caaaa fbbbbbf gaaaa fbbbbbf eaaaag fbbbbbf ge aaaag fbbbbbf gaaade daaac fbbbbbf gaaaa daaad fbbbbbf caaad caaaa fbbbbbf daaad gaaaa fbbbbbf aaaac gaaaae fbbbbbf eaaaag aaaag fbbbbbf gaaaae aaaac fbbbbbf caaaa daaad fbbbbbf caaad caaad fbbbbbf daaad gaaaa fbbbbbf aaaac gaaaae fbbbbbfaaaag aaaag fbbbbbaaaae aaaac fbbbdaaaa daaad fbbdaaad caaad fbaaaad caaaa faaaade gaaaae eaaaabbe eaaaag gaaaabbbe aaaac caaaabbbe daaad daaadbbe caaad daaacfe caaaa aaaac gaaaae eaaaag eaaaag gaaaae aaaac caaaa daaac daaad caaad daaac caaaa aaaag gaaaae eaaaag eaaaag gaaaa aaaac caaaa daaac daaad daaad aaaac caaaa aaaag gaaaae gaaaae eaaaag gaaaa aaaac caaad daaac daaad daaad aaaac ``` <!-- end of image --> Wow! I can see 1 intersection so clearly in area B! Answer: A: 0; B: 1; 0 + 1 = 1 I've found a single intersection point in the image.

<!-- image --> ```palette Key,Color ,#fefefeff a,#a46c9cff b,#8bd6f2ff c,#ceb1caff d,#b991b5ff e,#eeecf3ff f,#bfe8f8ff g,#e0cdddff ``` ```image bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbe bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbe fbb bbbe bbe bbbe bbb bbbe fbb bbb bbf bbb bbb ca bbb fbb aaae bbb bbf gaaaac bbb bbb daaadad bbb fbb aaad gaa bbb bbf caaae aa bbb bbb aaaa aa bbb fbb eaaac aa bbb bbf daaa aag bbb ead bbb aaad dad bbb cad fbb gaaag gaa bbb aac bbf daaa aa bbb aae bbb eaaac aa bbb aa ebb caaae aa bbb aa bbf aaad aag bbbaa bbb gaaag dad bdad ebb daaa gaa aad bbf aaad eaa aabb bbb caaae aa aabe ebb aaaa aa aa bbf eaaac aag gaa bbb daaa dac dad ebb aaad caa aag bbf gaaag eaa aa bbb eaaaa aa aa ebbe aaaac aa aa bbb daaad aag gaa fbb caaaa dac dad bbe gaaaae caa aag bbb eaaaag eaa aa fbb eaaaac aa aa be aaaad aa eaa daaad aae caa aaaa aac dac caae cad aag aac eaa aa aae aa aa aa aa eaa eaa aae caa caa aac dac aac cad aae aae gaa aa aa aa aa aa aa eaa gaa aae cad dac aac aac aag dad aae aa gaa aa aa aa aa gaa aa gaa dad aae cad aag aag aac aa dad aae aa gaa aa gaa aa aa dad aa gaa aag aa dad aa aag aag aa dad aa eaa gaa aa cad eaa aa aac aa gaa aa aa dad aa aagaag eaa dadaa caa caaaa aac eaaaa aae aaaa aa aaac eaa aaag caa daa e caa eaa ce ``` <!-- end of image -->

I'm examining this image closely. My goal: find any and all intersections. I have a hunch that these areas might contain the intersections we're looking for. <!-- image --> ```palette Key,Color ,#fefefeff a,#8ebec5ff b,#2a8692ff c,#adf27fff d,#e7f5e7ff e,#b1d8b1ff f,#569fa5ff g,#92c798ff ``` ```image df bb fbbf dbfbb bb ebd fbd bb dbb fb bb dba fba bb bb ab bb bf aba bb bb ebd a bb bb bbba aba fb dfbbbba bb dba dfbbbba bbd bb dfbbbba ebf ab dfbbbba bb bf dfbbbba fbd dddddbbdddddddddddddddd dfbbbba dbf geeeeegbgeeeeeeeeeeeeeegd dfbbbba bb geeeeeebbeeeeeeeeeeeeeeed dfbbbba fbe geeeeeebbeeeeeeeeeeeeeeed dfbbbba dbb geeeeeeebfeeeeeeeeeeeeeed dfbbbbabb geeeeeeebbeeeeeeeeeeeeeed dfbbba geeeeeeefbeeeeeeeeeeeeeed da geeeeeeeebfeeeeeeeeeeeeed geeeeeeeebbeeeeeeeeeeeeed geeeeeeeegbgeeeeeeeeeeeed geeeeeeeeebbeeeeeeeeeeeed geeeeeeeeebbeeeeeeeeeeeeecccccd geeeeeeeeeebgeccccccccccccccccd geeeccccccccccccccccceeed d ddecccccccccccccccccgfeeeeeeeeeeed cc cccccccccccceeeeeeeeeeebfeeeeeeeeeed ccc dced geeeeeeeeeeebbeeeeeeeeeed dcc cc geeeeeeeeeeegbgeeeeeeeeed dccd cc geeeeeeeeeeeebbeeeeeeeeed cce dcd geeeeeeeeeeeebbeeeeeeeeed ccc cc geeeeeeeeeeeeebfeeeeeeeed ccc cc geeeeeeeeeeeeebbeeeeeeeed ecc dcd geeeeeeeeeeeeefbeeeeeeeed dccd cc geeeeeeeeeeeeeebfeeeeeeed ccd cc geeeeeeeeeeeeeebbeeeeeeed cce dcd geeeeeeeeeeeeeegbgeeeeeed ccc cc egggggggggggggggbbgggggg ccc cc fb dcc dcd dba dccd cc bb cce cc ab ccc dcd bf ccc cc bb ecc cc ebd dccd dcd bb ccd cc fb ccc cc dba ccc dcd bb ecc cc ab dcc cc bf dcccd bb cc ebd d bb fb dba bb ab bf bb ebd bb fb dba bb ab bf bb ebd bb fb dba a ``` <!-- end of image --> Let's see if area A yields any clues. <!-- image --> ```palette Key,Color ,#fefefeff a,#86bbbeff b,#2b8692ff c,#acf37dff d,#ccf7afff e,#bad7dbff f,#509ca3ff g,#e5f6e2ff ``` ```image gbbba fbbf ebbbe bbba abbb ebbbe fbbf abbbg gbbba fbbf ebbbe bbba abbb ebbbe fbbf abbbg gbbba fbbf ebbbe bbba abbb ebbbe fbbf gg abbbg gggddddccccc gbbbaggdddcccccccccccccccc gggddddcccccccccccccccccccccccccc gggddddcccccccccccccccccccccccccccccddddggg cccccccccccccccccccccccccccccddddggg ccccccccccccccccccddddaffb ccccccccddddggg ebbbe ddggg fbbf abbbg gbbba fbbf ebbbe bbba abbb ebbbe fbbf abbbg gbbba fbbf ebbbe bbba abbb ebbbe fbbf abbbg gbbba fbbf ebbbe bbba ``` <!-- end of image --> Amazing! This area was hiding 1 intersection all along! Answer: A: 1; 1 = 1 I've found a single intersection point in the image.

<!-- image --> ```palette Key,Color ,#fefefeff a,#89bcc1ff b,#2a8692ff c,#aef37fff d,#d5f8beff e,#b9d7dbff f,#549ea7ff g,#ebf6edff ``` ```image ef bbg fbbf ebfbb bb ebe fbe bb gbb fb bb gba abe bb gbb abg bb bf aba bb bb ebe a bbg bb bbba eba fb gfbbbba bb gba gfbbbba bbg bb gfbbbba ebf abg gfbbbba bb bf gfbbbba fbg bb gfbbbba gbf ebe gfbbbba bb bb gfbbbba fbe fb gfbbbba gbb gba gfbbbbabb bb gfbbba abg ge bf bb ebe bb fb gddcccccd gbaddcccccccccccccccd gddcccccccccccccccddg g gdddcccccccccccccccdafg gcc cccccccccccddg bf ccc gcdgg bb dcc cc ebe gccg cc bb ccd gcd fb ccc cc gba ccc cc bb dcc gcd abg dccg cc bf gccd cc bb ccd gcd ebe ccc cc bb ccc cc fb dccg gcd gba gccg cc bb ccd cc abg ccc gcd bf ccc cc bb dcc cc ebe gccg gcd bb ccd cc fb ccc cc gba ccc gcd bb dcc cc abg dccgcc bf gcccd bb cc ebe g bb fb gba bb abg bf bb ebe bb fb gba bb abg bf bb ebe bb fb gba e ``` <!-- end of image -->

This is the image I'm working with. The goal is to count the intersections. Let's take a closer look at what's happening inside these zones. <!-- image --> ```palette Key,Color ,#fefefeff a,#b1d7b1ff b,#3ce637ff c,#598462ff d,#d5f0d5ff e,#7deb7aff f,#7ea284ff g,#97c798ff ``` ```image ad acccccd dfcccccccca gccccccccccccg accccccccccccacccg dfcccccccccccg cccf dafcccccccccccccfd fccf dafcccccccccccccccccfd fccf dgfcccccccccccccccccccccca fccc dccccccccccccccccccccccfad gccc acccccccccccccccfad gccc gccccccccgad accc fccccd accc ccccc dccc ccccc dccc ccccc dccc gaaaaaaaaaaaaaaaaaaaaagccccc ccc gaaaaaaaaaaaaaaaaaaaagccccf ccc gaaaaaaaaaaaaaaaaaaagccccg ccc gaaaaaaaaaaaaaaaaaafcccca ccc gaaaaaaaaaaaaaaaaafccccf ccc gaaaaaaaaaaaaaaaacccccag ccc gaaaaaaaaaaaaaaacccccaag ccc gaaaaaaaaaaaaaacccccaaag ccc gaaaaaaaaaaaaacccccaaaag ccc gaaaaaaaaaaagcccccaaaaag gaaaaaaaaaagccccfaaaaaag bbbbbbbbbbbbbbbbbbbbbbbbaag bbbbbbbbbbbbbbbbbbbbbbbbbag bbbbbbbbbbbbbbbbbbbbbbbbbbe aaaegggggacccccaaaaaaabbbbbb gaaaaacccccaaaaaaaaaebbbbb gaaaacccccaaaaaaaaaaaabbbbba gaaacccccaaaaaaaaaaaaaabbbbbb gagccccfaaaaaaaaaaaaaaagdbbbbb gfccccfaaaaaaaaaaaaaaaag bbbbbe fccccgaaaaaaaaaaaaaaaaag ebbbbb fccccgaaaaaaaaaaaaaaaaaag dbbbbbd cccccaaaaaaaaaaaaaaaaaaaag bbbbbe cccccaaaaaaaaaaaaaaaaaaaaag ebbbbb dccccaaaaaaaaaaaaaaaaaaaaaag dbbbbbd dccagggggggggggggggggggggga bbbbbe a ebbbbb dbbbbbd bbbbbe ebbbbb dbbbbbd bbbbbe bbbd ebbbbb bbba dbbbbbd dbbb bbbbbe bbbb ebbbbb bbba dbbbbbd dbbb bbbbbe bbbb ebbbbb bbba bbbbbd dbbb bbbbbd bbbb abbbb bbba dbbb dbbb bbbe bbbb ebbb bbba bbbd dbbb bbbb ebbb dbbb bbba bbbe dbbb ebbb ebbb bbbd bbba bbbb dbbb dbbb ebbb bbbe bbbe ebbb bbb bbbd ebbb bbbb bbbe dbbb bbb bbbeebbb ebbbbbbe bbbbbb bbbbbb abbbbe bbbb ebbb bba ``` <!-- end of image --> I'm going to scrutinize area A for any signs of an intersection. <!-- image --> ```palette Key,Color ,#fefefeff a,#b6f5b4ff b,#3ce537ff c,#598462ff d,#deeedfff e,#7bed77ff f,#84a48bff g,#b7cabbff ``` ```image f dfc dccc dcccc gccccc gcccccc gccccccc fcccccccc fccccccccc dfcccccccccd dcccccccccfd dcccccccccf gcccccccccf gcccccccccg gcccccccccg fcccccccccg fcccccccccd fcccccccccd dfccccccccfd dcccccccccf dcccccccccf daaaaaaaaaaaaaeeeeeeeeebbbbbbbbbbbbbbbbbe bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbd bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbba bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbe bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbd bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb bbbbbbbbbbbbbbbbbbbbbbbbbbbeeeeeeeeeeebbbbbbbbb aaaaaaddddddddgcccccccccf debbbbbbb gcccccccccf ebbbbbb gcccccccccg abbbbb gcccccccccg debbb fcccccccccd ebb fcccccccccd ab dfccccccccfd d dcccccccccf dcccccccccf gcccccccccf gcccccccccg gcccccccccg fcccccccccg fcccccccccd cccccccccd cccccccfd ccccccf cccccf ccccg cccg ccg cd ``` <!-- end of image --> Success! This area contains 1 intersection point! Answer: A: 1; 1 = 1 After careful examination, I conclude that there is one intersection.

<!-- image --> ```palette Key,Color ,#fefefeff a,#a8f3a5ff b,#3ce637ff c,#598462ff d,#d5eed6ff e,#76ed73ff f,#87a68dff g,#b1c5b5ff ``` ```image gd gcccccd dfccccccccg fccccccccccccg gccccccccccccgcccf dccccccccccccg cccf dgfcccccccccccccfd fccf dgfcccccccccccccccccfd fccc dgfccccccccccccccccccccccg fccc dccccccccccccccccccccccfgd fccc gcccccccccccccccfgd gccc fccccccccfgd gccc fccccd gccc ccccc dccc ccccc dccc ccccc dccc ccccc ccc dccccf ccc dccccf ccc gccccg ccc fccccd ccc ccccc ccc ccccc ccc ccccc ccc ccccc ccc dccccf dccccf bbbbbbbbbbbbbbbbbbbbbbbb bbbbbbbbbbbbbbbbbbbbbbbbb bbbbbbbbbbbbbbbbbbbbbbbbbba aaaaddddd ccccc ebbbbb ccccc abbbbb ccccc bbbbba ccccc ebbbbb dccccf dbbbbb gccccg bbbbba fccccd ebbbbb fccccd dbbbbbd ccccc bbbbba ccccc ebbbbb dcccc dbbbbbd dcc bbbbbe g ebbbbb dbbbbbd bbbbbe ebbbbb dbbbbbd bbbbbe bbbd ebbbbb bbba dbbbbbd dbbb bbbbbe bbbb abbbbb bbba dbbbbbd dbbb bbbbbe bbbb abbbbb bbba bbbbbd dbbb bbbbbd bbbb abbbb bbba dbbb dbbb bbbe bbbb ebbb bbba bbbd dbbb bbbb ebbb dbbb bbba bbbe dbbb ebbb ebbb bbbd bbba bbbb dbbb dbbb ebbb bbbe bbba ebbb bbb bbbd ebbb bbbb bbba abbb bbb bbbeebbb ebbbbbbe bbbbbb bbbbbb abbbbe bbbb ebbb bba ``` <!-- end of image -->

I'm curious to see if this image contains any intersection points. These spots are like clues. Let's see what they reveal about potential intersections. <!-- image --> ```palette Key,Color ,#fefefeff a,#575685ff b,#d7e97bff c,#bdbcd0ff d,#2b2668ff e,#888aa7ff f,#eef3e2ff g,#b0d7b0ff ``` ```image cf dddc cd edde de cdde fd cdda da fdddf d addc ad eddc df edde ed cdda dc fdddf ed addf de addc cd edde de cdda fd cdda da fdddf d addc ad edde df cdde ed cdda dc fd cd de fd da d ad df ed dc cd de cd da d ad df ad dc f ed bbf dc fbb cd bbf de fbb fd bbf da fbb d bbf ad fbb df bbf ed fbb dc bbf cd fbb de bbf fd bbb da bbf ffffffffffffffdf bbb gggggggggggggddgf bb gggggggggggggdggf bbb ggggggggggggadggf fbb ggggggggggggdeggf bbb gggggggggggedgggf fbb gggggggggggdegggf bbf ggggggggggedggggf fbb ggggggggggdaggggf bbf ggggggggggdgggggf fbb gggggggggddgggggf bbf gggggggggdggggggf fbb ggggggggadggggggf bbf ggggggggdgggggggf fbb gggggggadgggggggf bbf gggggggdegggggggf fbb ggggggedggggggggf bbf ggggggdaggggggggf fbb ggggggdgggggggggf bbf gggggdagggggggggf fbb gggggdggggggggggf bbf ggggadggggggggggf fbb ggggdgggggggggggf bbf gggbbbbbbbbbbbggff bbb gggaggbbbbbbbbbbbbbbbbbbf ggggggggggggggggf ggggggggggggggggf ggggggggggggggggf ``` <!-- end of image --> I'm determined to find out if an intersection exists in area A. <!-- image --> ```palette Key,Color ,#fefefeff a,#504d7fff b,#d8e976ff c,#aba9c1ff d,#2a2668ff e,#7d7ba2ff f,#e7f1b2ff g,#d8d7e3ff ``` ```image dda cddc add cddc add gdde eddg gdde eddg dda cddc ada cddc add gdde eddg gdde eddg dda cddc ada cddc add gdde addg gdde eddg gdda eddg dda cddc ada cddc add gdde eddg gdde eddg dda cddc ada cddc add gdde eddg faae fbbbbbbbbbbbbbbffffffffff fbbbbbbbbbbbbbbbbbbbbbbbb caacfffffffffffbbbbbbbbbb gaa ``` <!-- end of image --> Eureka! There's definitely 1 intersection in area A! Answer: A: 1; 1 = 1 There's one and only one intersection present in the image.

<!-- image --> ```palette Key,Color ,#fefefeff a,#565286ff b,#d8e978ff c,#b9b7ccff d,#2b2668ff e,#8784aaff f,#e9f3b5ff g,#eaece6ff ``` ```image gg dddc cd edde de cdde gd cdda da gdddg d addc ad eddc dg edde ed cdda dc gdddg cd addg de addc cd edde de cdda gd gdda da gdddg d addc ad edde dg cdde ed cdda dc gd cd de gd da d ad dg ed dc cd de gd da d aa dg ad dg g ed bbg dc gbb cd bbf de fbb gd bbf da fbb d bbg ad fbb dg bbg ed fbb dc bbg cd fbb de bbg gd fbb da bb d fbf ad bb dg fbf ed bb dc bbf cd gbb de bbf cd gbb de bbf gd gbb da bbf d gbb ad bbf dg fbb ed bbf dc fbb cd bbg de fbb gd bbg da fbb d bbg ad fbb dg bbg bbbbbbbbfffffgg fbb acfffffbbbbbbbbbbbbbbg ``` <!-- end of image -->

This image looks interesting. I wonder if there are any intersections hidden in there? These zones indicate regions where lines appear to be in close proximity. <!-- image --> ```palette Key,Color ,#fefefeff a,#a24c8eff b,#c158ecff c,#dfb7e5ff d,#b787aeff e,#b1d7b2ff f,#a2cda2ff g,#f1eff2ff ``` ```image bb cbbbg bbbb ag cbbbc aaa bbbb aaaaa bbbb gaaaaa cbbbc caaaad bbbb caaaad bbbb daaaac cbbbc aaaaag bbbb aaaaag gbbbb aaaaa bbbbg ggggggggggggggggggggggggaaaaa bbbb gfffffffffffffffffffffffaaaaa gbbbc gfeeeeeeeeeeeeeeeeeeeedaaaad bbbb gfeeeeeeeeeeeeeeeeeeedaaaac bbbb gfeeeeeeeeeeeeeeeeeeaaaaac cbbbc gfeeeeeeeeeeeeeeeeeaaaaag bbbb gfeeeeeeeeeeeeeeeeaaaaafg bbbb gfeeeeeeeeeeeeeeeaaaaaefg cbbbc gfeeeeeeeeeeeeeeaaaaaeefg bbbb bbbbbbccg gfeeeeeeeeeeeefaaaaaeeefg gbbbb gbbbbbbbbbbbbbbbbccg gfeeeeeeeeeeedaaaadeeeefg aaaaaad bbbbg cbbbbbbbbbbbbbbbbbbbbbbbbbbddeeeeeedaaaadeeeeefg aaaaaaa bbbb bbbbccbbbbbbbbbbbbbbbbbbbbbbbbbbbbaaaaafeeeeeefg aaaaaaa gbbbb bbbg gccbbbbbbbbbbbbbbbbbbaaaaabbbbbbbbbccg ddccaaa bbbbg bbb gcdbbbbbbbaaaaabbbbbbbbbbbbbbbbbbbcccg caaa bbbbcbbb gfeeeeeeaaaaabbbbbbbbbbbbbbbbbbbbbbbbbg caaa cbbbbbbb gfeeeefaaaaaeeeeeeeeddbbbbbbbbbbbbbbbb caaa bbbbbbc gfeeedaaaadeeeeeeeeeeeefg gccbbbbbb caaa bbbbb gfeeaaaaadeeeeeeeeeeeeefg caaa cbbbb gfeaaaaafeeeeeeeeeeeeeefg caaa bbbb gfaaaaaeeeeeeeeeeeeeeeefg caaa bbg daaaaaeeeeeeeeeeeeeeeeefg caaa aaaaadeeeeeeeeeeeeeeeeeefg caaa gaaaaafeeeeeeeeeeeeeeeeeeefg caaa caaaaaeeeeeeeeeeeeeeeeeeeeefg caaa daaaadfeeeeeeeeeeeeeeeeeeeeefg caaa aaaaacgfeeeeeeeeeeeeeeeeeeeeefg caaa gaaaaag gfffffffffffffffffffffffg caaa caaaaa caaa daaaad gaaa aaaaac gaaa gaaaaag gaaa caaaaa gaaa caaaad gaaa gaaaac gaaa aaaag gaaa daaac gaaa caaaa gaaa aaaa gaaa aaaag gaaa daaac gaaa caaaa gaaa aaaa aaa aaaag aaa daaad aaa caaaa aaa aaaa aaa aaaag aaa daaad aaa caaaa aaa aaaa aaa aaaag aaa daaad aaa gaaaa aaa aaaa aaa aaaag aaa daaad aaa gaaaa aaa aaaa aaa aaaag aaa daaad aaa gaaaa aaa aaaa aaaaaaac aaaaaad aaaaaa aaaaa aaaac aaad aaa ``` <!-- end of image --> I'm eager to see what's happening in this magnified view of area A. <!-- image --> ```palette Key,Color ,#fefefeff a,#a24c8eff b,#c157ecff c,#cfa3c5ff d,#b671aaff e,#d58ff2ff f,#e4c4e9ff g,#f1e1f4ff ``` ```image g fa faa caaa caaaa daaaaa gdaaaaaa gdaaaaaaa gaaaaaaaaa faaaaaaaaad caaaaaaaaad caaaaaaaaac caaaaaaaaac daaaaaaaaaf gdaaaaaaaaaf gdaaaaaaaadg faaaaaaaaadg faaaaaaaaad caaaaaaaaac fgg caaaaaaaaac bbbbbbeeeffgg daaaaaaaaaf bbbbbbbbbbbbbbbbeeeffggdaaaaaaaaaf bbbbbbbbbbbbbbbbbbbbbbaaaaaaaaaaf bbbbbbbbbbbbbbbbbbbbbaaaaaaaaaabbbbbeeeffgg bbbbbbbbbbbbbbbbbbbbaaaaaaaaaabbbbbbbbbbbbbbbee bbbbbbbbbbbbbbbbbbbaaaaaaaaaabbbbbbbbbbbbbbbbbb ffeeebbbbbbbbbbbbdaaaaaaaaadbbbbbbbbbbbbbbbbbbb ggffeeebdaaaaaaaaadbbbbbbbbbbbbbbbbbbbb daaaaaaaaabbbbbbbbbbbbbbbbbbbbbb gdaaaaaaaaaf ggffeeebbbbbbbbbbbb faaaaaaaaadg ggffeeebb caaaaaaaaadg caaaaaaaaad gdaaaaaaaaac faaaaaaaaaac caaaaaaaaaaf daaaaaaaaadg gdaaaaaaaaad faaaaaaaaaac caaaaaaaaaaf daaaaaaaaadg aaaaaaaaad aaaaaaaac aaaaaaaf aaaaadg aaaad aaac aaf dg ``` <!-- end of image --> Amazing! This area was hiding 1 intersection all along! Answer: A: 1; 1 = 1 My investigation reveals that there is exactly one intersection in this image.

<!-- image --> ```palette Key,Color ,#fefefeff a,#a24c8eff b,#c156edff c,#d8b5d0ff d,#bd80afff e,#d58ff2ff f,#e7c9ecff g,#f4e7f5ff ``` ```image be fbbbg bbbb ag fbbbe aaa bbbb aaaaa bbbb gaaaaa fbbbf faaaad bbbb caaaad bbbb daaaac ebbbf aaaaag bbbb aaaaa gbbbe aaaaa ebbbg gaaaaa bbbb gaaaaa fbbbe caaaad bbbb daaaac bbbb daaaaf fbbbe aaaaag bbbb aaaaa bbbb aaaaa ebbbf gaaaaa bbbb bbbbbeefg faaaad gbbbb gbbbbbbbbbbbbbbbeefg caaaad aaaaaad ebbbg ebbbbbbbbbbbbbbbbbbbbbbbbbeefg daaaac aaaaaaa bbbb bbbefebbbbbbbbbbbbbbbbbbbbbbbbbbbbaaaaaf aaaaaaa gbbbe bbbf gfeebbbbbbbbbbbbbbbbbaaaaabbbbbbbbeefg ddfcaaa bbbbg bbb gfeebbbbbbaaaaabbbbbbbbbbbbbbbbbbbeefg caaa bbbbebbb aaaaabbbbbbbbbbbbbbbbbbbbbbbbbg caaa fbbbbbbb faaaaa gfeebbbbbbbbbbbbbbb caaa bbbbbbf daaaad gfeebbbbb caaa bbbbb aaaaac caaa ebbbb aaaaag caaa bbbb faaaaa caaa bbg daaaad caaa aaaaac caaa aaaaag faaa faaaaa faaa daaaad faaa aaaaac faaa gaaaaag faaa caaaaa faaa daaaad faaa aaaaac faaa gaaaaag faaa caaaaa gaaa caaaad gaaa aaaac gaaa aaaag gaaa daaac gaaa caaaa gaaa aaaa gaaa aaaag gaaa daaac gaaa caaaa gaaa aaaa aaa aaaag aaa daaac aaa faaaa aaa aaaa aaa aaaag aaa daaad aaa faaaa aaa aaaa aaa aaaag aaa daaad aaa faaaa aaa aaaa aaa aaaag aaa daaad aaa gaaaa aaa aaaa aaa aaaaf aaa daaad aaa gaaaa aaa aaaa aaaaaaaf aaaaaad aaaaaa aaaaa aaaaf aaad aaa ``` <!-- end of image -->

I have an image in front of me. I need to determine if there are any intersection segments. My next step is to analyze the details within each area. <!-- image --> ```palette Key,Color ,#fefefeff a,#aa093dff b,#da70c4ff c,#dd9bc5ff d,#bc4c72ff e,#b1d7b1ff f,#98c696ff g,#f0cde5ff ``` ```image bg cbbc bbbbb bb bbb gbc cbbg bb gbbb bb bbb ba gbb bbbg caac cbg cbbc caaaa bb gbbb gaacaa bb bbb gaac aag gbc cbbg aab cad bb gbbbffffffffffffffffffffffffffffffe aad aa bb gbbbeeeeeeeeeeeeeeeeeeeeeeeeeeeeef aad aa gbb ebbbeeeeeeeeeeeeeeeeeeeeeeeeeeeef aad dac bbg eecbbceeeeeeeeeeeeeeeeeeeeeeeeeef aaa gaa bb eeeebbbeeeeeeeeeeeeeeeeeeeeeeeeef aaa bb eeeeeaabeeeeeeeeeeeeeeeeeeeeeeeef aaa cbg eeeefaaabceeeeeeeeeeeeeeeeeeeeeef aaa bb eeeeaaaaabbeeeeeeeeeeeeeeeeeeeeef daa bb eeefaaeaaabbeeeeeeeeeeeeeeeeeeeef daa gbc eeeaafeeaaabbeeeeeeeeeeeeeeeeeeef daa bbg eefaaeeeeaaabbceeeeeeeeeeeeeeeeef baa bb eeaafeeeeedaabbbeeeeeeeeeeeeeeeef caag bb edaaeeeeeeedaabbbeeeeeeeeeeeeeeefcaag cbg eaaeeeeeeeeedaabbceeeeeeeeeeeeeefaac bb daaeeeeeeeeeedaadbeeeeeeeeeeeeefaac bb aaeeeeeeeeeeeefaadbeeeeeeeeeeeeaab gbc daaeeeeeeeeeeeeefaadceeeeeeeeeeaad bbg aaeeeeeeeeeeeeeeefaadeeeeeeeeeaadf bb daaeeeeeeeeeeeeeeeefaaaeeeeeeeaaaef bb aaeeeeeeeeeeeeeeeeeeeaaaeeeeeaaaeef cbg dadeeeeeeeeeeeeeeeeeeeeaaaeeeaaaeeef bb aa eeeeeeeeeeeeeeeeeeeeeaaaeaaaeeeef bb dad eeeeeeeeeeeeeeeeeeeeebaaaaaeeeeef gbc aa eeeeeeeeeeeeeeeeeeeeeebaaaeeeeeef bb aab eeeeeeeeeeeeeeeeeeeeeeebdeeeeeeef bb aa eeeeeeeeeeeeeeeeeeeeeeecbbeeeeeef bb aac eeeeeeeeeeeeeeeeeeeeeeeebbceeeeef cg gaa eeeeeeeeeeeeeeeeeeeeeeeeebbeeeeef aac eeeeeeeeeeeeeeeeeeeeeeeeecbbeeeef gaa eeeeeeeeeeeeeeeeeeeeeeeeeebbceeef aag eeeeeeeeeeeeeeeeeeeeeeeeeeebbeeef gaa eeeeeeeeeeeeeeeeeeeeeeeeeeecbbeef aag eeeeeeeeeeeeeeeeeeeeeeeeeeeebbbef caa eeeeeeeeeeeeeeeeeeeeeeeeeeeeebbef aag eeeeeeeeeeeeeeeeeeeeeeeeeeeeeebbf caa ffffffffffffffffffffffffffffffbbb aa bbg baa bb aa cbb dad bbg aa bb dad cbb aa bbc dad bb aa gbb aad bbc aa bb aab gbb gaa bbb aac bbg gaa gbb aac cbb gaa bbg aag bb caa cbb aag bbg caa bb aa gbb baa bbc aa bb daa gbb aa bbc dad bbg aa gbb dad cbb aa bbg cad bb cbb b ``` <!-- end of image --> Let's put area A under the microscope. <!-- image --> ```palette Key,Color ,#fefefeff a,#aa083dff b,#db70c6ff c,#ebbad9ff d,#ca5a8fff e,#b92f63ff f,#e094c3ff g,#f5dfecff ``` ```image bbf bbbbg bbbbbc fbbbbbc cbbbbbfg gbbbbbbg gfbbbbbc cbbbbbf cbbbbbbg gbbbbbbc fbbdbbc faaadbfg daaaadbbg gaaaaaadbbc daaaaaaadbbf gaaaaaaaaadbbbg daaaefaaaaaebbbc caaaac caaaaaebbbc eaaae caaaaaebbbfg caaaac caaaaaebbbbg eaaad geaaaaebbbbc caaaac geaaaaebbbbf eaaad geaaaaebbbbbg faaaag geaaaaabbbbbc eaaad eaaaaabbbbbc faaaag daaaaadbbbbg eaaad daaaaadbbbf faaaag daaaaadbbbc aaaad daaaaadbbbg g faaaag faaaaadbbb ge gaaaaf faaaaadbbc gea daaaa faaaaadbbg geaa aaaaf faaaaaebb eaaa aaae caaaaaebf eaaaa aaaf caaaaaebc daaaad aae caaaaaebg daaaae aaf geaaaaef daaaae ae geaaaaec daaaaeg ac geaaaaeg faaaaeg e geaaaaeg faaaaeg c eaaaaag faaaaag eaaaaag caaaaac eaaaaac caaaaac geaaaaac caaaaac ceaaaaafaaaaaf fdaaaaaaaaaf gbdaaaaaaaf cbdaaaaad fbdaaad gbbded cbbbbc fbbbbg bbbbf gbbbbc cbbbbg bbbbf gbbbbc cbbbbg fbbbb gbbbbf cbbbbg fbbbb gbbbbf cbbbbc fbbbbg bbbbf gbbbbc cbbbbg bbbbf gbbbbc ``` <!-- end of image --> Eureka! There's definitely 1 intersection in area A! Answer: A: 1; 1 = 1 After careful examination, I conclude that there is one intersection.

<!-- image --> ```palette Key,Color ,#fefefeff a,#aa073cff b,#db70c6ff c,#e7a8d4ff d,#c34f7aff e,#b42454ff f,#d689a2ff g,#f3d8e9ff ``` ```image bg cbbc bbbbb bb bbb cbc bbbc bb gbbb bb bbb fa gbb bbbg faac cbg cbbc caaae bb gbbb gaacaa bb bbb gaaf aag cbc bbbc gaaf fad bb gbbb aad aa bb bbb aad aa gbb bbbg aae daf bbg cbbc aae gaa bb gbbb aaa bb eab aaa cbc gaaabc eaa bb aaaaabb eaa bb gaa aaabb daa gbb aac eaabbg daa bbg caa eaabbc faag bb aag daabbb faag bb faa daabbb caag cbc aag daadbc gaac bb faa faadb gaaf bb aa caadb gaaf gbc fae caadc aad bbg aa gaaeg aad bb dae gaae aae bb aa gaae aae cbc dad aae aaa bb aa gaaa aaa bb ead baaaaa gbc aa baaa bbg eaf bd bb aa cbb gbb aaf bbc cg gaa bb aac cbb gaa bbc aac bb caa gbb aag bbc caa bbg aag gbb faa bbb aa bbg fae gbb aa cbb dae bbc aa bb dad cbb aa bbc ead bb aa cbb eaf bbc aa bbg eaf gbb gaa bbb aaf bbg gaa gbb aac cbb caa bbg aag bb caa cbb aag bbc faa bb aag cbb fae bbc aa bb dae gbb aa bbb dae bbg aa gbb dad bbb aa bbg fad gbb cbb b ``` <!-- end of image -->

I'm on the case! Let's uncover any intersections hidden in this image. I'm going to focus my attention on these specific areas. <!-- image --> ```palette Key,Color ,#fefefeff a,#5fe39eff b,#69a224ff c,#15dc77ff d,#b0d8b2ff e,#8cb85cff f,#9dcc92ff g,#e6f6e9ff ``` ```image ddggggg acccccccccccccccccccccccccccccccccccccccaaaaaaaaddddddggggg c gggggddddddaaaaaaaaccccccccccccc c gc ad c c gc aa cg c c da cg c c da cd c c dc ad c c gc ad c c gc aa cg c gc aa cg c c da cg c ggggggggcgggggggg dddddddacdddddddfg dddddddcaddddddddg dddddddcdddddddddg dddddddcdddddddddg ddddddfcdddddddddg ddddddcadddddddddg ddddddcddddddddddg ddddddcddddddddddg dddddfcddddddddddg dddddaaddddddddddg dddddcdddddddddddg dddbfcdddddddddddg dddfbceddddddddddg ddddaabbeddddddddg ddddcdddbbeddddddg ddddcdddddebeddddg ddddcdddddddebbddg dddaadddddddddebbg dddcfdddddddddddebbg dddadddddddddddddgdbbg dddddddddddddddddg gbbd dddddddddddddddddg gbbd dddddddddddddddddg gbbf dddddddddddddddddg bbf dddddddddddddddddg ebe fffffffffffffffff ebe fbb fbbg dbbg dbbg gbbd gbbd bbf ebe ebe fbe ggdfeeb fbb gddfebbbbbbbbbbbeefdg dbbbbbbeefddg ``` <!-- end of image --> I'm now examining the contents of area A in detail. <!-- image --> ```palette Key,Color ,#fefefeff a,#5ce6a0ff b,#69a225ff c,#14dc75ff d,#c1d8a5ff e,#94bc63ff f,#9ef0c6ff g,#ddf4e2ff ``` ```image gcc fca aca ccf gccg fcc aca acf ccg fcc fca acf ccg gcc fca acf ccg gcc fca acf ccg gcc g fca bedaca dbbbccf gebccbd fccbbbd acadbbbbdg acf dbbbbeg ccg debbbeg fcc debbbeg aca gebbbeg acf gebbbed ccg gebbbed gcc gebbbbd fca gdbbbb acf dbb ccg d gcc gff ``` <!-- end of image --> Bingo! This close-up reveals 1 intersection in area A! Answer: A: 1; 1 = 1 I have found one intersection!

<!-- image --> ```palette Key,Color ,#fefefeff a,#4ee497ff b,#69a224ff c,#13dc76ff d,#bdd69eff e,#93bb61ff f,#89edbaff g,#d1f3dcff ``` ```image gggggg acaccccccccccccccccccccccccccccccccccccaaaaaafffffffgggggg c ggggggfffffffaaaaaacccccccccccc c gc af c c gc ff cg c c fa cg c c fa cg c c ga af c c gc af c c gc af c c c fa cg c c fa cg c c fa ag c c gc af c c gc af c bdc gbcd ffbbd cg ebe c ebe c ebe fa dbb cg dbb f dbbg gbbg gbbd bbd bbe ebe ebe ebb dbb dbbg gbbg gbbd bbd bbd ebe ebe ebe gddeeb dbb gddeebbbbbbbbbbbeeddg dbbbbbbeeddgg ``` <!-- end of image -->

I'm on the case! Let's uncover any intersections hidden in this image. I've spotted 2 narrow regions that might be worth examining further. Let's call them area A,, and B. <!-- image --> ```palette Key,Color ,#fefefeff a,#4ca93bff b,#c5bbb5ff c,#dcdcd4ff d,#71b863ff e,#b1d7b0ff f,#96ca93ff g,#f0f4efff ``` ```image caa gaaaa aaaaad aaadaaae bb aaad aaag bbb daaa caaa bbb faaa faaa bbbb eaaa aaad bbbb caaag aaac gbbbbb gaaac gaaa gbbbbb aaaf eaaa gbbcbbc aaad daaa gbbgbbb aaaa aaaf gbbggbbc daaa aaac gbb bbb faaa caaa gbb cbbc eaaa faaa gbb bbb gaaag aaad gbb cbbc aaae ggggggggaaaeggggggcbbggggbbbgggg aaaf gfeeeeeeefaaafeeeeeebbeeeebbbeeef aaad geeeeeeeeefaaaeeeeeebbeeeeebbbeef aaaa geeeeeeeeeedaaaeeeeebbeeeeebbbeef daaa geeeeeeeeeeeaaafeeebbbeeeeeebbbef eaaa geeeeeeebbeeeaaaeeebbbeeeeeebbbef caaag geeeeebbbbeeeaaaeeebbbeeeeeeebbbf gaaac geeebbbbbbeeeeaaaeebbbeeeeeeebbbf aaae geebbbbbbbbeeeaaaeebbbeeeeeeeebbb aaaf gbbbbbeebbbeeeeaaaebbbeeeeeeeebbb aaad cbbbbbeeebbbeeeeaaaebbbeeeeeeeeebbb daaa gbbbbbeeeeebbbeeeefaaabbbeeeeeeeeebbb faaa bbbbbeeeeeeeebbeeeeeaaabbbeeeeeeeeeebbb eaaa gbbbbbgeeeeeeeebbbeeeefaadbbeeeeeeeeeebbb caaag bbbbb geeeeeeeebbbeeeeeaaabbeeeeeeeeeefbbc gaaac cbbbbc geeeeeeeebbbeeeeefaadbeeeeeeeeeefbbb aaaf gbbbbb geeeeeeeebbbeeeeeeaaabeeeeeeeeeefgbbc aaad bbbbbg geeeeeeeeebbeeeeeefaadeeeeeeeeeef bbb aaaa cbbbbc geeeeeeeeebbbeeeeeeaaaeeeeeeeeeef gbbc daaa bbbbb geeeeeeeeebbbeeeeeefaadeeeeeeeeef bbb faaa cbbbbc geeeeeeeeebbbeeeeeebaaaeeeeeeeeef cbbc eaaa gbbbbb geeeeeeeeebbbeeeeeebdaafeeeeeeeef bbb gfffaaafffffffffe bbbbbg geeeeeeeeeebbeeeeeebbaaaeeeeeeeef cbbc geeaaafeeeeeeeeef cbbbbc geeeeeeeeeebbbeeeeebbdaafeeeeeeef bbb geaaadeeeeeeeeeefgbbbbb geeeeeeeeeebbbeeeeebbbaaaeeeeeeef cbbg gefadeeeeeeeeeeebbbbbg geeeeeeeeeebbbeeeeebbbdaafeeeeeef bbb geeeeeeeeeeeeeebbbbc geeeeeeeeeebbbeeeeebbbeaaaeeeeeef cbbg geeeeeeeeeeeebbbbb geeeeeeeeeeebbeeeeebbbedaafeeeeef bbb geeeeeeeeeebbbbbe geeeeeeeeeeebbbeeeebbbeeaaaeeeeef bbbg geeeeeeeeebbbbbef geeeeeeeeeeebbbeeeebbbeeaaaeeeeef bbb geeeeeeebbbbbeeef geeeeeeeeeeebbbeeeebbbeeeaaaeeeef bbb geeeeeebbbbbeeeef geeeeeeeeeeebbbeeeebbbeeeaaaeeeef b geeeeebbbbeeeeeef geeeeeeeeeeeebbeeeebbbeeeeaaaeeef geeeeebbeeeeeeeef geeeeeeeeeeeebbbeeebbbeeeeaaaeeef geeeeebbeeeeeeeef geeeeeeeeeeeebbbeeebbbeeeeeaaaeef geeeebbbeeeeeeeef geeeeeeeeeeeebbbeeebbbeeeeeaaaeef geeeebbbeeeeeeeef gfeeeeeeeeeeeebbeeebbbeeeeefaadef geeeebbbeeeeeeeef gggggggggggggbbcggbbbggggggaaagg geeeebbbeeeeeeeef bbc bbb caad geeeebbbeeeeeeeef bbb bbc aaa geeeebbeeeeeeeeef bbb bbc eaaf geeeebbeeeeeeeeef cbb bbc aaa gfffbbbfffffffffe bbc bbc eaaf bbb bbb bbc aaa bbb bbb bbc faae bbb bbb bbc aaa bbc cbb bbc faae gbbg bbcbbc aaa cbb bbbbbc daac bbb bbbbbc aaa bbb bbbbbc daac bbb cbbbbc aaa bbc bbbbg daag bbc bbbbg aaa gbbg bbbbg aaag cbb bbbbg gaaa bbb cbbbg aaa cbb bbbg gaad bbbg aaa bbbg gaad cbb aaa gbb caad bb aaa eaf ``` <!-- end of image --> Let's put area A under the microscope. <!-- image --> ```palette Key,Color ,#fefefeff a,#4ca93aff b,#c6bab5ff c,#e0dfd9ff d,#65b556ff e,#d2cbc5ff f,#90c985ff g,#f0f1edff ``` ```image caaaaaadg gdaaaaadg gdaaaaaac daaaaaae faaaaaab faaaaaaf caaaaaf cdaad gddg c gg cbb gebbb cbbbbb gebbbbbb ebbbbbbbb cbbbbbbbbbe gebbbbbbbbbg cbbbbbbbbbc gbbbbbbbbbeg gebbbbbbbbbc cbbbbbbbbbe cbbbbbbbbeg ebbbbbbbc bbbbbbeg bbbbbc gbbbbbg cbbbbb cbbbbb ebbbbe ebbbbc bbbbbc gbbbbbg gbbbbbg cbbbbb cbbbbe ebbbbe ebbbbc bbbbbc gbbbbbg gbbbbbg cbbbbb cbbbbe ``` <!-- end of image --> Based on this close-up, I can conclude that there's no intersection in area A. Let's move forward and inspect another region. This close-up of area B is like examining a piece of evidence. <!-- image --> ```palette Key,Color ,#fefefeff a,#4ca93aff b,#c6bab5ff c,#eae9e5ff d,#68b458ff e,#d7d4cdff f,#afd5a6ff g,#88c17bff ``` ```image faaaaaaf cbbbbb ebbbbbc gaaaaaac cbbbbb bbbbbb daaaaadc cbbbbb ebbbbbc caaaaaag cbbbbb bbbbbb eaaaaaaf cbbbbb ebbbbbc faaaaaae cbbbbb bbbbbe gaaaaaac cbbbbb ebbbbbc cdaaaaag ebbbbb cbbbbbe caaaaaac ebbbbb ebbbbbc cc faaaaag ebbbbb cbbbbbe cbbbb daaaaac ebbbbb ebbbbbc cebbbbbc faaaaag ebbbbe cbbbbbe ebbbbbbbe daaaaac ebbbbe ebbbbb cbbbbbbbbbb faaaaaf ebbbbe cbbbbb ebbbbbbbbbbb daaaaa ebbbbe bbbbb cbbbbbbbbbbbbbc faaaaaf ebbbbe cbbbb cbbbbbbbbbbbbbbbe aaaaaa ebbbbe bbbb ebbbbbbbbbe ebbbbe faaaaaf ebbbbe cbbb cbbbbbbbbbe ebbbbb caaaaad ebbbbe bbb ebbbbbbbbbc cbbbbbc faaaaaf ebbbbe cbb bbbbbbbbe bbbbbc caaaaad ebbbbe bb bbbbbbbc bbbbbe gaaaaaf ebbbbe eb bbbbbc ebbbbe caaaaad ebbbbe b bbbe ebbbbb gaaaaaeebbbbe e bbc cbbbbbc caaaaadebbbbe e bbbbbc gaaaaafbbbbe bbbbbe caaaaadbbbbe ebbbbe gaaaaafbbbe cbbbbb eaaaaadbbbe cbbbbbc daaaaafbbe bbbbbc eaaaaadbbe bbbbbe daaaaabbe ebbbbe eaaaaadbc cbbbbb daaaaabc cbbbbbc faaaaagc bbbbbc daaaaae bbbbbe faaaaag ebbbbb aaaaaac cbbbbb gaaaaaf cbbbbbc baaaaaa bbbbbc bgaaaaaf bbbbbe bbaaaaad ebbbbb bbgaaaaaf cbbbbb bbbaaaaad cbbbbbc bbbgaaaaaf bbbbbc bbbbaaaaad bbbbbe bbbbdaaaaae ebbbbb bbbbbaaaaad cbbbbb bbbbbgaaaaae cbbbbbc bbbbbeaaaaad bbbbbc cbbbbbcgaaaaae ebbbbe cbbbbbceaaaaag ebbbbb cbbbbbc gaaaaac cbbbbb cbbbbb eaaaaag cbbbbbc cbbbbb daaaaac bbbbbe cbbbbb eaaaaag ebbbbe cbbbbb daaaaac ebbbbb cbbbbb faaaaag cbbbbb cbbbbb daaaaac cbbbbbc cbbbbb faaaaaf bbbbbe cbbbbb daaaaac ebbbbe cbbbbb faaaaaf ebbbbb cbbbbb daaaaa cbbbbb cbbbbb faaaaaf bbbbbc cbbbbb aaaaad bbbbbe cbbbbb faaaaaf ebbbbe cbbbbb caaaaad ebbbbb cbbbbb gaaaaaf cbbbbb cbbbbb caaaaad bbbbbc cbbbbb gaaaaaf bbbbbe cbbbbb caaaaad ebbbbe ebbbbb gaaaaae ``` <!-- end of image --> Aha! I've found 1 intersection inside area B! Answer: A: 0; B: 1; 0 + 1 = 1 I've found a single intersection point in the image.

<!-- image --> ```palette Key,Color ,#fefefeff a,#4da93bff b,#c6bab5ff c,#e2e1dbff d,#76ba68ff e,#d1d0c6ff f,#a6d49dff g,#f1f2eeff ``` ```image caa gaaaa aaaaad aaadaaaf bb aaad aaag bbb daaa caaa bbb daaa daaa bbbb faaa aaad bbbb caaag aaae gbbbbe gaaae gaaa gbbbbb aaaf faaa gbbcbbe aaad daaa gbbgbbb aaaa aaaf gbbggbbe daaa aaac gbb bbb faaa caaa gbb cbbc eaaa faaa gbb bbb gaaac aaad cbb cbbc aaae aaaf cbb bbb aaaf aaag cbb cbbc aaad eaaa cbb bbb aaaa daaa cbb ebbg daaa aaag cbb bbb faaa cbe aaa cbb ebbg caaag bbbb aaag cbb bbb gaaac ebbbbbg aaa ebb ebbg aaaf gbbbbbbbc aaa ebb bbb aaad bbbbbg bbb gaaa ebb bbb aaad cbbbbe bbb aaa ebb bbb daaa gbbbbb ebb gaadebb bbb daaa ebbbbg gbbg aaaebb gbbe faaa cbbbbe bbc caadbb bbb caaag bbbbb bbb aaabb gbbe gaaae ebbbbc bbb eaadb bbb aaaf gbbbbb ebb aaab gbbe aaad bbbbbg gbbg eaad bbb aaaa cbbbbe bbe aaa cbbc daaa bbbbb bbb daaf bbb faaa ebbbbc bbb baaa cbbc eaaa gbbbbe ebb bdaaf bbb gaaag bbbbbg gbbg bbaaa cbbc aaae cbbbbc bbe bbdaae bbb aaaf gbbbbb bbb bbbaaa ebbg cad ebbbbg bbb bbbdaac bbb g cbbbbe ebb bbb aaa ebbg bbbbb gbbg bbb daac bbb ebbbbc bbe bbb aaa ebbg gbbbbb bbb bbb daag bbb bbbbbg bbb bbb aaa bbb cbbbbe cbb bbb aaag e bbbb gbbg bbb gaaa gbbc bbe bbb aaa cbb bbb bbb gaad ebb bbb bbb aaa bbb cbb bbe caad bbb gbbc bbe aaa bbe bbe bbe eaad bbc bbb bbe aaa gbbg bbb bbe eaaf cbb cbb bbe aaa ebb bbc bbe faaf bbb bbe bbe aaa bbb bbb bbe faaf bbe bbb bbc aaa bbc cbb bbc faae gbbg bbcbbc aaa cbb bbebbc daae ebb bbbbbc aaa bbb ebbbbc daac bbb cbbbbc aaa bbe bbbbc daag bbc bbbbg aaa gbbg bbbbg aaag cbb ebbbg gaaa ebb cbbbg aaa ebb bbbg gaad bbbg aaa bbbg caad ebb aaa cbb caad be aaa ead ``` <!-- end of image -->

I'm examining this image closely. My goal: find any and all intersections. I'm going to focus my attention on these specific areas. <!-- image --> ```palette Key,Color ,#fefefeff a,#dd8b05ff b,#edc7c4ff c,#a5cda0ff d,#f3f2edff e,#d682a3ff f,#b2d7b1ff g,#e2b159ff ``` ```image db ee eeb eee ebed de ee be beeed ee beeeb ee deeee eb beeeb e deeeb be eeeed ee beeeb ddddddddddddddddddddddab ee deeeed cccccccccccccccccccccaacd eb beeeb cfffffffffffffffffffaafcd ed deeee cffffffffffffffffffaacfcd d de beeed cfffffffffffffffffgacffcd ee be beeeb cffffffffffffffffgagfffcd bed ee eeeed cfffffffffffffffcaaffffcd ee ee beeecfffffffffffffffaafffffcd deb eb deeeeffffffffffffaaffffffcd ee ed ceeeecffffffffaafffffffcd ee be cfffeeeefffffaacfffffffcd bed be cfffffeeeeffaacffffffffcd ee ee cfffffffceegagfffffffffcd deb eb cfffffffffcaaeeffffffffcd ee eb cffffffffcaafeeeecfffffcd ee de cffffffffaafffffeeeefffcd bed be cfffffffaaffffffffeeeefcd ee ee cffffffaaffffffffffffeecd deb ee cfffffaacffffffffffffffcd ee eb cffffgagfffffffffffffffcd ee ed cfffgagffffffffffffffffcd bed de cffcaafffffffffffffffffcd ee be cffaaffffffffffffffffffcd deb ee cfaafffffffffffffffffffcd ee ee caaffffffffffffffffffffcd eeeb aaccccccccccccccccccccccd bee gabdddddddddddddddddddddd ee gag db bag daa aa aa aad gab gag bag daa aa aa ab aa aaa aad baag gab gaab bag aag daa gad aa aa aa dag aa ga aad aa gab bab gag aa bag aa daa bab aa aa aa ag aad gad gab aa gag dag bag ga daa aa aa bab aa aa aa aa aad gad gab aa bag agdaa gaaa aa ``` <!-- end of image --> Let's see what secrets area A holds. <!-- image --> ```palette Key,Color ,#fefefeff a,#e29c34ff b,#e5afc4ff c,#f2d5a5ff d,#f6e4deff e,#d680a2ff f,#de8a02ff g,#ebba6aff ``` ```image aff gfff gfffg cfffg cfffa dfffa dafffd afffd afffc gfffc cfffg cfffa dfffa dfffad b afffd eebd afffc eeeeeb gfffc eeeeeeebd gfffg dbeeeeeebd cfffg beeeeeeebd cfffa dbeeeeeebd dfffad beeeeeeeb dafffd dbeeeeeebd afffd dbeeeeeeedgfffc deeeeeafffg dbeafffabd cfffaeeeeb dfffabeeeeeebd dafffd dbeeeeeeeb afffd dbeeeeeebd afffc dbeeeeeebd gfffc beeeeeeebd cfffg dbeeeeeebd cfffa beeeeeee dfffa dbeeee dfffad dbee afffd d afffc gfffc gfffg cfffg cfffa dfffad dafffd afffd gfffc gfffg cfffg cfffa dfffa ``` <!-- end of image --> I am surprised, so clear, 1 intersection has appeared in area A. Answer: A: 1; 1 = 1 I've found a single intersection point in the image.

<!-- image --> ```palette Key,Color ,#fefefeff a,#e29a2aff b,#e7b5c9ff c,#f2d29fff d,#f6e4dfff e,#d681a3ff f,#de8a02ff g,#e9b35cff ``` ```image b ee eeb eee eded de ee be beeed ee beeeb ee deeee eb beeed e deeeb de eeeed be beeeb fc ee eeee ff eb beeeb ff ed deeeb afd d de beeed gfc ee be deeeb cfg be ee eeeed dfa ee ee beeeb ff deb eb deeee ff ee e beeed ff ee de deeeb ffd be be beeed afd ee ee beeafc deb eb cfaee ee ed dfa beeeb ee de ff deeee be be ff beeed ee ee ff deed deb ee afd ee eb gfc ee ed cfg be de dfa ee be ff deb ee ff ee eb ff eeed afd bee gfc ee cfg b dfa ff ff ff ffd afd gfc cfg dfa ff ff fc ff fff afd dffg gfc gffc cfg ffa dfa gfd ff ff ff dfg ff af afd ff gfc dfc cfg af dfa fa ff cfd ff ff ff fg ff gfd afd ff gfc dfg cfg af dfa ff ff cfc ff ff ff fa afd cfd gfc ff cfg fgdfa gfff ff ``` <!-- end of image -->

I'm curious to see if this image contains any intersection points. There are 1 areas where the lines seem to converge. We should take a closer look at area A. <!-- image --> ```palette Key,Color ,#fefefeff a,#285e59ff b,#9a0fc7ff c,#b0d7b1ff d,#b170caff e,#528275ff f,#eef3efff g,#88ac9aff ``` ```image aa gaaa ffffffffffffffffffaaaaffffffffffffffffffffffffff fcccccccccccccccccgaaaaacccccccccccccccccccccccccf fcccccccccccccccccaaaeaagccccccccccccccccccccccccf fcccccccccccccccccaaacaaaccccccccccccccccccccccccf fccccccccccccccccgaaccgaaecccccccccccccccccccccccf fccccccccccccccccaaacccaaacccccccccccccccccccccccf fccccccccccccccccaaecccgaaeccccccccccccccccccccccf fccccccccccccccceaacccccaaaccccccccccccccccccccccf fcccccccccccccccaaaccccccaaacccccccccccccccccccccf fccccccccccccccgaagcccccceaacccccccccccccccccccccf fccccccccccccccaaaccccccccaaaccccccccccccccccccccf fccccccccccccccaaecccccccceaagcccccccccccccccccccf fccccccccccccceaaccccccccccaaacccccccccccccccccccf fcccccccccccccaaaccccccccccgaaeccccccccccccccccccf fccccccccccccgaagcccccccccccaaaccccccccccccccccccf bd fccccccccccccaaacccccccccccccaaecccccccccccccccccf dbbbbd fccccccccccccaaecccccccccccccaaacccccccccccccccccf fbbbbbbbbd fccccccccccceaacccccccccccccccaaaccccccccccccccccf bbbbbffbbbbbd fcccccccccccaaaccccccccccccccceaagcccccccccccccccfdbbbbd fbbbbbf fccccccccccgaagccccccccccccccccaaacccccccccccccccbbbbb dbbbbbf fccccccccccaaaccccccccccccccccceaagccccccccccccdbbbbf dbbbbbf fccccccccccaaeccccccccccccccccccaaaccccccccccgbbbbd dbbbbbf fccccccccceaacccccccccccccccccccgaaeccccccccbbbbbf dbbbbbf fcccccccccaaaccccccccccccccccccccaaaccccccdbbbbdcf dbbbbb fccccccccgaagcccccccccccccccccccccaaaccccbbbbbcccf dbbbbb fccccccccaaaccccccccccccccccccccccaaaccbbbbbcccccf bbbbbb fccccccccaaecccccccccccccccccccccccaaabbbbdccccccf bbbbbd fccccccceaaccccccccccccccccccccccccebbbbbccccccccf bbbb fcccccccaaacccccccccccccccccccccccccbbbdcccccccccf fbd fcccccccaagcccccccccccccccccccccccccbbagcccccccccf fccccccaaaccccccccccccccccccccccccccbbaacccccccccf fccccccaaacccccccccccccccccccccccccdbbaaeccccccccf fcccccgaaccccccbbbcccccccccccccccccbbbaaaccccccccf fcccccaaacccccbbbbbdcccccccccccccccbbbcaaacccccccf fcccccaaeccccdbbbbbbbccccccccccccccbbbcaaacccccccf fcccceaacccccbbbccbbbbbccccccccccccbbdccaaaccccccf fccccaaaccccbbbccccdbbbbgccccccccccbbdcceaagcccccf fcccgaagccccbbbccccccbbbbbcccccccccbbccccaaacccccf fcccaaaccccbbbccccccccdbbbbdccccccdbbccccgaagccccf fcccaaecccdbbdccccccccccbbbbbcccccdbbcccccaaaccccf fcceaaccccbbbcccccccccccccbbbbbcccbbbcccccgaaecccf fccaaacccbbbcccccccccccccccdbbbbgcbbbccccccaaacccf fcgaagcccbbbcccccccccccccccccbbbbbbbdcccccccaaaccf fcaaacccbbbcccccccccccccccccccdbbbbbdcccccccaaaccf fcaaeccdbbdcccccccccccccccccccccbbbbcccccccccaaacf feaacccbbbccccccccccccccccccccccccbbccccccccceaagf faaaccbbbcccccccccccccccccccccccccccccccccccccaaaf caagcgbbbcccccccccccccccccccccccccccccccccccccgaag aaaccbbbcccccccccccccccccccccccccccccccccccccccaaa feecdbbdcccccccccccccccccccccccccccccccccccccccgaae fcccbbbcccccccccccccccccccccccccccccccccccccccccaaa fccbbbcccccccccccccccccccccccccccccccccccccccccccaaa fcgbbbccccccccccccccccccccccccccccccccccccccccccceaaf fcbbbccccccccccccccccccccccccccccccccccccccccccccfaaa fdbbdccccccccccccccccccccccccccccccccccccccccccccfgaac fbbbcccccccccccccccccccccccccccccccccccccccccccccf aaa bbbffffffffffffffffffffffffffffffffffffffffffffff caag fbd aaa faae aaa faaa eaaf aaa gaac af aaa faaa caag caaae aaa eaaag faae aaaaf aaa faaaa aaa caaae eaaf eaaag aaa aaaaf gaac faaaa aaa caaae caag gaaag aaaaaaaf faaaaa aaaa ag ``` <!-- end of image --> I'm going to scrutinize area A for any signs of an intersection. <!-- image --> ```palette Key,Color ,#fefefeff a,#285e59ff b,#9a0dc8ff c,#9ab4b1ff d,#b44ed6ff e,#5d8682ff f,#ddd9e6ff g,#d499e7ff ``` ```image eaaaaaaaae faaaaaaaaaaf caaaaaaaaaae aaaaaeeaaaaac faaaaaffaaaaae eaaaaa caaaaac aaaaac aaaaaa caaaaaf caaaaac eaaaae eaaaaaf faaaaac faaaaae eaaaaa eaaaaaf aaaaac faaaaae caaaaaf caaaaac eaaaae faaaaae faaaaac caaaaac caaaaa aaaaaa aaaaac caaaaac caaaaaf eaaaaaf eaaaae faaaaae faaaaac eaaaaaf caaaaa faaaaae aaaaae caaaaac caaaaaf aaaaaa eaaaae caaaaac faaaaac aaaaaa caaaaa caaaaac aaaaae eaaaaaf faaaaaf faaaaae eaaaae eaaaaaf faaaaac faaaaae caaaaaf caaaaac aaaaae aaaaaa faaaaaf caaaaac eaaaaa eaaaaaf aaaaac caaaaac caaaaaf eaaaaaf eaaaae faaaaae faaaaac eaaaaaf eaaaaa faaaaae gb aaaaac caaaaac fdbb caaaaaf aaaaaa gbbbb eaaaae caaaaac fdbbbbb faaaaac eaaaaaf dbbbbbbb caaaaa caaaaae gbbbbbbbbb aaaaac eaaaaaf fdbbbbbbbbdf caaaaaf faaaaae gbbbbbbbbbg eaaaae eaaaaaf fdbbbbbbbbd faaaaac faaaaae dbbbbbbbbdf caaaaa caaaaac gbbbbbbbbbg aaaaae aaaaaa fdbbbbbbbbdf caaaaaf caaaaac gbbbbbbbbbg eaaaae eaaaaabbbbbbbbbd faaaaac faaabbbbbbbbbdf caaaaa eabbbbbbbbbg aaaaae fabbbbbbbdf faaaaaf dbbbbbbg eaaaae dbbbbbe faaaaac bbbbbaac caaaaaf bbbbbaaa aaaaae fbbbbbaaac faaaaaf gbbbbbaaaaf eaaaaa fgf gbbbbbaaaae aaaaac gbbbd dbbbbbaaaaaf caaaaaf fbbbbbbg dbbbbdaaaaae eaaaae dbbbbbbbdf bbbbbgeaaaaac faaaaac gbbbbbbbbbbg bbbbbffaaaaae eaaaaa bbbbbbbbbbbbdf fbbbbb caaaaac aaaaac gbbbbbbbbbbbbbbd gbbbbb aaaaaa caaaaaf fbbbbbb gbbbbbbbbbg gbbbbd caaaaac eaaaae dbbbbbg fdbbbbbbbbdf dbbbbd eaaaaaf faaaaac gbbbbbd gbbbbbbbbbg dbbbbg faaaaae caaaaa bbbbbbf dbbbbbbbbdf bbbbbg eaaaaaf aaaaac gbbbbbg fdbbbbbbbbd bbbbbf faaaaae caaaaaf fbbbbbb gbbbbbbbbbg fbbbbb caaaaac eaaaae dbbbbbg fdbbbbbbbbdf gbbbbb faaaaaa faaaaac gbbbbbd gbbbbbbbbbg gbbbbd caaaaac caaaaa bbbbbbf dbbbbbbbbdf dbbbbd aaaaaa aaaaae gbbbbbg fdbbbbbbbbd dbbbbg caaaaac caaaaaf fbbbbbb gbbbbbbbbbg bbbbbg eaaaaaf eaaaae dbbbbbg fdbbbbbbbbdf bbbbbf faaaaae faaaaac gbbbbbd gbbbbbbbbbg fbbbbb eaaaaaf caaaaa bbbbbbf dbbbbbbbbdf gbbbbb faaaaae aaaaae dbbbbbg fdbbbbbbbbd gbbbbd caaaaac faaaaaf fbbbbbd gbbbbbbbbbdbbbbd aaaaaa eaaaae dbbbbbf fdbbbbbbbbbbbbg caaaaac faaaaac gbbbbbd gbbbbbbbbbbbg aaaaaaf caaaaaf bbbbbbf dbbbbbbbbbf caaaaac aaaaae dbbbbbg fdbbbbbbb eaaaaaf faaaaaf fbbbbbd gbbbbbb faaaaae eaaaaa dbbbbbf fdbbbg eaaaaaf aaaaac gbbbbbd fgf faaaaae caaaaaf bbbbbb caaaaa eaaaae dbbbbbg aaaaa faaaaac fbbbbbd caaaa eaaaaa dbbbbbf eaaa aaaaac gbbbbbd caaa aaaaaf bbbbbb eaa ceae dbbbbbg faa ff fbbbbbd ea dbbbbbf fa gbbbbbd c bbbbbb dbbbbbg fbbbbbd dbbbbbf gbbbbbd fbbbbbb dbbbbbg fbbbbbd ``` <!-- end of image --> 1 intersection present within area A. Answer: A: 1; 1 = 1 The image features one single intersection point.

<!-- image --> ```palette Key,Color ,#fefefeff a,#285f59ff b,#9a0dc8ff c,#a2b9b7ff d,#b650d7ff e,#648b87ff f,#e1dbe9ff g,#d293e6ff ``` ```image aa caaa aaaaf faaaaa aaaeaac aaa aaa caaf caac aaa aaa aac faae eaa aaa aaa aaa caaf eaaf aaa aaa aae eaac eaa aaa aaa caae caaf aaa bd aaa faae dbbbbg aae aaa fbbbbbbbbg eaa aaa bbbbb fbbbbbg aaa eaaf gbbbbg fbbbbbg faac aaa bbbbb gbbbbbf aaa caac dbbbbf gbbbbbf aae aaa fbbbbd gbbbbbf eaa caae bbbbb dbbbbb aaa aaa gbbbbg dbbbbb faac faae bbbbb dbbbbb aaa aaa dbbbbf dbbbbd aae aaabbbbd bbbbbd caa ebbbbb bbbb aaa bbbg bg faac bbac aaa fbbaa aaa ff gbbaae caaf fbbb dbbaaa aaa bbbbbg bbbfaaa aac gbbbbbbb bbb aaa eaa bbb fbbbbd bbd aaa aaa bbbf dbbbbf bbg eaaf caaf fbbb bbbbb fbb aaa aaa bbb gbbbbg gbb caac aae gbbg dbbbb dbb aaa eaa bbb fbbbbd bbb faae aaa bbbf dbbbbf bbb aaa caaf fbbd bbbbbbbd aaa aaa bbb gbbbbbg aaaf aae dbbg dbbb aaa eaa bbb fbb eaaf aaa bbbf aaa faac fbbd caac aaa bbb aaa ee dbbg faae bbb aaa bbb aaa fbbd eaaf bbb aaa dbbg eaac bbb aaa bbb caac fbd aaa faae aaa aaa eaaf aaa eaac af aaa aaa caac caaae aaa eaaac faae aaaaf aaa aaaa aaa caaaa eaaf eaaac aaa aaaaf caac aaaa aaa faaaa caae eaaae aaaaaaaf faaaaa aaaa ac ``` <!-- end of image -->

Based on a first glance, I suspect there could be intersection regions here. These spots are like clues. Let's see what they reveal about potential intersections. <!-- image --> ```palette Key,Color ,#fefefeff a,#246f5aff b,#fe2997ff c,#5b8879ff d,#ea80b2ff e,#b1d6b1ff f,#eceeecff g,#90c298ff ``` ```image bbf bbbd bbbbb fbbbbbb fbb bbbb fbb dbbbf dbb dbbbd dbb fbbbb dbb bbbb dbb bbbb dbb dbbbf bbb dbbbd bbb fbbbb bbb bbbb bbb bbbb bbb dbbbf bbb dbbbd ggggggggggggggg eac bbb fbbbbeeeeeeeeeeeeeeef aaa bbd bbbbeeeeeeeeeeeeeef caaa bbd bbbbeeeeeeeeeeeeef faaaa bbd bbbbeeeeeeeeeeeef aaaaa bbd fdbbbdeeeeeeeeeef gaaaaa fd bbd feebbbbeeeeeeeeef ffffffaaacaafffffbbdffffbbdffff feeebbbbeeeeeeeef geeeeeaaagcaaeeeeebbbeeeebbeeeegf feeeebbbbeeeeeeef geeeegaacecaaeeeebbbbeeeebbeeeeef feeeeebbbbeeeeeef geeeeaaaeecaaeeeebbbbeeeebbeeeeef feecgeedbbbdeeeef geeecaageecaaeeedbbbbeeeebbeeeeef fgaaaeeeebbbbeeef geeeaaaeeecaaeeebbbbbdeeebbeeeeef aaaaaaeeeebbbbeef geeaaaeeeecaaeeebbdbbdeeebbeeeeef caaaacaageeeebbbbef gecaaceeeecaaeedbbebbbeedbbeeeeef eaaaaceeaaaeeeeebbbbf geaaaeeeeecaaeebbbebbbeedbbeeeeef aaaaafeeegaaceeeeedbbbd gaaageeeeecaaeebbdedbbeedbbeeeeef caaaaf feeeeaaaeeeeeeebbbd ggaaeeeeeecaaedbbeeebbeedbbeeeeef eaaaag feeeeeaaaeeeeeeebbbb geeeeeeeeecaaebbbeeebbeedbbeeeeef aaaaa gggggcaacgggggg bbbb geeeeeeeeecaaebbdeeebbdebbbeeeeef aaaaf aaa bbbbf geeeeeeeeecaabbbeeeebbbebbbeeeeef caag faac dbbbd geeeeeeeeecaabbbeeeebbbebbbeeeeef faaa aaaf fbbbd geeeeeeeeecaabbeeeeedbbebbbeeeeef aaa aaa bbbb geeeeeeeeecaabbeeeeedbbebbbeeeeef eaag gaae bbbb geeeeeeeeecaabdeeeeeebbebbbeeeeef aaa aaa bbbbf geeeeeeeeecaabeeeeeeebbdbbbeeeeefcaaf faac dbbbd geeeeeeeeecaabeeeeeeebbbbbbeeeeefaaa caaf fbbbd geeeeeeeeecaadeeeeeeebbbbbdeeeeeaaa aaa bbbb geeeeeeeeecaaeeeeeeeebbbbbdeeeegaag gaag bbbb geeeeeeeeecaaeeeeeeeedbbbbdeeeeaaa aaa bbbbf geeeeeeeeecaaeeeeeeeeebbbbdeeecaaf faaa dbbbf geeeeeeeebcaaeeeeeeeeebbbbdeeeaaa caaf fbd geeeeeeeebcaaeeeeeeeeebbbbeeeaaaf aaa geeeeeeedbcaaeeeeeeeeebbbbeegaacf eaag geeeeeeebbcaaeeeeeeeeebbbbeeaaaef aaa geeeeeeebbcaaeeeeeeeeedbbbecaagef faaa geeeeeedbbcaaeeeeeeeeeebbbeaaaeef caaf geeeeeebbbgaaeeeeeeeeeebbbaaaeeef aaa geeeeeebbdgaaeeeeeeeeeebbcaaceeef eaag geeeeedbbegaaeeeeeeeeeebbaaaeeeef aaa geeeeebbbegaaeeeeeeeeeebaaageeeef aaa geeeeebbdegaaeeeeeeeeeedaaaeeeeef caae geeeebbbeegaaeeeeeeeeeeaaaeeeeeef aaa geeeebbbeegaaeeeeeeeeegaaceeeeeef eaac geeeebbeeegaaeeeeeeeeeaaaeeeeeeef aaa geeebbbeeegaaeeeeeeeeaaageeeeeeef aaa geeebbbeeegaaeeeeeeeeaaaeeeeeeeef gaae geedbbeeeegaaeeeeeeeaaaeeeeeeeeef aaa geebbbeeeegaaeeeeeecaaceeeeeeeeef faac eggbbdgggggaaggggggaaagggggggggg aaaf dbb eaa caaf aaa bbb eaa faac gaae bbd faa aaa aaa dbb faa gaag faac dbb faa aaa aaaf faa caaf aaa faa faac gaag faa aaa aaa faagaag faac faaaaa caaf faaaaf aaa faaac eaa faaa f faag cc ``` <!-- end of image --> Here's a close-up of the area A. <!-- image --> ```palette Key,Color ,#fefefeff a,#246f5aff b,#fe2897ff c,#689a8cff d,#fe6fb9ff e,#aecac2ff f,#ffb9ddff g,#8f4f79ff ``` ```image caaaaaecaaaae fbbbbd dbbbbf eaaaaac caaaae dbbbbb dbbbbf aaaaaa caaaae fbbbbbb bbbbbf caaaaae caaaae dbbbbbbf bbbbbf eaaaaac caaaae bbbbbbbf bbbbbf aaaaaa caaaae fbbbbbbbd bbbbb eaaaaae caaaae dbbbbbbbd bbbbb aaaaac caaaae bbbbbbbbd bbbbb caaaaae caaaae fbbbbbbbbb bbbbb eaaaaac caaaae dbbbbbbbbb bbbbb aaaaaa caaaae bbbbbbbbbbf fbbbbb caaaaae caaaae fbbbbbdbbbbf fbbbbb eaaaaac caaaae dbbbbddbbbbd fbbbbb caaaaa caaaae fbbbbbffbbbbd fbbbbd eaaaaac caaaae dbbbbb fbbbbb fbbbbd aaaaaa caaaae bbbbbd bbbbb fbbbbd caaaaae caaaae fbbbbbf bbbbbf fbbbbd eaaaaac caaaae dbbbbd dbbbbf fbbbbd aaaaaa caaaae bbbbbf dbbbbd dbbbbd eaaaaae caaaae fbbbbb fbbbbd dbbbbd eaaac caaaae dbbbbd fbbbbb dbbbbd cae caaaae bbbbbf bbbbb dbbbbf caaaae fbbbbb bbbbbf dbbbbf caaaae dbbbbd dbbbbf dbbbbf caaaae bbbbbf dbbbbd dbbbbf caaaaedbbbbb fbbbbd dbbbbf caaaaebbbbbd fbbbbb bbbbbf caaaacbbbbbf bbbbb bbbbbf caaaagbbbbb bbbbbf bbbbbf caaaagbbbbf dbbbbf bbbbb caaaagbbbb dbbbbd bbbbb caaaagbbbd dbbbbd bbbbb caaaagbbbf fbbbbd bbbbb caaaagbbb fbbbbb bbbbb caaaagbbd bbbbb fbbbbb caaaagbbf bbbbbffbbbbb caaaagbb dbbbbffbbbbb caaaagbd dbbbbdfbbbbd caaaagbf fbbbbdfbbbbd caaaagb fbbbbbfbbbbd caaaagd bbbbbdbbbbd caaaag bbbbbdbbbbd gaaaag dbbbbbbbbbd e gaaaac dbbbbbbbbbd a fgaaaac fbbbbbbbbbd ca dgaaaac fbbbbbbbbbf eaa bgaaaac bbbbbbbbbf caa fbgaaaac bbbbbbbbbf eaaa bbgaaaac dbbbbbbbbf aaaa fbbgaaaac dbbbbbbbbf caaaa dbbgaaaac fbbbbbbbbf eaaaaa bbbgaaaac fbbbbbbbbf caaaaa fbbbgaaaac bbbbbbbbf eaaaaac dbbbgaaaac bbbbbbbb aaaaaa bbbbgaaaac dbbbbbbb caaaaae fbbbbgaaaac dbbbbbbb eaaaaac dbbbbgaaaac dbbbbbbb caaaaa bbbbbcaaaac fbbbbbbb eaaaaac fbbbbbeaaaac fbbbbbbb aaaaaa dbbbbdeaaaac bbbbbbbcaaaaae fbbbbbfeaaaac bbbbbbbaaaaac dbbbbb eaaaac dbbbbbaaaaaa bbbbbd eaaaac dbbbbgaaaaac fbbbbbf eaaaac fbbbbaaaaaa dbbbbd eaaaac fbbbgaaaaae bbbbbf eaaaac bbbaaaaac fbbbbb eaaaac bbaaaaaa dbbbbd eaaaac dgaaaaac bbbbbf eaaaac daaaaaa fbbbbb eaaaac caaaaae dbbbbd eaaaac eaaaaac bbbbbf eaaaac caaaaa dbbbbb eaaaac eaaaaae bbbbbd eaaaac aaaaaa fbbbbbf eaaaac caaaaae dbbbbd eaaaac eaaaaac bbbbbf eaaaac caaaaa fbbbbb eaaaac eaaaaae dbbbbd eaaaac aaaaaa bbbbbf eaaaac caaaaae fbbbbb eaaaac eaaaaac dbbbbd eaaaac caaaaa bbbbbf eaaaac eaaaaae dbbbbb eaaaac aaaaaa ``` <!-- end of image --> There is 1 intersection point visible in this close-up of area A. Next up, a closer look at another region. Here's a close-up of the area B. <!-- image --> ```palette Key,Color ,#fefefeff a,#256f5bff b,#fe2897ff c,#599182ff d,#ffa6d3ff e,#9bbdb4ff f,#f0e1eaff g,#ff61b2ff ``` ```image gf bbf bbbd bbbbd bbbbbg bbbbbbgf gbbbbbbbf gbbbbbbbd dbbbbbbbd dbbbbbbbg fbbbbbbbgf fgbbbbbbbf gbbbbbbbd dbbbbbbbd dbbbbbbbg fbbbbbbbgf fgbbbbbbbf gbbbbbbbd feef dbbbbbbbd eaaaaf dbbbbbbbg eaaaaaac fbbbbbbbgf fcaaaaaaaae fgbbbbbbbf aaaaaaaaaaaf gbbbbbbbd aaaaaaaaaaac dbbbbbbbd aaaaaccaaaaae dbbbbbbbg aaaae faaaaaa fbbbbbbbg aacf eaaaaae fgbbbbbb cf caaaaaf gbbbbb faaaaac dbbbb caaaaae dbbb faaaaaa fbb eaaaaae fg caaaaaf faaaaac ``` <!-- end of image --> No intersection in area B, but I'll keep looking. Answer: A: 1; B: 0; 1 + 0 = 1 My investigation reveals that there is exactly one intersection in this image.

<!-- image --> ```palette Key,Color ,#fefefeff a,#256f5bff b,#ff2797ff c,#6a8f88ff d,#fe94cbff e,#a7c5bcff f,#eddde6ff g,#ff57aeff ``` ```image bbf bbbd bbbbg fbbbbbb fbb bbbb fbb gbbbf dbb dbbbd dbb fbbbg dbb bbbb dbb bbbb gbb gbbbf gbb dbbbd gbb fbbbg bbb bbbb bbb bbbb bbb gbbbf bbb dbbbd eac bbg fbbbg aaa bbg bbbb aaaa bbg bbbb faaaa bbd gbbbf aaaaa bbd dbbbd caaaaa fg bbd fbbbg aaacaa bbg bbd bbbb aaa caa fbbb bbf bbbb eaac caa bbbb bbf gbbbf aaa caa bbbb bb ef dbbbd caaf caa dbbbb fbb eaaa fbbbg aaa caa bbbbbf fbb aaaaaa bbbb aaa caa bbgbbd fbb caaaacaae bbbb eaae caa dbb bbb dbb eaaaac aaa gbbbf aaa caa bbb bbb dbb aaaaa faac dbbbd aaaf caa bbd dbb dbb caaaaf aaa fbbbg eac caa gbb fbb dbb eaaaac aaa bbbb caa bbb bbf gbb aaaaa caae bbbb caafbbf bbd gbb aaaaf aaa gbbbf caagbb bbg gbb caac faac dbbbd caabbg bbb bbb aaa aaaf fbbbg caabbf gbb bbb aaa aaa bbbb caabb dbb bbb eaac eaae bbbb caabg bbfbbb aaa aaa gbbbf caab bbdbbg caaf faac dbbbd caab bbgbbg aaa aaaf fbbbg caad bbbbbg aaa aaa bbbb caa gbbbbd eaac eaae bbbb caa dbbbbd aaa aaa gbbbf fcaa fbbbbd caaf faaa dbbb gcaa bbbbd aaa caaf fbd bcaa bbbbf aaa aaa fbcaa bbbbf eaac eaac bbcaa gbbbf aaa aaa bbcaa dbbb caaf aaa dbbeaa fbbbfaaa caaf bbbeaa bbbaaa aaa bbdeaa bbcaae eaac dbb eaa bbaaa aaa bbb eaa baaaf aaa bbd eaa daaa caae gbb eaa aaa aaa bbb eaa eaae eaac fbbf eaa aaa aaa bbb eaa caaf aaa bbg eaa faaa caae dbb eaa aaa aaa bbb eaa eaae faac bbd eaa aaa aaa dbb eaa caaf aaa bbb faa faaa caae bbd faa aaa aaa gbb faa eaae faac dbb faa aaa aaaf faa aaaf aaa faa faaa eaae faa aaa aaa faaeaae faaa faaaaa caaf faaaaf aaa faaac eaa faaa f aae cc ``` <!-- end of image -->

Based on a first glance, I suspect there could be intersection regions here. The image has some tight areas where segments are too close. I should investigate those closely. <!-- image --> ```palette Key,Color ,#fefefeff a,#ed6351ff b,#823556ff c,#daa598ff d,#9a707fff e,#f0f0ecff f,#b1d7b1ff g,#98c597ff ``` ```image e dd bb bb bb fbb ddb beb b b b be eb bf dd dc bc dd b cd b eb eb eb cd b dc b fggggggggggggbggggbgggggggggggggggggggggggggg e gffffffffffffbffffbffffffffffffffffffffffffffe caae gffffffffffffbffffbffffffffffffffffffffffffffe caac ac gfffffffffffgbffffbgfffffffffffffffffffffffffe caaae ca gfffffffffffddffffbdfffffffffffffffffffffffffe caaae ea gfffffffffffbgffffgbgffffffffffffffffffffffffe eaaae a gfffffffffffbfffffffbdfffffffffffffffffffffffe eaaac a gfffffffffffbffffffffbbffffffffffffffffffffffe eaaac a gffffffffffgbfffffffffbbfffffffffffffffffffffe caac ae gffffffffffddffffffffffdbffffffffffffffffffffe caac cc gffffffffffbgfffffffffffdbgffffffffffffffffffe caaae ca gffffffffffbfffffffffffffgbdfffffffffffffffffecaaae ea gffffffffffbcffffffffffffffbbffffffffffffffcaaae a gfffffffffgaafffffffffffffffbbffffffffffcaaace a gfffffffffdaaffffffffffffffffdbfffffffaaacfffe ae gfffffffffbaafffffffffffffffffdbgffaaacffffffe ac gfffffffffbaaffffffffffffffffffgaaaafffffffffe cc gfffffffffbaaffffffffffffffffcaaabdffffffffffe ea gfffffffffacacffffffffffffcaaaffffbbfffffffffe a gffffffffdafacfffffffffcaaacfffffffbbffffffffe a gffffffffbafcaffffffcaaacfffffffffffdbgffffffe a gffffffffbaffaffffaaacfffffffffffffffgbgfffffe ae gffffffffbaffafaaacffffffffffffffffffffbdffffe ac gffffffffacffaaaffffffffffffffffffffffffbbfffe ca gfffffffgafffffffffffffffffffffffffffffffbbffe ea gfffffffdaffffffffffffffffffffffffffffffffdbge a gfffffffbafffffffffffffffffffffffffffffffffgbf a gfffffffbaffffffffffffffffffffffffffffffffffgbd c gfffffffacfffffffffffffffffffffffffffffffffffebb gffffffgacfffffffffffffffffffffffffffffffffffe bb gffffffdaffffffffffffffffffffffffffffffffffffe dbe gffffffbaffffffffffffffffffffffffffffffffffffe cbe gffffffbaffffffffffffffffffffffffffffffffffffe ebc gffffffaaffffffffffffffffffffffffffffffffffffe bd gffffffacffffffffffffffffffffffffffffffffffffe bb gfffffdafffffffffffffffffffffffffffffffffffffe db gfffffbafffffffffffffffffffffffffffffffffffffe cbe gfffffbafffffffffffffffffffffffffffffffffffffe ebc gfffffbafffffffffffffffffffffffffffffffffffffe bd gfffffacfffffffffffffffffffffffffffffffffffffe bb gffffgaffffffffffffffffffffffffffffffffffffffe db gffffdaffffffffffffffffffffffffffffffffffffffe cbe gffffbaffffffffffffffffffffffffffffffffffffffe ebc gffffbaffffffffffffffffffffffffffffffffffffffe ebd gffffacffffffffffffffffffffffffffffffffffffffe bb gfffgafffffffffffffffffffffffffffffffffffffffe bb gfffdafffffffffffffffffffffffffffffffffffffffe dbe gfffbafffffffffffffffffffffffffffffffffffffffe fbf gfffbafffffffffffffffffffffffffffffffffffffffe ebd gfffacfffffffffffffffffffffffffffffffffffffffe bb gffgacfffffffffffffffffffffffffffffffffffffffe bb gffdaffffffffffffffffffffffffffffffffffffffffe dbe gffbaffffffffffffffffffffffffffffffffffffffffe cbe gffbaffffffffffffffffffffffffffffffffffffffffe ebc gffaaffffffffffffffffffffffffffffffffffffffffe bd gffacffffffffffffffffffffffffffffffffffffffffe bb gfdafffffffffffffffffffffffffffffffffffffffffe db gfbafffffffffffffffffffffffffffffffffffffffffe cbe gfbaffffffffffffffffffffffffffffffffffffffffge e ecaeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee ac a ``` <!-- end of image --> Let's get to the bottom of what's happening inside area A. <!-- image --> ```palette Key,Color ,#fefefeff a,#ef604eff b,#813457ff c,#c19daeff d,#a06681ff e,#edcfd1ff f,#f5998eff g,#b9474fff ``` ```image ebb cbd cbb cbd cbd cbb dbc ebb bbe ebb ebbe bbe cbb bbe cbd bbe dbc dbc bbc dbbe bbe ebbbe cbd dbbc dbd dbbd bbc cbbde bbe cbbbe ebb ebbbc cbb edbbc dbd dbbd dbc cbbde bbe cbbbe ebb ebbbc cbb edbb cbd dbd dgae cbd ef baaf bbbe efaaa ebaaa ebbbe efaaaaaf ebaaa ebbbc efaaaaafe cgaaa dbbd faaaaaf dgaaae dbbd efaaaafe bgaaae cbbbe efaaaaae baaaaf ebbbeefaaaaafe ebaafaf eggaaaaafe cgaafaa efaaaaaae dgafeaa efaaaaafdbbd baae aae efaaaafe cbbbe ebaae aae efaaaafe ebbbc cbaa faf efaaaaaf edbbc cgaa faf efaaaaafe dbbd dgaf faf efaaaaafe cbbd baaf eaa efaaaaafe cbbe ebaae eaa faaaaaaf ebbc cbaa aae faaaaafe ebbc cgaa aae efaaaafe dbbd dgaf faaaaaafe cbbd baaf faaaafe cbbbe baae eafe ebbbe ebaa ebbbc cgaa dbbd dgaf dbbd bgaf cbb baae eb ebaae e cgaa dgaf dgaf baae cbaa cgaa dgaf baaf ebaae ebaa cgaa dgaf baaf baae ebaa cgaa dgaf dgaf baae ebaae cgaa cgaf dgaf baae baae baa gaf aaf aae eaa caa daf baf bae eba cga dgf dgf bae ebae cga cga dga baa ebaa ebaa cgaa dgaf baaf ebaa cgaa dgaf daaf baae ebaa cgaa cgaf dgaf baae ebaae ``` <!-- end of image --> The close-up clearly shows 1 intersection point in area A. Answer: A: 1; 1 = 1 The image features one single intersection point.

<!-- image --> ```palette Key,Color ,#fefefeff a,#ee5e4cff b,#823456ff c,#c3a0b1ff d,#a06882ff e,#edd5d8ff f,#f7afa6ff g,#f38274ff ``` ```image dd bb bb bb ebb ddb beb b b b be eb be cd dc bc dd b cd b eb b b cd b dc b b b b b gaae b b faag gf cb be faag fg dc dc faage ea be ebe eaaae a b ebd eaaaf a b bd egaaf a eb bb gaaf ae dd db faag gf be cbe faag fa b ebc faage a bf bd eaaae a eag bb eaaaf a caa db gaaf a baa cbe gaaf gf baa eaaag fg bga faagbd ea afae faage bb a ca gf eaaae db a da fg eaaaf cbe a ba ea gaaf ebc ae bg a gaaf bd gf af aag bb fg ea bb ea da db a ba ebe a ba ebd f af bb eae bb ca db ba cbe ba ebc ag bd ae bb ca db da cbe ba ebc bg bd af bb ca db da cbe ba ebc ba bd af bb eae bb da db ba ebe ba ebd af bb eae bb ca db ba cbe ba ebc ag bd ae bb ca db da cb ba e fg gf a ``` <!-- end of image -->

I'm approaching this image with caution. Intersections might be tricky to spot. These zones indicate regions where lines appear to be in close proximity. <!-- image --> ```palette Key,Color ,#fefefeff a,#99f3a0ff b,#f9bde9ff c,#b1d7b1ff d,#f07cd1ff e,#96c996ff f,#68f374ff g,#d1fbd5ff ``` ```image d dd dd bbd d d d a b d db gg d b bb f d b bd a b bb d a d b d f bb b d gg d d d f b d d f d d d a d dd f b db ag d f bb f d ga d f d a d f b f d cg b a d f d f d gg d f bb f d a b a d f d f b gg d a bb f d f d gg d f d a f ceeeeeeeeeeeeeeeedeeeeec gfg a eccccccccccccccccdccccce fa a eccccccccccccccccdccccce af f ecccccccccccccccdcccccce gfg f ecccccccccccccccdcccccce fa gg eccccccccccccccdccccccce af a eccccccccccccccdccccccce gfg f ecccccccccccccccccccccce fa gfg ecccccccccccccdcccccccce af gfg ecccccccccccccdcccccccce fg af eccccccccccccdccccccccce fa af eccccccccccccdcccccccccegffa ff ecccccccccccdcccccccafffg fa ecccccccccccdcccafffacce fa eccccccccccccfffacccccce gfg eccccccccfffacccccccccce gfg eccccaffaccdccccccccccce afeafffcccccdcccccccccccce fcccccccccdcccccccccccce eccccccccdccccccccccccce eccccccccdccccccccccccce ecccccccccccccccccccccce ecccccccdcccccccccccccce ecccccccdcccccccccccccce eccccccdccccccccccccccce eccccccdccccccccccccccce ecccccdcccccccccccccccce ecccccdcccccccccccccccce ecccccdcccccccccccccccce eccccdccccccccccccccccce eccccdccccccccccccccccce d d bb d b bd ddddddddddddddddddddddbbbbbbbbbbbbbb ``` <!-- end of image --> I'm analyzing this close-up of area A with precision. <!-- image --> ```palette Key,Color ,#fefefeff a,#84f38dff b,#f7a7e2ff c,#aaf9b1ff d,#f475d3ff e,#fad5f0ff f,#62f46fff g,#d2fbd6ff ``` ```image db bde db ede dd edb bd db bde dd ede bd edb bd db ede dd ede bd db bde db ede dd edb gc bd gcafff db gcafffacg bde gcafffacg dd gcafffacg edecaffffcg gaffffacg gcafffacg gcafffacbd gcafffacg db gcafffacg bde aggcafffacg dd fffffcg ede ccg bd edb bde db ede dd edb bd db bde db ede dd edb bd db bde dd ede bd edb bd db ede ``` <!-- end of image --> The lines cross each other within area A, forming 1 intersection. Answer: A: 1; 1 = 1 One intersection, that's it, but I found it.

<!-- image --> ```palette Key,Color ,#fefefeff a,#91f79aff b,#f79fe0ff c,#b4f9baff d,#f474d2ff e,#faceeeff f,#65f572ff g,#d9fcdcff ``` ```image d bd dd eed d d d a b b be gg d b bb f d e eb a b ee ed a d e d f ee b d cg d b d f b d d f d d d a d dde f b de cg d f ee f d gc b f b a d f ee f d cg eb a d f d a b gg d f ee f d a b c d f d f b cg d a ee f d a b gc d f d a f be gfg a d fa c ee af f d gfg f b fa cg b cf a d gfg f ee fa gfc d cf cfg b gfg cfg d fa af d cffa af b gffag fa d gafag fa eeaffc gfc affc gfg cffc b cfgcffa d cg d b d ee d b b d ee d b d d b d ee d b eeed dddddddddddddddddbbbbbbbbbbbeeeeeeee ``` <!-- end of image -->

I'm analyzing this image to identify any points where lines intersect. I have a hunch that these areas might contain the intersections we're looking for. <!-- image --> ```palette Key,Color ,#fefefeff a,#6ad997ff b,#9046e5ff c,#3cd581ff d,#ecf5efff e,#b1d7b2ff f,#a28dcfff g,#a0d1a4ff ``` ```image dddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddffdddddddddd ggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggbbbgggggcaggg geeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeefbbbbeeeegceeee geeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeebbbefbeeeecceeee geeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeebbbfeeebeeeecceeee geeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeebbbeeeeebfeeecaeeee geeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeebbbeeeeeeebbeegcgeeee geeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeefbbbeeeeeeeebbeeaceeeee geeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeebbbeeeeeeeeeebbeecceeeee geeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeefbbfeeeeeeeeeeebbeecceeeee geeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeebbbeeeeeeeeeeeeefbeecaeeeee geeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeefbbfeeeeeeeeeeeeeefbeaceeeeee geeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeebbbeeeeeeeeeeeeeeeeebfcceeeeee geeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeefbbfeeeeeeeeeeeeeeeeeebfcceeeeee geeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeebbbeeeeeeeeeeeeeeeeeeeebbcaeeeeee geeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeebbbfeeeeeeeeeeeeeeeeeeeeebfcgeeeeee geeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeebbbeeeeacaeeeeeeeeeeeeeeeebcceeeeeee geeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeebbbeeeeecccceeeeeeeeeeeeeeeefcceeeeeee geeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeefbbbeeeeaccacceeeeeeeeeeeeeeeefcaeeeeeee geeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeebbbeeeeeccceecceeeeeeeeeeeeeeeegcgeeeeeee geeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeefbbfeeeegccaeeecceeeeeeeeeeeeeeeeacfeeeeeee geeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeebbbeeeeeccceeeeecceeeeeeeeeeeeeeeeccbeeeeeee geeeeeeeeeeeeeeeeeeeeeeeeeeeeeefbbfeeeegccaeeeeeeaceeeeeeeeeeeeeeeeccbeeeeeee geeeeeeeeeeeeeeeeeeeeeeeeeeeeebbbeeeeeaccgeeeeeeeaceeeeeeeeeeeeeeeecfbeeeeeee geeeeeeeeeeeeeeeeeeeeeeeeeeefbbfeeeeeccceeeeeeeeegceeeeeeeeeeeeeeeacfbeeeeeee geeeeeeeeeeeeeeeeeeeeeeeeeebbbeeeeeaccgeeeeeeeeeegcgeeeeeeeeeeeeeeccfbeeeeeee geeeeeeeeeeeeeeeeeeeeeeeefbbfeeeeeccceeeeeeeeeeeeecgeeeeeeeeeeeeeeccebfeeeeee geeeeeeeeeeeeeeeeeeeeeeebbbeeeeeaccaeeeeeeeeeeeeeecaeeeeeeeeeeeeeecaebfeeeeee geeeeeeeeeeeeeeeeeeeeebbbfeeeeeccceeeeeeeeeeeeeeeecaeeeeeeeeeeeeegcgebbeeeeee geeeeeeeeeeeeeeeeeeeebbbeeeeegccaeeeeeeeeeeeeeeeeecceeeeeeeeeeeeeaceebbeeeeee geeeeeeeeeeeeeeeeeebbbeeeeeecccgeeeeeeeeeeeeeeeeeecceeeeeeeeeeeeecceebbeeeeee geeeeeeeeeeeeeeeefbbbeeeeegccceeeeeeeeeeeeeeeeeeeecceeeeeeeeeeeeecceefbeeeeee geeeeeeeeeeeeeeebbbeeeeeeaccgeeeeeeeeeeeeeeeeeeeeecceeeeeeeeeeeegcgeefbeeeeee geeeeeeeeeeeeefbbfeeeeeeccceeeeeeeeeeeeeeeeeeeeeeecceeeeeeeeeeeeaceeeebeeeeee geeeeeeeeeeeebbbeeeeeeaccaeeeeeeeeeeeeeeeeeeeeeeeeaceeeeeeeeeeeecceeeebfeeeee geeeeeeeeeefbbfeeeeeeccceeeeeeeeeeeeeeeeeeeeeeeeeeaceeeeeeeeeeeecceeeebbeeeee geeeeeeeeebbbeeeeeegccaeeeeeeeeeeeeeeeeeeeeeeeeeeeaceeeeeeeeeeeecaeeeebbeeeee geeeeeeefbbfeeeeeecccgeeeeeeeeeeeeeeeeeeeeeeeeeeeegcgeeeeeeeeeeaceeeeebbeeeee geeeeeebbbeeeeeegccaeeeeeeeeeeeeeeeeeeeeeeeeeeeeeegcgeeeeeeeeeecceeeeebbeeeee geeeebbbfeeeeeeaccgeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeecaeeeeeeeeeecceeeeefbeeeee geeebbbeeeeeeeccceeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeecaeeeeeeeeeecaeeeeeebeeeee gebbbeeeeeeegccgeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeecaeeeeeeeeegcgeeeeeebfeeee fbbbeeeeeeeecceeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeecceeeeeeeeeaceeeeeeebfeeee bbbgggggggggccggggggggggggggggggggggggggggggggggggggccgggggggggccgggggggbbgggg dbbfdddddddddgcgddddddddddddddddddddddddddddddddddddddccdddddddddcadddddddbbdddd bbbd dcc cc ce bb fbbf cc ac ec fb bbb acd ac cc dbd bf eca ec cc bd cc ec cg fd cc dcd ecd ace ce ac dcc ce cc cc ca ca ccd ca dcd gcg cc gc dcc cc cc cc cc cc acd cc ce eca ac ec cc gc cc cc ec cc ace dcd cg dcc dcd dcd cc ce ac ccd cg cc ecg ca ca dcc cc dce cc cc gc cd cc cc cc cc ac ce acecd ecac eccc dcca ccd cc cc ca ``` <!-- end of image --> Let's see if area A yields any clues. <!-- image --> ```palette Key,Color ,#fefefeff a,#61d69bff b,#9043e7ff c,#3cd681ff d,#dec8f7ff e,#91e7b8ff f,#af78edff g,#c6f2daff ``` ```image dbbb aeg dbbbbb ccg fbbbbbb gcc dbbbf bb eca dbbbf bb ccg dfbbbd bbd gccg dfbbbd bbd aca bbbbf fbf cce dbbbfd fbf ccg dbbbfd dbb cc fbbbb dbbd cc fbbbd bbd gcc dbbbf fbf eca bbbbf fbf ccg dfbbbd dbb gccg bbbbf dbb ecc bbbb bbdcce dbbbfd bbfccg dbbbf bbfcc fbbbb bbbcc dbbbf bbbcc bbbbf gag bbacc dfbbbd cca bbace dfbbbd ccccc fbccg bbbb gaccccc dacc dbbbfd eccccgcc daca dbbbfd gcccc gccg gcce fbbbb cccag ccg gccd fbbbd ecccc cce accf bbbbf gccce ace cccb bbbbf gccca eca cccbd dfbbbd eccce eca ccabd bbbb ccca eca ccabd fbbbb eccca gcc eccfbf dbbbfd gccce gcc ecafbb dbbbf gccca ccg ccgdbb fbbbd ecccg ccg gcc bb dbbbf accca ccg eca bb bbbbf accca cce ccg bb dfbbbd gccce cce ccg bb dfbbbd gccca cca cc bb fbbbb ecccg ccc cc bbd dbbbfd accca ccc gcc bbd dbbbfd accca ccc eca fbf fbbbd gccce ccc ace fbf fbbbd gccce ccc gcc dbb bbbbf ecccg ccc eca dbbd dfbbbd accca acc ace bbd dfbbbd accca ecc gccg fbf fbbbb gccce ecc ecc fbf fbbbb cccce ecc ccc dbb dbbbfd ecccg gcc ccc dbb dbbbf ecccg gccg cca bb fbbbd accc ccg cce bb bbbbf eccce ccg ccg bb bbbbf cccce ace ecc bb dfbbbd ecccg ace aca bbd dfbbbd gcccg eca gccg bbd fbbbb acc eca ecc fbf dbbbfd ecce eca eca fbf bbfd ccc gcc ccg dbb ``` <!-- end of image --> Wow! I can see 1 intersection so clearly in area A! Answer: A: 1; 1 = 1 I have found one intersection!

<!-- image --> ```palette Key,Color ,#fefefeff a,#6add9fff b,#9145e7ff c,#3cd681ff d,#dfc9f7ff e,#9ce9bfff f,#b888efff g,#cef4dfff ``` ```image ff bbb ce fbbbb gc dbbb fb ac fbbd dbd cc dbbb bf ca bbbd bf gcg dbbf bb ac bbb bb cc dbbf bb ca bbb fb ce fbbf db ec bbb bdcc fbbd bfcc bbb bbce fbbd bbc dbbb aca bcc bbbd cccc fcc dbbb eccecc dca bbbd ccc cc gce dbbf gcce cc ecf bbb acc ac ccb fbbf gcca ac ccb bbb accg ec cab fbbf ccc gc ecfb bbb eccg gcg ccdb fbbd ccc cg cc bd dbbb ecce ce ca bf fbbd ccc ca gcg bb dbbb gcca ca ac bb bbbd accg cc cc bb dbbf cca cc ca fb bbb accg cc cg db dbbf ccc cc ec dbd bbb ecce ac cc bf fbbf ccc ec cc bf bbb gcce ec ce bb fbbd acc gc ec bb bbb gcca cg ac fb fbbd accg ce cc fb dbbb ccc ce ca dbd bbbd gccg ca gcg bd dbbb cc cc ac bf bbbd cc cc cc bb dbbf ece cc ca bb bbb cc cc ce bb fbbf cc ac ec fb bbb acg ac cc db bf eca ec cc bd cc gc ce fd cc gcg gc ace cg ac gcc ce cc cc ca ca cc ca gcg ece cc ec cc cc cc cc cc cc acg cc ce gca ac ec cc ec cc cc ec cc ace gc ce gcc cg gcg cc ce ac ccg ce cc ece ca ca cc cc cg cc cc ec cg cc cc cc cc ac ce acec ecac gccc gcca ccg cc cc ca ``` <!-- end of image -->

Here's an image. My task is to find intersections or areas where lines come close together. The image has some tight areas where segments are too close. I should investigate those closely. <!-- image --> ```palette Key,Color ,#fefefeff a,#0fd987ff b,#f01a56ff c,#aed7b0ff d,#ee99aeff e,#e9f4edff f,#e45b7dff g,#57e0a5ff ``` ```image ea aaa aaag caeaac aa aae ag aa gae eaa aa gag eag aag ga aae aa aa eac eaa aa caa aa gag cae aac aa aae ag aa ga eaa eeeeeeeeeeeeeeeeaaeeeee caa eccccccccccccccccagccccce gag ecccccccccccccccaacccccce aae ecccccccccccccccaacccccce aae eccccccccccccccgagcccccce eaa eccccccccccccccaaccccccce caagce eccccccccccccccaaccccccce gaaaaaaaaaggce ecccccccccccccgacccccccce ecggaaaaaaaaaaaagce ecccccccccccccaacccccccce ecggaaaaaaaaaaaagce ecccccccccccccagcccccccce ecgaaaaaaaaac eccccccccccccgaccccccccce ecge eccccccccccccaaccccccccce eccccccccccccagccccccccce ecccccccccccaacccccccccce ecccccccccccaacccccddccce eccccccdffffafbbbbbbbbbbfd ddffbbbbbbbbbbbbaabbbffdccfbbbbbbbfd bbbbbbbbbffdccccaaccccccccccceedbbbbbbbfe e ecccccccccgacccccccccccce efbbbbbbbde ecccccccccaacccccccccccce dfbbbbbbbd ecccccccccagcccccccccccce dfbbbbbbfd eccccccccgaccccccccccccce dbbbbbbbfd eccccccccaaccccccccccccce edbbbbbbbfe eccccccccagccccccccccccce efbbbbbbbde ecccccccaacccccccccccccce dfbbbbbbbd ecccccccaacccccccccccccce dfbbbbbbfd eccccccgagcccccccccccccce dbbbbbd eccccccaaccccccccccccccce ede eccccccaaccccccccccccccce ecccccgacccccccccccccccce ecccccaacccccccccccccccce cccccagcccccccccccccccc ga aa eac aa aa cae aa ag gae aa eag ga aa eac aa aa cae aa ag gae aa eag ga aa eac aa aa cae aa ag e ``` <!-- end of image --> Could this be where the intersection is hiding, in area A? <!-- image --> ```palette Key,Color ,#fefefeff a,#0ed986ff b,#f01956ff c,#87e9c1ff d,#f9aec3ff e,#c7f4e2ff f,#ef5d85ff g,#47dc9fff ``` ```image caaae gaaa eaaac caaae gaag eaaac caaa aaag eaaae gaaa aaac caaae gaaa eaaac caaae gaag eaaac caaa aaag eaaae gaaa aaac caaae gaag eaaac caaae aaag eaaac caaa ddddd aaagddffffbbbbbbbbbbffdd ddddffffbfaaafbbbbbbbbbbbbbbbbbbbb ddddffffbbbbbbbbbbbbbgaaabbbbbbbbbbbbbbbbbbbbb bbbbbbbbbbbbbbbbbbbbbbaaagbbbbffffdddd ddfbbb bbbbbbbbbbbbbbbbbbfffcaaae d bbbbbbffffdddd gaag dd eaaac caaae aaag eaaac gaaa aaag caaae gaaa aaac caaae gaag eaaac caaae aaag eaaac gaaa aaag caaae gaaa eaaac caaae gaag eaaac caaa aaag eaaac gaaa ``` <!-- end of image --> There is 1 intersection point visible in this close-up of area A. Answer: A: 1; 1 = 1 There's one and only one intersection present in the image.

<!-- image --> ```palette Key,Color ,#fefefeff a,#0fd987ff b,#f11956ff c,#88ecc3ff d,#f9a9c0ff e,#c6f5e2ff f,#ef5e86ff g,#4ce2a5ff ``` ```image a aaa aaag caeaae aa aa ag aa ga eaa aa cag ac aac ga aae aa aa eac aa aa caa aa gag cae aac aa aae ag aa ga eaa aa caa eac gac ga aae aa aa eae aa aa eaagce aa gaaaaaaaaagce cae ecgaaaaaaaaaaaagce aa eccgaaaaaaaaaaaagce ag ecgaaaaaaaaac ga ecge aa eac aa aa dd ddfffafbbbbbbbbbbfd ddffbbbbbbbbbbbbaabbffdd dbbbbbbbfd bbbbbbbbffdd ag fbbbbbbbfd cae dfbbbbbbbf aa dfbbbbbbbd ag dfbbbbbbfd ga dbbbbbbbfd aa fbbbbbbbfd eac dfbbbbbbbf aa dfbbbbbbbd aa dfbbbbbbfd cae dbbbbbf aa f ag ca aa ag ga aa eac aa aa cae aa ag ca aa ac ga aa eac aa aa cae aa ag ga aa ac ga aa eac aa aa cae aa ag e ``` <!-- end of image -->

This image looks interesting. I wonder if there are any intersections hidden in there? I have a hunch that these areas might contain the intersections we're looking for. <!-- image --> ```palette Key,Color ,#fefefeff a,#a3bba8ff b,#59d28eff c,#cbe1d3ff d,#b1d7b2ff e,#7fdaa6ff f,#eaf3edff g,#95ca97ff ``` ```image c b b fb ce af ec aa b ccca b a af b a a b dc ca ce a ac dc fa a bf af fa b c a dc b aa cc af b aca a fa bf af a fa dd bc af a af af bd faf df a a be fa cc cd ca ee fa fd a dgaggggggggggggggggggggbb ca a a gddaddddddddddddddddddebf ca a cc gdddaddddddddddddddddgbdf ca a a gdddaadddddddddddddddbddf da a fa gddddaddddddddddddddbdddf da a af gdddddaddddddddddddbddddf aa a a gdddddaaddddddddddbgddddf ad df cd gddddddadddddddddbedddddf f cc a gdddddddadddddddbeddddddf cd a gdddddddaadddddbbdddddddf fa dc gddddddddaddddebddddddddf a a gdddddddddaddebdddddddddf a fa gdddddddddaagbddddddddddf a af gddddddddddgbdddddddddddf a a gddddddddddbadddddddddddf a cd gdddddddddbddaddddddddddf b df a gddddddddbgddaadddddddddf ce cc a gdddddddbeddddadddddddddf b cc dc gddddddbeddddddaddddddddf ed fa a gdddddbbdddddddaadddddddf b a fa gddddbbdddddddddadddddddf ec a af gdddebdddddddddddaddddddf b a a gddebddddddddddddaadddddf bf a cc gdgbddddddddddddddadddddf fb a a gdbddddddddddddddddaddddf bf af a gbdddddddddddddddddaadddf cb dc dc bdddddddddddddddddddadddf b cc a bgggggggggggggggggggggagg de fd fa bd fa b a af be ac ed a a ee a b a cc eb fa ec a a db dd b afa cb af bf aaf fb a fb da fb ca b cd bf af cb bf a b bc ca de bd ac b be a ed ee fa b db d bc cb b cb bf fb fb bf b bf ce bc b bd de be b ee ed eb b db bc cb fb fb bffb fbbf bf ``` <!-- end of image --> I'm eager to see what's happening in this magnified view of area A. <!-- image --> ```palette Key,Color ,#fefefeff a,#a2baa9ff b,#59d28fff c,#cce6d6ff d,#b9cbbdff e,#7adba5ff f,#e7f3ecff g,#9fe5beff ``` ```image faac caaf g dad cb aac cbb caaf cbbg dad fbbg aac fbbe faaf febe caa ebe dad ebbf faaf gbbf caa gbbf dad gbbc faac cbbc caaf cbbg dad fbbg aac fbbg faaf fbbe dad ebe aac ebef faaf ebbf caa gbbf dad gbbc faaf cbbc caa cbbc daabbg fabbg fbbbf febbad ebefaac ebbf faaf gbbf dad gbbf aac gbbc faaf cbbc caa cbbg dad fbbg faaf fbbg caa fbbe dad ebe faac ebef caaf ebbf dad gbbf aac gbbc faaf cbbc dad cbbc aac cbbg faaf fbbg caa fbbe dad febe faaf ebe caa ebbf dad bbf faac ``` <!-- end of image --> Oh my, look at that! It's 1 intersection in area A! Answer: A: 1; 1 = 1 My investigation reveals that there is exactly one intersection in this image.

<!-- image --> ```palette Key,Color ,#fefefeff a,#a3baa8ff b,#59d28fff c,#d2e7daff d,#bccdc0ff e,#7fdca8ff f,#ecf4efff g,#a8e7c4ff ``` ```image c b b fb ge af ec aa b cdca b a ac b a a b dc ca ce a ac gg ca a bf af fa b d a dd b aa dd af b aca a fa bc ac a fa dd bc af af ac af bg faf dc a a be faf cc cd ca ee fa cd a ac gb ca fa a a gb ca a dc ca cb da a a ac fb da a fa a bf da a af fa bf aa a a dd bc ad df cd af bg f dc a fa be cd a dd ee fa dc af eb a a a gb a fa cacb a af ab a a fba a cd bfca b df a bc ac ge dc a bc a b cd dc bg fa eg fa a be dd b a fa ee af eg a af gb fa b a a gb dd bc a cd cb af fb a a fb a bf af a bf ca cb dc dc bf ac b cd a bc a ge fd ca bg fa b a af be ad eg a a ee a b a dd eb fa ec a a gb dd b afa cb af bf aac fb a fb da fb da b cd bf af cb bc a b bc ca ge bg ac b be a eg ee fa b gb d bc gb b cb bf fb fb bf b bf ce bc b bg ge be b ee eg eb b gb bc cb fb fb bffb cbbf bc ``` <!-- end of image -->

I'm ready to tackle this image and find those intersections! These zones are intriguing. I bet there's something interesting happening within them. <!-- image --> ```palette Key,Color ,#fefefeff a,#3c1115ff b,#bed898ff c,#8f867aff d,#b1d7b1ff e,#654b48ff f,#9ac398ff g,#edf3e9ff ``` ```image gg dbbb gbbbbbb gbbbbbbbd dbbbbbbbg gbbbbbbbg gbbbbbbbd dbbbbbbbg gbbbbbbbg gbbbbbbbd dbbbbbbbg gbbbbbbbg gbbbbbbbd bbbbbbbb gbbbbbbbg gbbbbbbbg gbbbbbbb bbbbbg gbbb bbb bbb dbbg bbb gbbd bbb fac bbb caaaa dbbg eaaaaaae bbb gaaaaaacaaa gbbg daaaaaac caaf bbb caaaaaad aaa fffffffffffffffffffffffffffffffffffbbbffff caaaaaag aaag ddddddddddddddddddddddddddddddddddbbbdddddg eaaaaae gaae ddddddddddddddddddddddddddddddddddbbbdddddg gaaaaaac aaa ddddddddddddddddddddddddddddddddddbbddddddg daaaaaaf faac dddddddddddddddddddddddddddddddddbbbddddddg caaaaaag aaa dddddddddddddddddddddddddddddddddbbbddddddg eaaaaaeg eaag ddddddddddddddddddddddddddddddddbbbdddddddg gaaaaaae aaa ddddddddddddddddddddddddddddddddbbbdddddddgdaaaaaac aaa dddddddddddddddddddddddddddddddbbbdddddddcaaaaaad daae dddddddddddddddddddddddddddddddbbbdddddeaaaaaag aaa dddddddddddddddddddddddddddddddbbbdddeaaaaae caad ddddddddddddddddddddddddddddddbbbdfaaaaaaeg aaa ddddddddddddddddddddddddddddddbbcaaaaaacddg aaag dddddddddddddddddddddddddddddbcaaaaaafddddg gaae dddddddddddddddddddddddddddddaaaaaadddddddg aaa dddddddddddddddddddddddddddeaaaaedddddddddg caac dddddddddddddddddddddddddfaaaaadddddddddddg aaa ddddddddddddddddddddddddaaaaacbdddddddddddg eaag ddddddddddddddddddddddcaaaaabbddddddddddddg f dddddddddddddddddddddaaaaafbbbddddddddddddg dddddddddddddddddddeaaaaeddbbdddddddddddddg dddddddddddddddddcaaaaadddbbbdddddddddddddg ddddddddddddddddaaaaafddddbbbdddddddddddddg ddddddddddddddeaaaaedddddbbbddddddddddddddg ddddddddddddfaaaaadddddddbbbddddddddddddddg dddddddddddaaaaacdddddddbbbdddddddddddddddg dddddddddcaaaaedddddddddbbbdddddddddddddddg dddddddfaaaaafddddddddddbbbdddddddddddddddg ddddddeaaaacdddddddddddbbbddddddddddddddddg ddddcaaaaadddddddddddddbbbddddddddddddddddg dddaaaaafdddddddddddddbbbdddddddddddddddddg ddaaaaedddddddddddddddbbbdddddddddddddddddg ddcaadddddddddddddddddbbbdddddddddddddddddg dddcdddddddddddddddddbbbddddddddddddddddddg dddddddddddddddddddddbbbddddddddddddddddddg ddddddddddddddddddddbbbdddddddddddddddddddg ddddddddddddddddddddbbbdddddddddddddddddddg ddddddddddddddddddddbbbdddddddddddddddddddg dddddddddddddddddddbbbddddddddddddddddddddg dddbdddddddddddddddbbbddddddddddddddddddddg ddbbbdddddddddddddbbbdddddddddddddddddddddg ddbbbbbdddddddddddbbbddddddddddddddddddddfg ggggbbbbgggggggggdbbgggggggggggggggggggggg bbbb bbb bbbbg gbbd bbbbd bbb gbbbb bbb gbbbb dbbg bbbbbbb bbbbbd gbbb gbd ``` <!-- end of image --> This is a magnified view of the region A. <!-- image --> ```palette Key,Color ,#fefefeff a,#3c1014ff b,#bed898ff c,#846a69ff d,#d2d9beff e,#5c393aff f,#aa9b96ff g,#e8edddff ``` ```image dbbbbbg bbbbbb gbbbbbg bbbbbb gbbbbbd dbbbbbg bbbbbb gbbbbbg bbbbbb gbbbbbd dbbbbbg bbbbbd dbbbbbg bbbbbb gbbbbbd dbbbbb gbbbbbd dbbbbbg bbbbbb gfa gbbbbbg gcaaa bbbbbb dcaaaaa gbbbbbd feaaaaaaa dbbbbbg feaaaaaaaaa bbbbbb gcaaaaaaaaaaaa gbbbbbgdcaaaaaaaaaaaafg bbbbbfeaaaaaaaaaaaef gbbbceaaaaaaaaaaaed dbfeaaaaaaaaaaacd beaaaaaaaaaaacg faaaaaaaaaaefg deaaaaaaaaaef caaaaaaaaaed feaaaaaaaaaf gcaaaaaaaaacg faaaaaaaaaefg deaaaaaaaaacbb gcaaaaaaaaaebbbd faaaaaaaaaefbbbb deaaaaaaaaafbbbbbd gcaaaaaaaaacgdbbbbbg feaaaaaaaaef bbbbbb geaaaaaaaaac gbbbbbg faaaaaaaaaed bbbbbb deaaaaaaaaaf gbbbbbd gcaaaaaaaaacg dbbbbbg faaaaaaaaaed bbbbbb deaaaaaaaaaf gbbbbbg gcaaaaaaaaacg bbbbbb faaaaaaaaaed gbbbbbd deaaaaaaaaaf dbbbbbg caaaaaaaaaeg bbbbbd feaaaaaaaaef dbbbbbg gcaaaaaaaaacg bbbbbb faaaaaaaaaed gbbbbbd deaaaaaaaaaf dbbbbb gcaaaaaaaaacg gbbbbbd faaaaaaaaaed dbbbbbg deaaaaaaaaaf bbbbbb gcaaaaaaaaacg gbbbbbg feaaaaaaaaef bbbbbb geaaaaaaaaac gbbbbbd faaaaaaaaaed dbbbbbg deaaaaaaaaaf bbbbbb caaaaaaaacg gbbbbbg eaaaaaed bbbbbb daaaaf gbbbbbd cacg dbbbbbg gd bbbbbd dbbbbbg bbbbbb gbbbbbd dbbbbb gbbbbbd dbbbbbg bbbbbb gbbbbbg bbbbbb gbbbbbd g dbbbbbg gbd bbbbbb gbbbbg gbbbbbg bbbbbbg bbbbbb dbbbbbbbd gbbbbbd ``` <!-- end of image --> Bingo! This close-up reveals 1 intersection in area A! Answer: A: 1; 1 = 1 After careful examination, I conclude that there is one intersection.

<!-- image --> ```palette Key,Color ,#fefefeff a,#3c1014ff b,#bed898ff c,#8d7574ff d,#d4e0beff e,#5e3b3eff f,#b5a6a5ff g,#ebefe1ff ``` ```image g dbbb gbbbbbb gbbbbbbbd dbbbbbbbg gbbbbbbbg gbbbbbbbd dbbbbbbbg dbbbbbbbg gbbbbbbbd dbbbbbbb dbbbbbbbg gbbbbbbbd dbbbbbbb dbbbbbbbg gbbbbbbbd gbbbbbbd bbbbbg gbbd bbb bbb dbbg bbb gbbd bbb fac bbb caaaa dbbg eaaaaaac bbb gaaaaaacaaa gbbd daaaaaaf caaf bbb faaaaaad aaa bbb caaaaaag eaag bbb eaaaaae gaae bbb gaaaaaac aaa dbbg faaaaaaf faac bbb caaaaaad aaa bbd eaaaaae eaad bbb geaaaaac aaa bbb daaaaaac aaa dbbg faaaaaaf daac bbb caaaaaag aaa gbbd eaaaaae caaf bbb gaaaaaac aaa bbcaaaaaaf aaag dfaaaaaad gaae aaaaaeg aaa caaaae faac gaaaaag aaa eaaaacb eaag faaaaebb f gaaaaagbbb eaaaac gbbd faaaaa bbb aaaaad bbb caaaac bbb daaaaa bbb eaaaaf dbbg caaaae bbb gaaaaag gbbd eaaaac bbb faaaae bbb aaaaad dbbg aaaac bbb faa gbbd f bbb bbb dbbg bbb gbbd bbb b bbb bbbg bbb dbbbd bbb gbbbb dbbg bbbb bbb bbbbg gbbd dbbbd bbb gbbbb bbb bbbb dbbg bbbbbbb bbbbbd dbbb gbd ``` <!-- end of image -->

This image seems promising for intersection detection. These regions highlight areas that look suspicious. Lines seem to converge within them. <!-- image --> ```palette Key,Color ,#fefefeff a,#1723ecff b,#dc90e4ff c,#e7caf4ff d,#8693e6ff e,#b2d7b2ff f,#4653e8ff g,#a1cea2ff ``` ```image c b bc bc bc bc cb cb cb cb b b b b b b b b bc bc bc bb cb cb cb b b gggggbgggggggggggg eeeeebeeeeeeeeeeeg eeeeebeeeeeeeeeeeg eeeeebeeeeeeeeeeeg cdaa eeeeebeeeeeeeeeeeg dfaaaadaf eeeeebeeeeeeeeeeeg cfaaaafc ac eeeeebeeeeeeeeeeeg cdaaaafd ca eeeeebeeeeeeeeeeeg dfaaaad fa eeeeebbeeeeeeeeeeg cfaaaafc af eeeeebbeeeeeeeeeeg daaaafd ac eeeeebbeeeeeeeeeeg dfaaaadc da eeeeebbeeeeeeeeegfaaaafc fa eeeeeebeeeeedaaaaad af eeeeeebdfaaaafgeeg ac eeefaabafdeeeeeeeg da eeeadebeeeeeeeeeeg fa eeeeeebeeeeeeeeeeg ad eeeeeebeeeeeeeeeeg ac eeeeeebeeeeeeeeeeg da eeeeeebeeeeeeeeeeg aa eeeeeebeeeeeeeeeeg ad eeeeeebeeeeeeeeeeg cac eeeeeebeeeeeeeeeeg da eeeeeebeeeeeeeeeeg aa eeeeeebbeeeeeeeeeg ad eeeeeebbeeeeeeeeeg ca eeeeeebbeeeeeeeeeg da eeeeeebbeeeeeeeeeg af eeeeeeebeeeeeeeeeg ggggadggggggggggg gggggggbgggggggggg geeegaeeeeeeeeeee b geeeefaeeeeeeeeee b geeeeeafeeeeeeeee b geeeeeeadeeeeeeee b geeeeeedaeeeeeeee b geeeeeeefaeeeeeee b geeeeeeeeafeeeeee b geeeeeeeeeadeeeee bc geeeeeeeeedaeeeee bc geeeeeeeeeefaeeee bc geeeeeeeeeeeageee bc cbbbbbbc geeeeeeeeeeeeeeee cb cbbbbbc cbbbeeeeeeeeeeeeeeee cb cbbbbbc cbbbeeeeeeeeeeeeee cb cbbbbbc gebbbbeeeeeeeeeee cb cbbbbbc geeeebbbeeeeeeeee b cbbbbbc geeeeeebbbeeeeeee b cbbbbbc geeeeeeeeebbbeeee b ccbbbbcc ggggggggggggbgggg b cbbbbbc b cbbbbbc b cbbbbcc b cbbbbbc bbbc ``` <!-- end of image --> Time to investigate area A up close. <!-- image --> ```palette Key,Color ,#fefefeff a,#1823edff b,#de8ce6ff c,#edd4f6ff d,#7d84f4ff e,#b2b3f7ff f,#4a50efff g,#e8afedff ``` ```image bbc bbc bbc bbg bbg gbg gbg gbg gbb cbb cbb cbb cbb cbbc bbc bbc bbc bbc bbg bbg gbg gbg gbg gbb gbb ced cbb cedfaaaa cbb edfaaaaaaaaf cbb cedfaaaaaaaafdec cbbcedfaaaaaaaafdec eebbfaaaaaaafde edfaaabbfaafdec eaaaaabbec cafde bbc bbc bbg bbg gbg gbg gbg gbb cbb cbb cbb cbb cbbc cbbc bbc bbc bbc bbc bbg gbg gbg gbg gbb gbb cbb cbb cbb cbb ``` <!-- end of image --> I've cracked the case! This area contains 1 intersection. Onward to the next region of interest. Let's take a closer look at area B. <!-- image --> ```palette Key,Color ,#fefefeff a,#1824edff b,#de8de6ff c,#ece0f9ff d,#8086f4ff e,#b6b9f8ff f,#464ff0ff g,#eab7efff ``` ```image caaf eaad faae cfaac eaaf daad faae caaac eaaf daad faae caaac eaaf daad faae caaac eaaf daad faae caaac eaaf daad faae caafc eafc e g bbgc bbbbbg gbbbbbgc cgbbbbbc cgbbbbbg gbbbbbgc cgbbbbbg gbbbbbgc cgbbbbbc cgbbbbbgc cbbbbbgc cgbbbb ``` <!-- end of image --> It's a shame, but area B doesn't contain an intersection. Answer: A: 1; B: 0; 1 + 0 = 1 One intersection, that's it, but I found it.

<!-- image --> ```palette Key,Color ,#fefefeff a,#1723edff b,#de8de6ff c,#efdbf7ff d,#7f85f4ff e,#b6baf9ff f,#4851f0ff g,#e9b3eeff ``` ```image g bc bc bc bg gg gg gb cb cb b b b b b b b bc bc bc bg gg gb cb cb cb b b b b b cdaa b dfaaaadaf b efaaaade ae bc cdaaaafe ea bc efaaaadc fa bg efaaaafe af gg cdaaaafe ae gg efaaaadc ea gb edaaaafe fa cb daaaafd af cbefaaaadc ac daabafe ea adcb fa b ad b cac b da b aa b ad bc cac bc da bc aa bg ad gg cac gb da gb af cb ae cb ea b fa b af b ae b ea b fa b af b ae bc ea bc fa bg c ac bg cbbbbbbc gg cgbbbbgc cbbg gb cgbbbbgc bbbc cb cbbbbbg gbbg cb cgbbbbgc cbbb cb gbbbbgc gbbc b cbbbbbg cbbg b cgbbbbgc b b gbbbbbc b cgbbbbg b cgbbbbgc b gbbbbbc bbbg ``` <!-- end of image -->

Based on a first glance, I suspect there could be intersection regions here. These regions highlight areas that look suspicious. Lines seem to converge within them. <!-- image --> ```palette Key,Color ,#fefefeff a,#b48a5aff b,#a885b9ff c,#d8c5c3ff d,#c0aa85ff e,#f0f0edff f,#b1d7b1ff g,#a2cda0ff ``` ```image edaaa edaaaaaaaa caaaaaaaaaaaad cdaaaaaaaade aaac edaaaaaaaaac aaae caaaaaaaaac eaaa caaaaaaaaade caaa edaaaaaaaadc daaa daaaaaaaaac aaad caaaaaaaaade aaac edaaaaaaaade aaae eaaaaaaaac eaaa daaaac caaa daa daad aaa aaac aaa aaae aaa eaaa aad caaa aac daaa aac aaad eaae aaac caa aaae caa eaaa daa cad aaa c aaa gggggggggggggggggggggaaaggggggggg fffffffffffffffffffffaaaffffffffge fffffffffffffffffffffaadffffffffge fffffffffffffffffffffaadffffffffge fffffffffffffffffffffaagffffffffge ffffffffffffffffffffgaafffffffffge ffffffffffffffffffffdaafffffffffge ffffffffffffffffffffdaafffffffffge ffffffffffffffffffffaaafffffffffge fffbffffffffffffffffaaafffffffffge ffbbbbbbffffffffffffaaafffffffffge ffbbbbbbbbbgffffffffaaafffffffffge fffffbbbbbbbbbbfffffaadfffffffffge ffffffffgbbbbbbbbbbfaadfffffffffge ffffffffffffbbbbbbbbbbbfffffffffge ffgddfffffffffffbbbbbbbbbbffffffge ffaaaffffffffffffffdbbbbbbbbbbffge ffdaaffffffffffffffdaafbbbbbbbbbbc ffdaaffffffffffffffaaafffffbbbbbbbbbbe ffdaaffffffffffffffaaafffffffffbbbbbbbbbce ffdaaffffffffffffffaaaffffffffffgecbbbbbbbbbc ffdaaffffffffffffffaaaffffffffffge ecbbbbbbbbbc ffdaaffffffffffffffaadffffffffffge ebbbbbbbbbbe ffdaaffffffffffffffaadffffffffffge cbbbbbbbbbc ffgaaffffffffffffffaagffffffffffge cbbbbbbbbbc ffgaafffffffffffffgaafffffffffffge ebbbbbbbbbbe ffgaafffffffffffffdaafffffffffffge cbbbbbbbbbce ffgaafffffffffffffdaafffffffffffge cbbbbbbbbc fffaafffffffffffffaaafffffffffffge ecbbbbbe fffaagffffffffffffaaafffffffffffge ebbb gggaagggggggggggggaaagggggggggggge cbbc eeeaaceeeeeeeeeeeeaaaeeeeeeeeeeee bbb aac aad ebbb aac aac bbb aac aac bbb aac eaae bbbe aac caa bbb aad caa cbbc aad daa bbb aad aaa ebbb aad aaa bbbe aad aaa bbb aad aad cbbc aaa aac bbb aaa aac ebbb aaa eaae bbbe aaaae caa bbb eaaaaae caa cbbc daaaaa daa bbb daaaad aaa ebbb aaaaac aaa bbb eaaaaaaaa bbb caaaaad bbbe caaad c da ``` <!-- end of image --> Let's get to the bottom of what's happening inside area A. <!-- image --> ```palette Key,Color ,#fefefeff a,#b48a5aff b,#a783b9ff c,#e0d2d3ff d,#c6a684ff e,#efe8eaff f,#c4acceff g,#d7c1a8ff ``` ```image caaaaa gaaaad gaaaad gaaaad daaaag daaaag aaaaac aaaaac eaaaaae eaaaaa caaaaa caaaaa gaaaad gaaaad daaaag daaaag aaaaac aaaaac ebfce aaaaae cbbbbbfce eaaaaae fbbbbbbbbbfe caaaaa bbbbbbbbbbbbbfce caaaaa ebbbbbbbbbbbbbbbbbfce gaaaad ecfbbbbbbbbbbbbbbbbbbfc gaaaad ecfbbbbbbbbbbbbbbbbbffe daaaag cfbbbbbbbbbbbbbbbbbbfce daaaag ecfbbbbbbbbbbbbbbbbbbfc daaaag ecfbbbbbbbbbbbbbbbbbbdaaac efbbbbbbbbbbbbbbbbbbbfe ecfbbbbbbbbbbbbbbbbbbfce cggggc ecfbbbbbbbbbbbbbbbbbbfe daaaag effbbbbbbbbbbbbbbbbbfce daaaag fbbbbbbbbbbbbbbbbbbbfce daaaag gaaaabbbbbbbbbbbbbbbbbbbfe daaaag daaaad effbbbbbbbbbbbbbbbb daaaag daaaag cfbbbbbbbbbbbbb daaaag daaaag ecfbbbbbbbbb gaaaag aaaaac ecfbbbbb gaaaad aaaaac efbb gaaaad eaaaaae e gaaaad eaaaaa gaaaad caaaaa gaaaad gaaaad gaaaad gaaaad gaaaad gaaaad gaaaad daaaag caaaad daaaag caaaaa aaaaac caaaaa aaaaac caaaaa eaaaaae caaaaa eaaaaa caaaaa caaaaa eaaaaa caaaaa eaaaaa gaaaad eaaaaa gaaaad eaaaaae daaaag eaaaaae daaaag eaaaaae aaaaac aaaaae aaaaac aaaaae eaaaaae ``` <!-- end of image --> Case closed! This is definitely 1 intersection point in area A. Answer: A: 1; 1 = 1 After careful examination, I conclude that there is one intersection.

<!-- image --> ```palette Key,Color ,#fefefeff a,#b48a5aff b,#a783b9ff c,#e2d3ccff d,#c5a580ff e,#efe7e8ff f,#c3abceff g,#d5bfa5ff ``` ```image edaaa gaaaaaaaa gaaaaaaaaaaaad cdaaaaaaaade aaag edaaaaaaaaac aaae gaaaaaaaaag eaaa caaaaaaaaade caaa edaaaaaaaadc daaa gaaaaaaaaag aaad caaaaaaaaage aaac cdaaaaaaaade aaae aaaaaaaac eaaa gaaaag gaaa daa daad aaa aaag aaa aaae aaa aaa aad caaa aag gaaa aac aaad eaae aaag caa aaae gaa eaaa daa cad aaa c aaa aaa aad aag aac eaae caa gaa daa aaa efe aaa fbbbbf aaa bbbbbbbbbc aad efbbbbbbbbfe aag cbbbbbbbbbf aac fbbbbbbbbbf cgg efbbbbbbbbbe daa fbbbbbbbbbfe daa gaa fbbbbbbbbbf gaa daa efbbbbbbbbbe gaa aaa ebbbbbbbbbfe gaa aaa cbbbbbbbbbf gaa aad efbbbbbbbbbc gaa aad efbbbbbbbbfe caa aag cbbbbbbbbbf caa aac fbbbbbbbbbc caa eaa efbbbbbbbbfe eaa caa cbbbbbbbbbf eaa gaa fbbbbbbbbf eaae daa efbbbbb aae aaa ebbb aae aaa fbbc aac aaa bbb aac aad ebbf aac aag bbb aac aac bbb aag eaae fbbe aag caa bbb aag gaa cbbf aag daa bbb aad aaa ebbb aad aaa bbbe aad aaa bbb aad aad fbbf aaa aag bbb aaa aac ebbb aaa eaae bbbe aaaae caa bbb eaaaaa gaa fbbc gaaaad daa bbb daaaad aaa ebbf aaaaag aaa bbb eaaaaaaaa bbb caaaaad fbb gaaag f da ``` <!-- end of image -->

This is the image I'm working with. The goal is to count the intersections. I need to zoom in on these areas to get a better look. <!-- image --> ```palette Key,Color ,#fefefeff a,#9865d2ff b,#7b9f48ff c,#c9a6edff d,#99c289ff e,#b1d7b1ff f,#761cd2ff g,#eef1efff ``` ```image ggg fff fff fff fff fff fff aff aff aff aff aff affg affg affg affg affg cffg cffc cffc cffc cffc eg cffc bbbe cffc bbbbb cffc gbbbbbbg cffc bbbebbbbe cffc bbb bbbbb cffc gbbb dbbbbg gffc dbbg gbbbbe gffa bbb bbbbb gffa gbbb dbbbbg gffa dbbe gbbbbe gffa bbb bbbbb gffa gbbb dbbbbg ffa dbbe gbbbbe ffa bbb bbbbb ffa bbb dbbbbg ffa dbbe gbbbbe ffa bbb bbbbb fff bbb dbbbbg fff ebbe gbbbbe fffggggggggggggggggggggggggggggggggggggggbbbggg bbbbb fffeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeebbbeedg dbbbbg fffeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeedbbdeeeg gbbbbe fffeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeebbbeeeeg bbbbb fffeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeebbbeeeeg dbbbbg fffeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeedbbdeeeeg gbbb fffeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeebbbeeeeeg bg fffeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeebbbeeeeeg fffeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeedbbbeeeeeg fffeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeebbbeeeeeeg fffeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeebbbeeeeeeg fffeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeedbbbeeeeeeg fffeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeebbbeeeeeeeg ffffaeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeebbbeeeeeeeg ffffffffeeeeeeeeeeeeeeeeeeeeeeeeeeeedbbbeeeeeeeg afffffffffaeeeeeeeeeeeeeeeeeeeeeeeebbbeeeeeeeeg deeefffffffffaeeeeeeeeeeeeeeeeeeeeebbbeeeeeeeeg deeeeeefffffffffaeeeeeeeeeeeeeeeeeebbbeeeeeeeeg deeeeeeeeeaffffffffaeeeeeeeeeeeeeebbbdeeeeeeeeg deeeeeeeeeeeeaffffffffaeeeeeeeeeeebbbeeeeeeeeeg deeeeeeeeeeeeeeeafffffffffeeeeeeeebbbeeeeeeeeeg deeeeeeeeeeeeeeeeeeafffffffffeeeebbbdeeeeeeeeeg deeeeeeeeeeeeeeeeeeeeeafffffffffabbbeeeeeeeeeeg deeeeeeeeeeeeeeeeeeeeeeeeefffffffbbbeeeeeeeeeeg bdeeeeeeeeeeeeeeeeeeeeeeeeeeeeaffbbbaffaeeeeeeeg bbbbdeeeeeeeeeeeeeeeeeeeeeeeeeeeeebbbffffffaeeeeg bbbbbbdeeeeeeeeeeeeeeeeeeeeeeeeeeebbbaffffffffaeg ebbbbbbdeeeeeeeeeeeeeeeeeeeeeeeedbbdeeeafffffffffg debbbbbbbeeeeeeeeeeeeeeeeeeeeeebbbeeeeeeeafffffffffc deeebbbbbbbeeeeeeeeeeeeeeeeeeeebbbeeeeeeeeeeefffffffffc deeeeebbbbbbbeeeeeeeeeeeeeeeeedbbdeeeeeeeeeeeeggaffffffffc deeeeeeedbbbbbbdeeeeeeeeeeeeeebbbeeeeeeeeeeeeeg gaffffffffa deeeeeeeeedbbbbbbdeeeeeeeeeeeebbbeeeeeeeeeeeeeg affffffffag deeeeeeeeeeedbbbbbbdeeeeeeeeedbbdeeeeeeeeeeeeeg cffffffffag deeeeeeeeeeeeeebbbbbbdeeeeeeebbbeeeeeeeeeeeeeeg cfffffffffc deeeeeeeeeeeeeeeebbbbbbbeeeeebbbeeeeeeeeeeeeeeg cfffffffffc deeeeeeeeeeeeeeeeeebbbbbbbeedbbdeeeeeeeeeeeeeeg cfffffffffc deeeeeeeeeeeeeeeeeeeedbbbbbbbbbeeeeeeeeeeeeeeeg gaffffffffc deeeeeeeeeeeeeeeeeeeeeedbbbbbbbeeeeeeeeeeeeeeeg gaffffff deeeeeeeeeeeeeeeeeeeeeeeedbbbbbeeeeeeeeeeeeeeeg afff deeeeeeeeeeeeeeeeeeeeeeeeeedbbeeeeeeeeeeeeeeeeg c deeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeg deeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeg ``` <!-- end of image --> Could this be where the intersection is hiding, in area A? <!-- image --> ```palette Key,Color ,#fefefeff a,#a062e0ff b,#7a9f48ff c,#c9a6edff d,#9eb979ff e,#e5e4e5ff f,#761cd2ff g,#c2d2acff ``` ```image fff ebbbbbd fff gbbbbbg fff dbbbbbe fff ebbbbbb fff gbbbbbg fff dbbbbbe fff ebbbbbb fff gbbbbbd fff dbbbbbe fff ebbbbbb fff gbbbbbd fff dbbbbbg fffe bbbbbb fffe gbbbbbd fffe dbbbbbg fffe bbbbbb fffe gbbbbbd fffe dbbbbbg fffe bbbbbb fffe gbbbbbd fffe dbbbbbg fffe bbbbbbe fffe ebbbbbd fffc dbbbbbg fffc bbbbbbe ffface ebbbbbd fffffface gbbbbbg ffffffffface bbbbbbe fffffffffffffae ebbbbbd ffffffffffffffffac gbbbbbg cafffffffffffffffffac bbbbbbe cafffffffffffffffffac ebbbbbb caffffffffffffffffface gbbbbbg ecffffffffffffffffface dbbbbbe ecafffffffffffffffffce ebbbbbb ecafffffffffffffffffac gbbbbbg cafffffffffffffffffac dbbbbbe cafffffffffffffffffac ebbbbbb cafffffffffffffffffac gbbbbbd eaffffffffffffffffface dbbbbbe ecafffffffffffffffface ebbbbbb ecafffffffffffffffffae gbbbbbd ecafffffffffffffffffac dbbbbbg cafffffffffffffffffac bbbbbb cafffffffffffffffffacgbbbbbd caffffffffffffffffbbbbbbg eafffffffffffffbbbbbbe ecafffffffffbbbbbbface e ecafffffbbbbbbffffffae bde ecaffbbbbbbfffffffffac bbbde gbbbbbbffffffffffffac bbbbbdg dbbbbbffffffffffffffffac bbbbbbbdg bbbbbbcafffffffffffffffffac bbbbbbbbbbg ebbbbbd ecffffffffffffffff bbbbbbbbbbbbge dbbbbbg ecaffffffffffff edbbbbbbbbbbbbde bbbbbbe ecafffffffff edbbbbbbbbbbbbde ebbbbbd caffffff egbbbbbbbbbbbbdg gbbbbbg cafff gbbbbbbbbbbbbdg bbbbbbe ca gdbbbbbbbbbbbbg ebbbbbd gdbbbbbbbbbbbbge gbbbbbg edbbbbbbbbbbbbde dbbbbbe edbbbbbbbbbbbbde ebbbbbb egbbbbbbbbbbbbde gbbbbbg gbbbbbbbbbbbbdg dbbbbbe gbbbbbbbbbbbbbg ebbbbbb gdbbbbbbbbbbbbg gbbbbbg edbbbbbbbbbbbbde dbbbbbe edbbbbbbbbbbbbde ebbbbbb egbbbbbbbbbbbbde gbbbbbd gbbbbbbbbbbbbdg dbbbbbe gbbbbbbbbbbbbbg bbbbbb gdbbbbbbbbbbbbg gbbbbbd edbbbbbbbbbbbbge dbbbbbg edbbbbbbbbbbbbdbbbbbb edbbbbbbbbbbbbbbbbd gbbbbbbbbbbbbbbg gbbbbbbbbbbbb gdbbbbbbbbd edbbbbbbg edbbbd eee ``` <!-- end of image --> Eureka! There's definitely 1 intersection in area A! Answer: A: 1; 1 = 1 One intersection, that's it, but I found it.

<!-- image --> ```palette Key,Color ,#fefefeff a,#924bdaff b,#7b9f48ff c,#b686e7ff d,#afc591ff e,#ddc7f3ff f,#761bd3ff g,#dbe5ceff ``` ```image eee fff fff fff fff aff aff aff aff aff aff aff aff cff cffe cffe cffe cffe cffe cffe cffe cffe d cffe bbbd effc bbbbb effc gbbbbbb effc bbbgbbbbd effc bbb bbbbb effc gbbb dbbbb effc bbbg gbbbbd effc bbb bbbbb effc bbb dbbbb effc dbbg gbbbbd ffc bbb bbbbb ffa bbb dbbbb ffa dbbg gbbbbd ffa bbb bbbbb ffa bbb dbbbb ffa dbbd gbbbbd ffa bbb bbbbb ffa bbb dbbbb ffa dbbd gbbbbd fff bbb bbbbb fff bbb dbbbb fff dbbd gbbbbd fff bbb bbbbb fff bbb dbbbb fff gbbd gbbb fff bbb bg fff bbb fff gbbd fff bbb fff bbb fff gbbd fff bbb ffffae bbb fffffffae gbbb efffffffffe bbbg efffffffffc bbb eaffffffffc gbbb affffffffc bbbg cffffffffa bbb cffffffffae bbb cfffffffffe dbbg efffffffffebbb eaffffffbbb b eaffbbbaffc bbbbg bbbffffffc bbbbbbg bbbcffffffffa gbbbbbbd dbbd cffffffffae gbbbbbbd bbb efffffffffe bbbbbbb bbb efffffffffc dbbbbbb dbbd eaffffffffc dbbbbbbg bbb affffffffc dbbbbbbg bbb cffffffffa gbbbbbbd dbbd cffffffffae gbbbbbbd bbb cffffffffae bbbbbbb bbb efffffffffe bbbbbbb gbbd eaffffffffc dbbbbbbbbb eaffffffffc dbbbbbbb affffff gbbbbd cfff gbb e ``` <!-- end of image -->

Here's an image. My task is to find intersections or areas where lines come close together. I've spotted 2 narrow regions that might be worth examining further. Let's call them area A,, and B. <!-- image --> ```palette Key,Color ,#fefefeff a,#1b404bff b,#97df37ff c,#b1d7b1ff d,#527172ff e,#a9e06fff f,#ecf3ebff g,#94bf9aff ``` ```image gcccccccccccccccccccccccccc gcccccccccccccccccccccccccc gcccccccccccccccccccccdcccc gccccccccccccccccccccdaaccc gcccccccccccccccccccgaaaccc gcccccccccccccccccccaaacccc gccccccccccccccccccaaagcccc gcccccccccccccccccdaadccccc gccccccccccccccccgaaacccccc gccccccccccccccccaaaccccccc fcfffffffffffff gcccccccccccccccaaaeebbbccc gbbbcccccccccccgf gcccccccccceebbaaabbbbbbccc gcbbecccccccccccf gccccbbbbbbbbbdaadbbbbeeccc gcbbbcccccccccccf gccebbbbbbbbbbaaacccccccccc gccbbeccccccccccf gcbbbbbeeccccaaaccccccccccc gccbbbccccccccccf gbbbbcccccccaaagccccccccccc gcccbbbcccccccccf cbbbecccccccdaadcccccccccccc gccgebbcccccccccf ebbbccccccccgaaaccccccccccccc gaaacbbbccccccccf bbbbcccccccccaaacccccccccccccc ggaacebbecccccccf fcebbbbbegccccccccaaaccccccccccccccc gcaagcbbbcccccccf cebbbbbbbbbbf gcccccccaaagccccccccccccccc gcaadccbbeccccccf febbbbbbbbbbbbecf gccccccdaadcccccccccccccccc gcdaaccbbbccccccf febbbbbbbbbbbbbcf gcccccgaaaccccccccccccccccc gcgaacccbbbcccccf fcebbbbbbbbbbbbef gcccccaaacccccccccccccccccc gccaagccebbcccccf cebbbbbbbbbbbbec gccccaaaccccccccccccccccccc gccaaacccbbbcccccebbbbbbbbbbbbecf gcccdaadccccccccccccccccccc gccdaacccebbbbbbbbbbbbbbecf ffcaadffffffffffffffffffff gccgaaccccbbbbbbbbbef faaa gcccaadcccgbbeegf aaa fffaaafffffffff aaaf gaa gaad aaf faaa aad aaa daa aaaf caa daac aac caad aad faaa daa aaa faa aaaf aag daag aaa faaa gaa aaa faaf aaaf aag daac aaa gaad gaa faaa aaf aaa aad aaaf daa daag caa caaa aac aaa aad aaa daac daac aaa gaad aaa faaa caad aaa daac aaaf aaa daag aaa caad caad aaa daac aaa aaa daac aaa aad caad aac daac aaf aaa aa aaa faa caad caa daac gaa aaa daa aaa daa caad aad daac aad aaa aag aaa aac caad aaf daac aa aaa faa aaacaa caaaaa daaaa aaaa aad fd ``` <!-- end of image --> Could this be where the intersection is hiding, in area A? <!-- image --> ```palette Key,Color ,#fefefeff a,#1c414cff b,#97e036ff c,#99aaafff d,#5b757dff e,#c9ee98ff f,#dfeed2ff g,#ade661ff ``` ```image ebf fgbbg fbbbbbf gbbbbg fbbbbbe ebbbbb bbbbbe ebbbbbf gbbbbg fbbbbbf gbbbbg fbbbbbe gbbbbb bbbbbe f ebbbbb fcdad bbbbbe aaaaaf ebbbbbf daaaac gbbbbg caaaad fbbbbbf faaaaa gbbbbg aaaaaf fbbbbbe daaaac ebbbbb caaaad bbbbbe aaaaa ebbbbbf daaaaf gbbbbg caaaac fbbbbbf faaaad gbbbbg aaaaa fbbbbbf daaaac gbbbbg caaaad fbbbbbe faaaaa ebbbbb aaaaaf bbbbbe feeg daaaac ebbbbbbbbbbb caaaad gbbbbbbbbbb faaaaa fbbbbbbbbbb daaaaf gbbbbbbbbb caaaac gbbbggeff ``` <!-- end of image --> Area A doesn't meet the criteria for an intersection. Time to investigate another area. I'm determined to find out if an intersection exists in area B. <!-- image --> ```palette Key,Color ,#fefefeff a,#1c414bff b,#97df38ff c,#a7b5b9ff d,#466866ff e,#bfea86ff f,#dcead2ff g,#768c93ff ``` ```image c gad caaadf faaaaad faaaaaaf daaaaac gaaaaag caaaaad faaaaaaf daaaaac gaaaaag caaaaad faaaaad faaaaaaf daaaaac gaaaaag fff caaaaadeeebbbbbb feaaaaaabbbbbbbbbb ffeeebbbbaaaaaabbbbbbbbbbbf ffeeebbbbbbbbbbbdaaaaadbbbbbbbbbbbf feebbbbbbbbbbbbbbbbbdaaaaadbbbbbbbbbeeef ebbbbbbbbbbbbbbbbbbbbaaaaaabbeeeff ebbbbbbbbbbbbbbbbbbbbaaaaaaf fbbbbbbbbbbbbbbbbeeeffdaaaaac fbbbbbbbbbeeeff gaaaaag ebbbbbbbf caaaaad ebbbbbbbf faaaaaaf fbbbbbbbe daaaaaf bbbbbbbe daaaaac bbbbbbf gaaaaag bbbbb caaaaad bbbe faaaaaaf bbf daaaaac bf gaaaaag caaaaad faaaaaaf daaaaaf daaaaac gaaaaag caaaaad faaaaaaf daaaaac gaaaaag caaaaad faaaaadf fdaaaaaf daaaaac ``` <!-- end of image --> The close-up clearly shows 1 intersection point in area B. Answer: A: 0; B: 1; 0 + 1 = 1 The image features one single intersection point.

<!-- image --> ```palette Key,Color ,#fefefeff a,#1b404bff b,#98e038ff c,#b6c2c5ff d,#4b696eff e,#c1ec89ff f,#e0ecd8ff g,#81969cff ``` ```image g gaa faaa aaa aaaf daag caad aaa ef aaaeebbb bbb febbaaabbbbbb fbbe fbbbbbbbbbdaadbbbbee bbb ebbbbbbbbbbaaa bbe bbbbbef aaa ebb bbbb aaaf bbb ebbbe daag febb bbbbf caad aaa bbb bbbb aaa caa fbbf ebbbbbbe aaa aaf bbb febbbbbbbbbbf daac aad bbe febbbbbbbbbbbbbe gaag daa bbb febbbbbbbbbbbbbef faaa caa bbb febbbbbbbbbbbbbef aaa aac ebb eebbbbbbbbbbbbef aaaf aad bbb febbbbbbbbbbbbee daac gaa ebbbbbbbbbbbbbbbef caad faa bbbbbbbbbef aaa aag bbef aaa aaa aaaf gaa gaag aaf faaa aag aaa daa aaa caa daac aac caad aad aaa daa aaa faa aaaf aac gaag aaa faaa gaa aaa aa aaa aag daac aaa caad caa faaa aaf aaa aad aaaf daa gaag caa caaa aac aaa aad aaa gaac daac aaa gaad aaa faaa caad aaa daac aaaf aaa daag aaa caad caad aaa daac aaa aaa daac aaa aad caad aac daac aaf aaa aa aaa faa caad caa daac gaa aaa gaa aaa daa caad aad daac aad aaa aag aaa aac caad aaf daac aa aaa faa aaacaa caaaaa daaaa aaaa aad fd ``` <!-- end of image -->

I'm optimistic that I'll find some intersections in this image. I'm going to focus my attention on these specific areas. <!-- image --> ```palette Key,Color ,#fefefeff a,#58c56bff b,#c980c8ff c,#b2d7b2ff d,#edf4edff e,#8fca93ff f,#a5d2a6ff g,#cca1cbff ``` ```image ad daf aae aaa daaa eaaa aaaa aeea cadfa c aa ca faae aa dad daaaaae dac dac aa daaae aa af eac daaae aa ae ddddddddddddddddddddddddaa daaaf daf aa effffffffffffffffffffffaa daaaf ea aa ecccccccccccccccccccccaad daaac aa aa ecccccccccccccccccccceaad daaac ae aa eccccccccccccccccccccaafd caaac cad ea ecccccccccccccccccccaaffd caaac aa fa ecccccccccccccccccceaecfd caaac aa ca ecccccccccccccccccfaaccfd caaac dac dad ebbcccccccccccccccaacccfd caaad ddddddddaadddddddacdddddddd ebbbcccccccccccccaaecccfd faaad dffffffffaafffffffaefffffffe ecbbbccccccccccceaaccccfd faaadfcccccccaecccccccaaccccccce eccbbbccccccccccaacccccfd faaafccccceaccccccccaaccccccce ecccbbbccccccccaafcccccfd eaaafcccaaccccccccaaccccccce eccccbbbccccccfaaccccccfd dfaaaafcaaccccccccaaccccccce ecccccbbbcccccaacccccccfd dfccaaaaafgbccccccaaccccccce eccccccbbbcccaaecccccccfd dfccccaaacbbccccccaaccccccce ecccccccbbbcfaaccccccccfd dfcccccccbbbgccccceaccccccce eccccccccbbbaacccccccccfd dfcccccccbbbbccccceaccccccce ecccccccccbeaecccccccccfd dfccccccbbcbbcccccfafcccccce eccccccccccaabcccccccccfd dfccccccbbcgbccccccaecccccce ecccccccccaabbbccccccccfd dfcccccbbcccbgcccccaecccccce ecccccccceaecbbbcccccccfd dfccccgbgcccbbcccccaacccccce eccccccccaacccbbbccccccfd dfccccbbccccbbcccccaacccccce ecccccccaafccccbbbcccccfd dfcccgbcccccgbcccccaacccccce ecccccceaaccccccbbbccccfd dfcccbbccccccbgccccaacccccce eccccccaaccccccccbbbcccfd dfccbbcccccccbbccccaacccccce ecccccaafcccccccccbbbccfd dfccbbcccccccbbccccaacccccce eccccfaacccccccccccbbbcfd dfccbgcccccccgbcccceacccccce eccccaacccccccccccccbbbfd dfcbbcccccccccbgccceacccccce ecccaaeccccccccccccccbbbd dfcbbcccccccccbbcccfafccccce eccfaaccccccccccccccccbbb dfcbgcccccccccbbccccaeccccce eccaaccccccccccccccccccbbb dfbbccccccccccgbccccaeccccce eceaeccccccccccccccccccfgbb dfbbcccccccccccbccccaaccccce ecaacccccccccccccccccccfdgbb dfbccccccccccccbbcccaaccccce eaaccccccccccccccccccccfd gbb dbbccccccccccccbbcccaaccccce eaeccccccccccccccccccccfd gbb dbbccccccccccccgbcccaaccccce eccccccccccccccccccccccfd gbb dbccccccccccccccbcccaaccccce efffffffffffffffffffffffd gbb bbccccccccccccccbbccaaccccce dddddddddddddddddddddddd gbb bbccccccccccccccbbcceaccccce gbb dbfccccccccccccccbbcceaccccce gbb bbfcccccccccccccccbccfafcccce gbb bbfcccccccccccccccbgccaecccce gbb dbdfcccccccccccccccbbccaecccce gbb bbdfcccccccccccccccbbccaacccce gbb bbdfccccccccccccccccbccaacccce gbb dbddfccccccccccccccccbgcaacccce gbb bb dfccccccccccccccccbbcaacccce gbb bb dfccccccccccccccccbbcaacccce gbb dbd dfccccccccccccccccgbcaacccce gbb bb dfcccccccccccccccccbgeacccce gbb bb dfcccccccccccccccccbbeacccce gbb gbd dfcccccccccccccccccbbfafccce gbb bb dfcccccccccccccccccgbcaeccce gbb bg dfccccccccccccccccccbgaeccce gbb gbd dfccccccccccccccccccbbaaccce gbb bb dfccccccccccccccccccbbaaccce gbbbg dfccccccccccccccccccgbaaccce gbbd dfcccccccccccccccccccbaaccce gb dfcccccccccccccccccccbaaccce dfcccccccccccccccccccbaaccce dfcccccccccccccccccccgeaccce dfcccccccccccccccccccceaccce dfccccccccccccccccccccbafcce dfccccccccccccccccccccbaecce dfccccccccccccccccccccgefcce dfcccccccccccccccccccccbgcce dfccccccccccccccccccccccccce dfccccccccccccccccccccccccce dfccccccccccccccccccccccccce ``` <!-- end of image --> Let's see what secrets area A holds. <!-- image --> ```palette Key,Color ,#fefefeff a,#57c56bff b,#c97cc8ff c,#a5e0b0ff d,#f7f3f7ff e,#79ce88ff f,#d4efd9ff g,#d190d0ff ``` ```image d c fa daa eaa caaa faaaa eaaaf caaae faaaed daaaaf eaaac faaae dd daaaaf dbgd eaaac dbbbgd caaae dgbbbgd faaaad dgbbbgd deaaaf dgbbbgd caaac dgbbbgd faaaed dgbbbgd daaaaf dgbbbgd caaac dgbbbgd faaae dgbbbgd deaaaf dgbbbgd caaac dgbbbgd faaaed dgbbbgd eaaaf dgbbbgd caaac dgbbbgd faaaad dgbbbgd eaaaf dgbbbgd caaae dgbbbgd daaaad dgbbbgd eaaac dgbbbgfaaae dgbbbaaaaf dgbeaaac dgaaaed deaaabgd caaaebbgd faaaegbbbgd eaaafdgbbbgd caaac dgbbbgd faaaad dgbbbgd eaaaf dgbbbgd caaae dgbbbgd daaaad dgbbbgd eaaac dgbbbgd faaae dgbbbgd daaaaf dgbbbgd caaac dgbbbgd faaae dgbbbgd deaaaf dgbbbgd caaac dgbbbgd faaaed dgbbbgd eaaaf dgbbbgd caaac dgbbbgd faaaad dgbbbg eaaaf dgbbb caaae dgbb daaaad dgb eaaac dg faaae d daaaaf caaac faaae deaaaf caaac faaaed eaaaf faaac fead f ``` <!-- end of image --> Aha! I've found 1 intersection inside area A! Hmm, interesting. Let's check out another area. Time to investigate area B up close. <!-- image --> ```palette Key,Color ,#fefefeff a,#56c56aff b,#ca7ec9ff c,#a9e1b3ff d,#edd5edff e,#7ece8dff f,#d9f1ddff g,#ddacdcff ``` ```image eaae aaac faaac aaac caaaf aaac eaae eaae ef faaaf caae aaef eaaa caaa aaaaf aaae caaa aaaaaef faaac faaaf feaaaaacf caaa faaaf feaaaaacf eaae faaaf eaaaaaacaaac dd aaac feaaaaaaaaf gbb aaac feaaac gbbb eaae faafdbbbbd eaae f bbbbbg caae dbbbbbg caaa bbbbgbb caaa gbbbddbbd faaa bbbb bbg faaa gbbbd bbg faaa bbbd dbbd aaa dbbg bbg eaa bbb bbg eaa dbbg bbb eaa bbb bbbd caa gbbd bbbd caa bbb bbbg caa gbbb gbbb faaf gbbbd bbbd faaf dbbbg bbbg aac bbbb gbbb aac dbbbg dbbbd eac gbbb bbbd eae bbbg bbbg eae dbbbd gbbb cae gbbb dbbb caa bbbd bbbg faaf bbb gbbb faaf bbg dbbb faaf dbbd dbbb aac gbb bbb aac bbg gbb eac dbbd dbb eae gbb dbbd eae dbbd gbb caa gbb gbb caa bbb dbbd faaf dbbb bbg faaf gbbb gbb faaf bbbg gbb aac bbbd dbbd aac bbb bbg aac bbd bbb aae bb bbbd aae bg bbbg aaa bd gbbg aaa b gbbb aaaf g dbbbd aaaf d bbbg aaaf bbbg aaac dbbbd eaac bbbg eaae bbbg eaae gbbb caae dbbbd caaa bbbd caaa bbbg faaaf gbbb faaaf bbbd aaac bbbg aaac gbbb eaac dbbb eaae bbb eaae bbb caae gbb caaa dbb caaa bbgfaaaf gbbfaaaf dbbdaaac dbbdaaac bbgeaac gbbeaae dbbeaae dbbeaae bbeaaa bbbaaaf bbbaaaf bbbaaaf gbbaaac gbbaaac dbbaaac bbeaae gbeaae dbeaaa beaaa gbaaaf gbaaaf dbaaaf baaac baaac dbbbd bbbg bbbg dd ``` <!-- end of image --> Area B does not contain any intersection points. Answer: A: 1; B: 0; 1 + 0 = 1 My investigation reveals that there is exactly one intersection in this image.

<!-- image --> ```palette Key,Color ,#fefefeff a,#56c56aff b,#ca7dc9ff c,#a8e0b2ff d,#ebceeaff e,#7ccd8bff f,#d5f0daff g,#d395d3ff ``` ```image a fac eae aaa aaa eaaa aaaa aeea cafca c aa ca caae aa faf aaaaae faf ac aa faaae ea ac eac faaae aa ae faa faaac ac aa aa faaac ea aa aaf faaac aa aa cae faaac ae aa aa faaac caf ea aa caaac aa ca eac caaaf aa ca faa caaaf faf faf dbg aa caaaf ea ac gbg eaf caaaf aa ac gbg fae caaaf ac ae gbg aa caaaf ca aa gbg eaf eaaaf aa aa gbg fae eaaa ae aa gbg aa eaaaafdb aa gbg eaf eaa bb ea gbg aa gbbd ca gbgaa bbbb ca geac bb bb faf aag bg db ac aagbg bb bd ac cac gbg dbd bb ae aa gbg bb bb aa aa gbg gbd gb aa fae gbg bb bd aa aa gbg gb bb aa eaf gbg bb bb ea fae gbg dbd gb ca aa gbg bb bd ca eaf gbg bb bg faf aa gbg dbd bb ac aa gbg bb gb ac cac gbg bb dbd ae aa gbg dbd bg aa aa gbg bb bb aa fac gbb bb gb aa gbb dbd dbd aa gbb bb bg ea gbb bb bb ca gbb dbd gb ca gbb bb dbd faf gbb bb bg ac gbb dbd bb ac gbb bb gb ae gbb bb dbd aa gbb dbd bg aa gbb bb bb aa gbb bg gb aa gbb dbd db ea gbb bb bgca gbb bg bbca gbb dbd bbfaf gbb bb db ac gbb bg bgac gbb db bbae gbb bb bbaa gbbbg dbaa gbb baa gb baa bea dea ea baf bac def bd d ``` <!-- end of image -->

I'm analyzing this image to identify any points where lines intersect. These areas seem to enclose narrow spaces where lines might be close. <!-- image --> ```palette Key,Color ,#fefefeff a,#f54d26ff b,#412e81ff c,#f29075ff d,#b1d6b1ff e,#817aa9ff f,#97c796ff g,#efcecdff ``` ```image dfffffffffffffffffafffff fddddddddddddddddaaaaddd fdddddddddddddddcaaaaacd fdddddddddddddddaaddcaaag fdddddddddddddddaaddddaaaa fddddddddddddddaaddddddfaaaa fddddddddddddddaaddddddd gaaac fdddddddddddddaacddddddd caaag fdddddddddddddaadddddddd aaaa fddddebbeddddcacdddddddd aaac fdebbbbbbedddaaddddddddd gaaac ebbbbbedfbbfdcacddddddddd caaag dbbbbbedddddfbbfaadddddddddd aaaa gbbbbbefddddddddfbbaadddddddddd gaaac bbe fdddddddddebbfdddddddddd caaag fddddddddddabbdddddddddd caaa fddddddddddabbbddddddddd aaaa fddddddddddaaebbdddddddd gaaac fddddddddddaadbbbddddddd caaag fddddddddddaaddbbbdddddd aaaa fddddddddddaadddbbbddddd aaaa fddddddddddaaddddbbbdddd gaaac fddddddddddaadddddbbbddd caaag fddddddddddaaddddddbbbdd aaaa fddddddddddaadddddddbbbd aaac fddddddddddaaddddddddbbb gaaac fddddddddddaadddddddddbbe caaag fddddddddddaaddddddddddbbe aaaa fddddddddddaaddddddddddfbbe gaaac dffffffffffaafffffffffff bbd caaag gac bbd caaa gac gbbg aaaa gac gbbg gaaac gac gbbg cag gac dbb gac ebb cag ebb cag ebb cag ebb cag bbb cag bbb aa bbb gaaa bbb aaac bbb gaaa bbb caac bbe aaag bbe caaa bbe aaag bbe gaaa bbd aaac gbbd gaaa gbbg aaac gbbg gaag dbb c dbb ebb ebb ebb ebb bbb bbb bbb bbb bbb bbe bbe bbe bbe bbe bbd gbbg gbbg gbbg dbb ebb ebb ebb ebb ebb bbb b ``` <!-- end of image --> Here's a close-up of the area A. <!-- image --> ```palette Key,Color ,#fefefeff a,#f54c25ff b,#402c80ff c,#fab3a2ff d,#a398c0ff e,#6d5492ff f,#f77c60ff g,#e5d5ddff ``` ```image caafg aaaaac caaaaaaac faaaaaaaafg caaaafaaaaaaf faaac caaaaaaa gaaaa caaaaa faaac gfaaa gaaaag gfa faaaf c aaaag caaaf aaaag caaaf aaaac caaaa faaac gded gaaaa gdbbbbbd faaac gdebbbbbbbbd gaaaa gdebbbbbbbbbbbbd faaaf gdebbbbbbbbbedebbbbd aaaag bbbbbbbbbedg gbbbbbg caaaf bbbbbbedg gbbbbbg aaaag bbbbdg gbbbbbgcaaaf bdg gbbbbbaaaac gbbbbbaaa gbbbbbac dbbbbbg dbbbbe gebbbbe caebbbbe caaebbbbe caaaebbbbe caaacebbbbe caaac ebbbbd caaac ebbbbd caaac ebbbbd caaac ebbbbd caaac ebbbbd caaac gebbbbd faaag gbbbbbg faaag gbbbbbg faaag gbbbbbg faaag gbbbbbg faaag gbbbbbg faaag gbbbbbg faaa dbbbbeg faaa dbbbbe faaa dbbbbe faaa dbbbb aaaa dbbb aaaa dbb aaaa db aaaa e aaaa aaaf ``` <!-- end of image --> I am surprised, so clear, 1 intersection has appeared in area A. Answer: A: 1; 1 = 1 I've found a single intersection point in the image.

<!-- image --> ```palette Key,Color ,#fefefeff a,#f54c25ff b,#402c81ff c,#faad9bff d,#a9a0c5ff e,#7463a0ff f,#f87e61ff g,#ecd7daff ``` ```image cag aaaa gaaaaaf aa caaac gaa faaa aag aaaf aa gaaac aac caaag aa aaaa dbbd fac aaaf dbbbbbbd aa caaac dbbbbbd gbbg caf faaag dbbbbbd gbbgaa aaaa gbbbbbe gbbaa gaaaf bbe dbbg caaac abb faaag aebb aaaa aaebb gaaaf aa ebb caaag aa ebb faaa aa bbb aaaf aa bbb gaaac aa bbb faaag aa bbb aaaa aa bbe gaaaf aa bbe caaac aa bbe faaag aa bbe aaaa af bbd gaaaf af bbd caaac gaf gbbd faaag gaf gbbg aaaa gaf gbbg gaaaf gac dbbg cac cac dbb cac dbb cac ebb cac ebb fag ebb fag ebb fag bbb aa bbb caaa bbb aaac bbb gaaa bbe faaf bbe aaag bbe faaa bbe aaag bbd caaa bbd aaac gbbd gaaa gbbg faaf gbbg gaag dbbg f dbb dbb ebb ebb ebb ebb bbb bbb bbb bbb bbe bbe bbe bbd bbd gbbd gbbg gbbg gbbg dbbg dbb dbb ebb ebb ebb bbb b ``` <!-- end of image -->

I'm ready to tackle this image and find those intersections! These areas seem to enclose narrow spaces where lines might be close. <!-- image --> ```palette Key,Color ,#fefefeff a,#8366e3ff b,#d10fdaff c,#531de5ff d,#d8b1f5ff e,#afd5afff f,#d75dddff g,#f0f1f3ff ``` ```image g c c ad ga c c fffddg dd gddffbbbbbbffddg c gddffbbbbbbffddg c gdf ag b da f c b c f ad b gc f c b ag gf da b c gf c b ad gf ga b c gf gggggggggggggggggggggcg bgeeeeeeeeeeeeeeeeeeeeaaeg gfeeeeeeeeeeeeeeeeeeeeceeg ffeeeeeeeeeeeeeeeeeeceeeg gffeeeeeeeeeeeeeeeeaeeeeg geffeeeeeeeeeeeeeeeaeeeeg geeffeeeeeeeeeeeeeceeeeeg geeeffeeeeeeeeeeeceeeeeeg geeeeffeeeeeeeeeaaeeeeeeg geeeeebeeeeeeeeeceeeeeeeg geeeeeebeeeeeeeceeeeeeeeg geeeeeeebeeeeeceeeeeeeeeg geeeeeeeebeeeeaeeeeeeeeeg geeeeeeeeebeeceeeeeeeeeeg geeeeeeeeeebceeeeeeeeeeeg geeeeeeeeeeabeeeeeeeeeeeg geeeeeeeeeecebeeeeeeeeeeg geeeeeeeeeceeebeeeeeeeeeg geeeeeeeeceeeeebeeeeeeeeg geeeeeeeeaeeeeeebeeeeeeeg geeeeeeeceeeeeeeebeeeeeeg geeeeeeceeeeeeeeeebeeeeeg d geeeeeaeeeeeeeeeeeebeeeeg dfbbbfd geeeeeceeeeeeeeeeeeebeeeg gdfbbfdg geeeeceeeeeeeeeeeeeeebbbbfdg geeeceeeeeeeeeeeeeeeeeeeg a geeaaeeeeeeeeeeeeeeeeeeeg a geeceeeeeeeeeeeeeeeeeeeeg dd geceeeeeeeeeeeeeeeeeeeeeg a gaeeeeeeeeeeeeeeeeeeeeeeg c ga c c a c c dd c gc gc c gc ag gc da da c da c da ad aa gc ad c ad cg cd da cg c cg c c ad c ga c c c cg c dd gc c gc c dcag da ``` <!-- end of image --> This close-up might reveal an intersection in area A. <!-- image --> ```palette Key,Color ,#fefefeff a,#8058edff b,#d20adcff c,#531be6ff d,#e884edff e,#e7cbf8ff f,#dd43e3ff g,#b097f3ff ``` ```image ace gcg eca f ace bd gcg dbd eca dbd cc dbd ace dbd gcg dbd eca fbd ac fbd gce fbd ecg fbd ca fbd ace fbe gcg fbe eca fbe cc fbe ace fbe gcg fbe eca fbe ace fbe gcg fbe eca bbe cc ebbe ace ebbegcg ebbca ecce gcbbe ecaebb cc ebf ace ebf gcg ebf eca ebf ac ebf gce ebf ecg ebf ca ebf ace ebf gcg dbf eca dbf cc dbf ace dbf gcg dbf eca dbd ace dbd e gcg dbffbb eca dffde cc ace gcg eca ace gce eca ``` <!-- end of image --> The lines cross each other within area A, forming 1 intersection. Answer: A: 1; 1 = 1 The final count is: one intersection.

<!-- image --> ```palette Key,Color ,#fefefeff a,#7e55ecff b,#d20cdcff c,#521be6ff d,#e989edff e,#e6d0f8ff f,#de4be5ff g,#af96f3ff ``` ```image e c c ae ea c c ffdde gg eddfbbbbbbfddee c eddffbbbbbffdee c edf ae b ea f c b c f gg b c f c b ae f eg b c f c b ae d ea b c ed c b gg ef c dd c dd ae fd ea fd c fd c fd gg fe c fe c fe ae be ea be c bc gbe c b c b a b eg b c b c b e ae b dfbbbde ea b edfbbfde c bbbbfd c a gg g c eg c a ae c ea c c a c c gg c c c c c ae ec ea ea c ga c ga ge gg a ag c ae a ce eg ce c c c c ae c ea c c c c c gg c c ec c eaae ea ``` <!-- end of image -->

Hmm, I'm not sure what to expect from this image. Let's see if any lines cross. It's crucial to examine these regions more closely. <!-- image --> ```palette Key,Color ,#fefefeff a,#a1e17bff b,#63ce7cff c,#d2f1cdff d,#3dc45dff e,#eff8eeff f,#92ce97ff g,#b0d8b0ff ``` ```image c d be ed d cb d fg d bc ed de cb d gf d bc d de cb d gf d bc d de eb d gf d fg d de ed d cb d g fg ea d gc bc ae ed a d ca cb ac d a fg c a d a ca bc a ac ed a a effffffffffffffffffdffffe cc ea egggggggggggggggggfdgggge ge cg egggggggggggggggggdggggge a ae eggggggggggggggggbbggggge ea a eggggggggggggggggdgggggge caage ea egggggggggggggggbfgggggge gaac cg egggggggggggggggdggggggge eaaae ae eggggggggggggggdgggggggge caag a egggggggggggggfdgggggggge egaac ea egggggggggggggdgggggggggcaage gc eggggggggggggfbggggggaaag ae eggggggggggggdggggaaaggge a egggggggggggbffaaagggggge ea eggggggggggadafggggggggge gc egggggggaaadgggggggggggge ae egggaaaagggdgggggggggggge a caaaggggggdggggggggggggge ca caagggggggggfbggggggggggggge ac gaac eggggggggdgggggggggggggge acaaae egggggggbfgggggggggggggge c egggggggdggggggggggggggge eggggggdfggggggggggggggge eggggggdgggggggggggggggge egggggdggggggggggggggggge eggggfbggggggggggggggggge eggggdgggggggggggggggggge egggbfgggggggggggggggggge efffdfffffffffffffffffffe dddddbfgce bc ecgbbdddddbfgce ed ecfbddddddbfgc d cgfbdddb ``` <!-- end of image --> Let's get to the bottom of what's happening inside area A. <!-- image --> ```palette Key,Color ,#fefefeff a,#9fe178ff b,#65d07cff c,#cdefc8ff d,#3dc55dff e,#e7f7e6ff f,#8fdda1ff g,#b5e8a7ff ``` ```image fdf edd fdg cdb bdc cdb dde fdf edd fdg edb bdc cdb bde gdf edde fdg edb bdc cdb bde ecg gdf egaaaa edde cgaaaagc fdg ecgaaaage edb cgaaaagce bdcecgaaaagc cdbaaaaace cgddaagce ecgaabdbe egaaaagcdde ecgaaaagc fdf ecaaaaace edd cgaaaagce bdc ecgaaaage cdb aaagce bdc gc gdf dde fdf edd fdg cdb bdc cdb dde fdf edd fdg edb bdc cdb bde gdf edde fdg edb ``` <!-- end of image --> The lines cross each other within area A, forming 1 intersection. Answer: A: 1; 1 = 1 One intersection, that's it, but I found it.

<!-- image --> ```palette Key,Color ,#fefefeff a,#a0e178ff b,#64d07eff c,#caeec4ff d,#3dc55dff e,#e3f6e1ff f,#8edda0ff g,#b5e8a1ff ``` ```image c d be ed d cb d ff d be d d cb d ff d bc d d eb d gf d bc d de ed d cf d fc d de ed d cb d g fg ea d gc be a d a d ea cb gc d a ff e a d a cg be a ae d g a d cc a eb g cg d a ae ff ea a d caag a bc gaac cg d egaae ae d caag a eb gaac ea d eaage gc gf caac a d egaae a bccaag ea gdac gc eaagde a caac ed a egaae d ea caag cf gc gaac d aeaage fc c d de ed d cb d fg d dddddbfgce be ecfbbdddddbfgc d ecfbddddddbfge d ecfbdddb ``` <!-- end of image -->

I'm curious to see if this image contains any intersection points. I'm going to focus my attention on these specific areas. <!-- image --> ```palette Key,Color ,#fefefeff a,#0d200cff b,#cf86bbff c,#70886fff d,#e6cadfff e,#97c297ff f,#394f39ff g,#b1d7b1ff ``` ```image dbd db db b bb b b b db eggggggggggggggggggggggggggggggggggggedd bd egggggggggggggggggggggggggggggggggggggb db egggggggggggggggggaggggggggggggggggggb bd egggggggggggggggggacggggggggggggggggbg d egggggggggggggggggcagggggggggggggggbgg eggggggggggggggggceecgggggggggggggbggg eggggggggggggggggfggagggggggggggggbggg eggggggggggggggggaggecgggggggggggbgggg eggggggggggggggggagggaggggggggggbggggg eggggggggggggggggfggggfggggggggbgggggg egggggggggggggggecggggaggggggggbgggggg egggggggggggggggfggggggfggggggbggggggg egggggggggggggggaggggggagggggbgggggggg egggggggggggggggagggggggfgggbggggggggg egggggggggggggggfgggggggfggbgggggggggg egggggggggggggggcggggggggagbgggggggggg eggggggggggggggceggggggggfbggggggggggg eggggggggggggggfgggggggggbaggggggggggg eggggggggggggggaggggggggbgfegggggggggg g eggggggggggggggagggggggbgggagggggggggg a eggggggggggggggfgggggggbgggceggggggggg ae egggggggggggggecggggggggggggaggggggggg ef egggggggggggggcgggggggbgggggcegggggggg a egggggggggggggagggggggbggggggagggggggg fe egggggggggggggagggggggbggggggccggggggg ef egggggggggggggagggggggbgggggggaggggggg a egggggggggggggcgggggggbgggggggecgggggg fe eggggggggggggcegggggggbggggggggagggggg ea eggggggggggggfggggggggbggggggggecggggg a eggggggggggggaggggggggggggggggggaggggg fc eggggggggggggagggggggbggggggggggefgggg ea eggggggggggggfgggggggbgggggggggggagggg ad egggggggggggecgggggggbggggggggggggfggg fc egggggggggggcggggggggbggggggggggggaggg ga egggggggggggaggggggggbgggggggggggggfgg ad egggggggggggaggggggggbgggggggggggggfgg fcegggggggggggaggggggggbggggggggggggggag gagggggggggggcgggggggggggggggggggggggfe eaeggggggggcegggggggbgggggggggggggggga egffgggggggfggggggggbggggggggggggggggfd eggeaggggggaggggggggbggggggggggggggggga eggggaeggggaggggggggbgggggggggggggggggcd egggggffgggfggggggggbggggggggggggggggg a eggggggeagecggggggggbggggggggggggggggg cd eggggggggafgggggggggbggggggggggggggggg a d geeeeeeeeefeeeeeeeeeeeeeeeeeeeeeeeeeee eg dbbbd d a dbbbd b ge dbbd b a dbbbd b de dbbbd b a dbbd b dc dbbbd d a dbbbd d c dbbb a f f f f f f a c a cd a ed a eg a ge a dc a ``` <!-- end of image --> I'm focusing my attention on this specific region, area A. <!-- image --> ```palette Key,Color ,#fefefeff a,#0c1f0bff b,#d37fbdff c,#6c776bff d,#d5bbceff e,#9ea59eff f,#3a4939ff g,#e9dee6ff ``` ```image d eae d caf db caae gbd fcff bb aedae bb dad fa dbg eag dae dbg ca ca gbd ff gac bb ac cag bb gae gac dbg eag cag gbd ea gac gbd cf cag bb fc gac bb ae eag dbg dad ac gbd eag ead gbd ca af bb ff ead bbg ac ff dbg gae ead gbd dad ff gbd ea eae bb cf ff dbg fc dae dbg ae ff gbd dad daebb eag cbb ca bbe ff dbcag ac gbdgac gae bb cag dad bb gac ea dbg cag cf gbg gac fc bd cag ae bg gac gae gbg ead eag gb af ca db ead ff db ff ac bd ead gae bd ff dad bd eae ea bg ff cf gbg dae fc gb ff ac db dae gae db fa eag bd dae ca bd ca ff bd gae fc bg cag gae gbg gac dad gb cag ea db gac cf db cag fc bb gac ac bd eag gae bd ac eag bg ead ca gbg af cf gb ead fc db ff ae db ead dad db ff eag bd eae cf bd ff fg ff bg dae aae ac gbg ff gfac gae gb da cafg eag db f daae ca db d gfac cf db eafg fc bd daae ae bd gfac dad bg eafg eag gbg daae ca gb gfac ff db eafg ac db dfae gae db gcac ead bd eafca bd dfaf bg ``` <!-- end of image --> Oh my, look at that! It's 1 intersection in area A! Answer: A: 1; 1 = 1 There's only one, but is an intersection after all.

<!-- image --> ```palette Key,Color ,#fefefeff a,#0d200cff b,#d482bfff c,#757f74ff d,#debed5ff e,#a5aca5ff f,#3d4c3dff g,#eee3ebff ``` ```image dbd gd gb b bd b bg b db dg bg gb db a b bd ae b g ea b egde dd f a b a gc b a a b c gc bg de a gd c f b a f b a f b f f bg c agd eg fb f ba a b cg e a dg a ga c d cg ae de gg a ef c d ed gag a b a fe a b ee ef f b a gag c b de fe eg b a ea f d dc ag a gg a fc a d gc ea f b a ag ge b gf fc c b a ea f b f ag a b f fc a d f ea c gg f ag ed d a fc f b cg da a b a ad a b cg fc f b a da ge b cd ac d a dg c gg ed gbbbd d a dbbbg d ee gdbbdg b a gbbbd b de dbbbg b a gdbbdg b gc gbbbd d a dbbbg gg gc gdbbb a f f f f f f a cg a cg a ed a ee a de a dc a ``` <!-- end of image -->

I have a feeling there might be some intersections in this image. I'd describe these as 'hotspots' for potential intersections. <!-- image --> ```palette Key,Color ,#fefefeff a,#a9dd58ff b,#5ed441ff c,#d2f1c3ff d,#99d191ff e,#f0f8edff f,#b1d7b1ff g,#7cd865ff ``` ```image dfffffffffffffffffffffffffffffffffffffffffffd dfffffffffffffffffffffffffffffffffffffffffffd dfffffffffffffffffffffffffffffffffffffffffffd dfffffffffffggffffffffffffffffffffffffffffffd dfffffffffffbbbbdfffffffffffffffffffffffffffd dfffffffffffbbbbbbgfffffffffffffffffffffffffd dfffffffffffbgffgbbbbfffffffffffffffffffffffd dffffffffffdbdffffdbbbbgffffffffffffffffffffd dffffffffffdbdfffffffgbbbbffffffffffffffffffd dffffffffffgbffffffffffdbbbbdfffffffffffffffd dffffffffffbbfffffffffffffbbbbgfffffffffffffd dffffffffffgbfffffffffffffffgbbbbdffffffffffd dfffffffffdaaaffffffffffffffffdbbbbgffffffffd dfffffffffaaaaaafffffffffffffffffgbbbbffffffd dffffffffaagbfaaaafffffffffffffffffdbbbbdfffd dffffffffaabgfffaaaaffffffffffffffffffbbbbgfd dfffffffaafbgfffffaaaaffffffffffffffffffgbbbbc dffffffdaadbdfffffffaaaaffffffffffffffffffdbbbbd dffffffaafgbffffffffffaaaaffffffffffffffffffddbbbbe dfffffaaffgbffffffffffffaaaaffffffffffffffffd cbbbbf dfffffaaffbbffffffffffffffaaaaffffffffffffffd gbbbge dffffaafffbbffffffffffffffffaaaaffffffffffffd fbbbbc dfffaadfffbbffffffffffffffffffaaaaffffffffffd egbbbg dfffaaffffbbffffffffffffffffffffaaaaffffffffd dbbbbc dffaafffffbbffffffffffffffffffffffaaaaffffffd cbbbbd dfdaafffffbgffffffffffffffffffffffffaaaaffffd dbbbbe dfaafffffdbgffffffffffffffffffffffffffaaaaffd cbbbbf daadfffffdbdffffffffffffffffffffffffffffaaaad egbc daaffffffgbfffffffffffffffffffffffffffffffaaaae aafffffffgbfffffffffffffffffffffffffffffffffaaaae faafffffffbbfffffffffffffffffffffffffffffffffdeaaaae aaffffffffbbfffffffffffffffffffffffffffffffffd eaaaa aaeeeeeeeeebbeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee eaaaa caa bb eaaaa aa bg eaaaa aac bd eaaaa eaa cbf eaaaa aae fbc eaaaa cad db eaaaa aa gb eaaaa aac bb eaaaa eaa bb eae aa bb dac bb aa bg aae ebd caa cbc aa fbe eac gb bb bb bb bb bg bd ebf cbc dbe gb bb bb bb bb bg bd cbf fbc db gb bb bb bb bb be bg cbbb ebd bbbg cbc ebbbd fbe cbbbf gb fbbbc bb dbbbe bb gbbb bb bbbbb ebbg e ``` <!-- end of image --> I'm analyzing this close-up of area A with precision. <!-- image --> ```palette Key,Color ,#fefefeff a,#aadd57ff b,#5fd441ff c,#d9f3cdff d,#a7e58cff e,#f4fbeeff f,#cbeca7ff g,#7fdc65ff ``` ```image egbgc fbbbbbde dbbbbbbbdc gbbbbbbbbbgfe gbbgdbbbbbbbbdc bbbg efgbbbbbbbgf bbbd cdbbbbbbbbde ebbbd edgbbbbbbbgc cbbbf cgbbbbbbbgde cbbbc edbbbbbbbbdc fbbbc fgbbbbbbbgfe dbbbe cdbbbbbbbbdc dbbb efgbbbbbbbgf gbbb cdbbbbbbbbde gbbg edbbbbbbbbgc bbbg cgbbbbbbbgfe eggbd cdbbbbbbbbdc daaade efgbbbbbbbgfe caaaaaafe cdbbbbbbbbde eaaaaaaaaafe efgbbbbbbbgc faaaaaaaaaaafe cgbbbbbbbgde eaaaabbfaaaaaaafe edbbbbbbbbdc daaagbb faaaaaaafe fgbbbbbbbgfe faaaabbg faaaaaaafe cdbbbbbbbbdc eaaaagbbg faaaaaaafe efgbbbbbbbgf daaafbbbd faaaaaaafe cdbbbbbbbbd caaaaebbbd faaaaaaafe edbbbbbbb aaaaccbbbf faaaaaaafe cgbbbb faaad cbbbf efaaaaaaafe edbb eaaaae fbbbc efaaaaaaafe ef daaaf dbbbe efaaaaaaafe caaaa dbbbe efaaaaaaafe eaaaac gbbb efaaaaaaafe faaaf gbbg efaaaaaaafe caaaae bbbg efaaaaaaafe aaaac bbbd efaaaaaaafe faaad ebbbd efaaaaaaafe eaaaae cbbbf efaaaaaaafe daaaf cbbbc efaaaaaaafe caaaa fbbbc efaaaaaaafe eaaaac dbbbe efaaaaaaafe faaad dbbb efaaaaaaafe eaaaae gbbb efaaaaaaafe daaaf gbbg efaaaaaaafe faaad bbbg efaaaaaaafe eaaaae ebbbd efaaaaaaafe faaaf ebbbd efaaaaaaafe caaaae cbbbf efaaaaaaafe aaaac fbbbc efaaaaaaaf faaad fbbbc efaaaaaa eaaaae dbbbe efaaaa daaaf dbbb efaa aaaa gbbg ef aaac gbbg aaf bbbd aae ebbbd ``` <!-- end of image --> As I suspected, there's 1 intersection within area A. Answer: A: 1; 1 = 1 My investigation reveals that there is exactly one intersection in this image.

<!-- image --> ```palette Key,Color ,#fefefeff a,#aadd58ff b,#5ed440ff c,#d3f2c6ff d,#97e283ff e,#f2faecff f,#b9e99fff g,#79da5eff ``` ```image gg bbbbc bgbbbbd bd dbbbbe cbf cbbbbf fbc gbbbge db fbbbbc gb egbbbd gb dbbbbc caaae cbbbbd aaaaaae dbbbge aagb aaaae cbbbbf eaabg aaaae egbbbg aaebd aaaae fbbbbc fafcbc aaaae ebbbbd aa fbe aaaae dbbbbe aae db aaaae cbbbbf caa gb eaaaae gbbbge aa bb eaaaae fbbbbc faf bb eaaaae egbbbd eaa bb eaaaae fbbbbc aae bg eaaaae cbbbbd caa bd eaaaae dbbbge aa ebf eaaaae cbbbbf aac cbc eaaaae egbc eaa dbe eaaaae aa gb eaaaae faf bb eaaaae aa bb eaaaae aae bb eaaaa caa bb eaaaa aa bg eaaaa aac bd eaaaa eaa cbf eaaaa aae fbc eaaaa faf db eaaaa aa gb eaaaa aac bb eaaaa eaa bb eae aa bb faf bb aa bg aae ebf caa cbc aa fbe eac db bb bb bb bb bg bd ebf cbc dbe gb bb bb bb bb bg bd cbf fbc db gb bb bb bb bb be bg cbbb ebf bbbg cbc ebbbd fbe cbbbf db fbbbc bb dbbbe bb gbbbebb bbbbb ebbg e ``` <!-- end of image -->

I'm approaching this image with caution. Intersections might be tricky to spot. I need to zoom in on these areas to get a better look. <!-- image --> ```palette Key,Color ,#fefefeff a,#c8db36ff b,#4cd215ff c,#e7f3c2ff d,#76d94dff e,#b1d8b0ff f,#d6e47cff g,#97ce91ff ``` ```image c aaa aaa caaaa faaaa cd aaaaaa bbb aaaaaa bbbe aaaaaaa gbbb aaa aaac geebbbgeeeeegaaaeaaaaeeg geedbbbeeeeefaaaeeaaaeeg geeebbbeeeeeaaafeeaaaaeg geeebbbdeeeeaaaeeeeaaaeg geeeebbbeeeeaaaeeeeaaaag geeeebbbdeeeaaaeeeeeaaag geeeegbbbeeeaaaeeeeeaaaa geeeeebbbgeeaaaeeeeeeaaac geeeeedbbbefaaaeeeeeeaaaa geeeeeebbbeaaafeeeeeeeaaac geeeeeebbbbaaaeeeeeeeefaaa geeeeeeebbbaaaeeeeeeeeeaaac geeeeeeebbbaaaeeeeeeeeeaaaa geeeeeeegbbaaaeeeeeeeeegaaac geeeeeeeebbaaaeeeeeeeeegfaaa geeeeeeeeddaaaeeeeeeeeeg aaac geeeeeeeeeaaafeeeeeeeeeg faaa geeeeeeeeeaaabeeeeeeeeeg aaac geeeeeeeeeaaabeeeeeeeeeg faaa cf geeeeeeeeeaaabdeeeeeeeeg aaac faaa geeeeeeeeeaaabbeeeeeeeeg caaa faaaaaac geeeeeeeeeaaabbgeeeeeeeg aaaf caaaaaaaaf geeeeeeeefaaabbbeeeeeeeg caaa faaaaaaaa geeeeeeeeaaafbbbgeeeeeeg aaaf caaaaaaaac geeeeeeeeaaaedbbbeeeeeeg caaa aaaaaaaaf geeeeeeeeaaaeebbbeeeeeeg aaaa faaaaaaaac geeeeeeeeaaaeebbbdeeeeeg aaac caaaaaaaac geeeeeeeeaaaeegbbbeeeeeg faaa faaaaaaaf geeeeeeeeaaaeeebbbdeeeeg aaaf caaaaaaaac geeeeeeefaaaeeegbbbeeeeg caaa aaaaaaaaf geeeeeeeaaafeeeebbbgeeeg aaaa faaaaaaaa geeeeeeeaaaeeeeedbbbeeeg aaac caaaaaaaac geeeeeeeaaaeeeeeebbbeeeg faaa faaaaaaaf geeeeeeeaaaeeeeeebbbbeeg aaaf faaaaaaaac egggggggaaagggggggbbbgge caaa caaaaaaaaf caaa bbbg aaaaaaaaaaa faaf ebbb aaaaaaac aaac bbbc faaaf aaa gbbb cc aaa bbb aaa dbbb aaa bbb caaa bbbd faaf cbbb aaac bbbe aaa gbbb aaa bbbbc aaa dbbbbbe aaa bbbbbbbd caaa dbbbbbbbc faaf ebbbbbbbg aaac bbbbbbbb aaa gbbbbbbbe aaa cbbbbbbbd fffaaa dbbbbbbbc aaaaaa gbbbbbbbg aaaaaa cbbbbbbbd aaaaaf dbbbbbbbc aaaaac ebbbbbbbg faaaa bbbbbbbb faaaa gbbbbbbbe faaaa cbbbbbbbd caaaa dbbbbbbbc caaaa gbbbbbbbg aaaf cbbbbbbbd aaac dbbbbbbbe aaa ebbbbbbbd aaa dbbbbbbbc aaa gbbbbbbbe f cbbbbbbbd dbbbbbbbc ebbbbb cbbb c ``` <!-- end of image --> This close-up might reveal an intersection in area A. <!-- image --> ```palette Key,Color ,#fefefeff a,#c8db35ff b,#4bd214ff c,#d5eea8ff d,#74d93aff e,#edf7d5ff f,#d8e56fff g,#98e478ff ``` ```image bbbbbbd aaaaaae caaaaaaf gbbbbbbe eaaaaaa faaaaaae ebbbbbbg eaaaaaa eaaaaaaf dbbbbbb caaaaaf faaaaaae cbbbbbbg faaaaaf eaaaaaaf dbbbbbd faaaaac faaaaaae cbbbbbbc aaaaaac eaaaaaaf bbbbbbd aaaaaae faaaaaae gbbbbbbe eaaaaaa eaaaaaaf ebbbbbbg eaaaaaa faaaaaae gbbbbbbe caaaaaf eaaaaaaf ebbbbbbg faaaaaf faaaaaa dbbbbbb faaaaac eaaaaaa cbbbbbbc aaaaaac faaaaa dbbbbbd aaaaaae eaaaaa gbbbbbbc eaaaaaa faaaa ebbbbbbg eaaaaaa eaaaa gbbbbbbe caaaaaf faaa ebbbbbbg faaaaaf eaaa dbbbbbb faaaaac faa cbbbbbbc aaaaaac eaa dbbbbbd aaaaaae fa gbbbbbbcaaaaaa ea bbbbbbdaaaaaa f gbbbbbdaaaaaf e ebbbbbdaaaaaf dbbbbaaaaaac cbbbbaaaaaae dbbbaaaaaae cbbbaaaaaa bbdaaaaaa gbdaaaaaf ebdaaaaaf gaaaaaac caaaaaag aaaaaad eaaaaaabc caaaaaabd caaaaaabbe faaaaadbbg faaaaadbbbe aaaaaadbbbg aaaaaabbbbb eaaaaaabbbbbc caaaaaabbbbbd caaaaaabbbbbbc faaaaafbbbbbbd faaaaacgbbbbbbe aaaaaaeebbbbbbg aaaaaae dbbbbbb eaaaaaa cbbbbbbg caaaaaa dbbbbbd caaaaaf cbbbbbbc faaaaaf bbbbbbd faaaaac gbbbbbbe aaaaaae ebbbbbbg eaaaaaae gbbbbbbe eaaaaaa cbbbbbbg caaaaaf dbbbbbd caaaaaf cbbbbbbc faaaaac bbbbbbd faaaaac gbbbbbbe aaaaaae ebbbbbbg eaaaaaae gbbbbbbe eaaaaaa ebbbbbbg caaaaaf dbbbbbb caaaaaf cbbbbbbc faaaaac dbbbbbd faaaaac gbbbbbbc ``` <!-- end of image --> Gotcha! I've found 1 intersection hiding in area A! Answer: A: 1; 1 = 1 I have found one intersection!

<!-- image --> ```palette Key,Color ,#fefefeff a,#c9db35ff b,#4cd215ff c,#e0eea3ff d,#7cdd51ff e,#ebf6d2ff f,#d7e46dff g,#abe991ff ``` ```image e aaa eaaa caaaa faaaa ed aaaaaa bbb aaaaaa bbbg aaaaaaa gbbb aaa aaa bbbe eaaa faaa dbbb caaf aaae bbb faac faaa bbbd aaae aaae ebbb aaa faaa bbbg aaa aaae gbbb aaa faaa bbbe eaaa aaae dbbb caaf faaa bbb faac aaae bbbdaaae faaa bbbaaa aaae bbbaaa faaa cbbaaa aaae bbaaa caaa gdaaf aaac aaac caaa aaab aaac aaab caaa ef aaabd aaac faaa aaabb caaa caaaaaae eaaabbg aaac eaaaaaaaac caaabbb caaa faaaaaaaf faacbbbe aaac caaaaaaaac aaaedbbb caaa faaaaaaaf aaa bbb aaaa caaaaaaaae aaa bbbd aaae eaaaaaaaac aaa ebbb faaa faaaaaaaf eaaa bbbg aaaf caaaaaaaae caaf gbbb caaa eaaaaaaaaf faac bbbe aaaa faaaaaaaae aaae dbbb aaae eaaaaaaaac aaa bbb faaa faaaaaaaf aaa bbbd aaaf caaaaaaaae aaa bbb eaaa eaaaaaaaac eaaa bbbg aaaaaaaaaaf caaf cbbb aaaaaaac faac bbbc faaaf aaa gbbb ee aaa bbb aaa dbbb aaa bbb eaaa bbbd faaf ebbb aaac bbbg aaa gbbb aaa bbbbe aaa dbbbbbg aaa bbbbbbbd eaaa dbbbbbbbe faaf gbbbbbbbg aaae ebbbbbbbb aaa dbbbbbbbg aaa cbbbbbbbd cffaaa dbbbbbbbe aaaaaa gbbbbbbbg aaaaaa ebbbbbbbd aaaaaf dbbbbbbbc aaaaae gbbbbbbbd faaaa ebbbbbbbbe faaaa gbbbbbbbg caaaa ebbbbbbbd caaaa dbbbbbbbe eaaaa gbbbbbbbg aaac ebbbbbbbd aaae dbbbbbbbc aaa cbbbbbbbd aaa dbbbbbbbe aaa gbbbbbbbg f ebbbbbbbd dbbbbbbbe gbbbbbe ebbb e ``` <!-- end of image -->

I have an image in front of me. I need to determine if there are any intersection segments. These zones are intriguing. I bet there's something interesting happening within them. <!-- image --> ```palette Key,Color ,#fefefeff a,#c3883aff b,#e2dd69ff c,#ebdfadff d,#a3cfa1ff e,#b2d7b1ff f,#ccad74ff g,#f2f5eaff ``` ```image ggggggggggggggggggggggg ddbbbddddddddddddddddddg eeebbeeeeeeeeeeeeeeeeedg eeebbeeeeeeeeeeeeeeeeedg eeebbbeeeeeeeeeeeeeeeedg eeebbbeeeeeeeeeeeeeeeedg gaa eeeebbeeeeeeeeeeeeeeeedg caaag eeeebbbeeeeeeeeeeeeeeedg caaaac eeeebbbeeeeeeeeeeeeeeedg faaaaaf eeeeebbeeeeeeeeeeeeeeedg faa aaaa eeefebbbeeeeeeeeeeeeeedg faa aaaa eeaaabbbeeeeeeeeeeeeeedg faa faaag eefaaabbeeeeeeeeeeeeeedg faa caaaf eeefaabbbeeeeeeeeeeeeedg faa aaaa eeeeaabbbeeeeeeeeeeeeedg faa aaaa eeeeeaabbeeeeeeeeeeeeedg aaa faaag eeeeeeabbbeeeeeeeeeeeedg aaa caaac eeeeeedbbbeeeeeeeeeeeedg aaa gaaaf eeeeeeefbbaeeeeeeeeeeedg aaa aaaa eeeeeeeebbffeeeeeeeeeedg aaa faaag eeeeeeeebbbadeeeeeeeeedg aaf caaac eeeeeeeeebbaaeeeeeeeeedg aaf gaaaf eeeeeeeeebbfaaeeeeeeeedg aaf aaaa eeeeeeeeebbbaaaeeeeeeedg aaf aaaag eeeeeeeeeebbfaaaeeeeeedg aaf faaac gggggggggggggggggg eeeeeeeeeebbeaaafeeeeedg aaf gaaafdddddddddddddddddd eeeeeeeeeebbbeaaadeeeedg aaf aaaaeeeeeeeeeeeeeeeee eeeeeeeeeeebbeeaaaeeeedg aac aaaaeeeeeeeeeeeeeeee eeeeeeeeeeebbeedaaaeeedg aac faaadeeeeeeeeeeeeee eeeeeeeeeeebbbeefaaaeedg aac gdaaafeeeeeeeeeeeee eeeeeeeeeeeebbeeefaafedg aac gdeaaaaeeeeeeeeeeee eeeeeeeeeeeebbeeeeaaaddg aac gdeeaaaaeeeeeeeeeee eeeeeeeeeeeebbbeeeeaaadg aac gdeeeaaaadeeeeeeeee eeeeeeeeeeeebbbeeeeeaaag aac gdeeeefaaafeeeeeeee eeeeeeeeeeeeebbeeeeedaaa aag gdeeeeeeaaaaeeeeeee dddddddddddddbbbdddddfaaf aag gdeeeeeeeaaaaeeeeee cbb faac aag gdeeeeeeeeaaaaeeeee bbg aaag aag gdeeeeeeeeefaaafeee bbb aaa aa gdeeeeeeeeeedaaaeee cbb gaaa aa gdeeeeeeeeeeeeadeee bbg caaa aa gdeeeeeeeeeeeeeeeee bbb faaf aa gdeeeeeeeeeeeeeeeee cbb aaac gaa gdeeeeeeeeeeeebeeee gbb aaag gaa gdeeeeeeeeeeebbbeee bbc aaa gaa gdeeeeeeeeeebbbeeee bbb gaaa gaa gdeeeeeeeeebbbeeeee gbb caaa gaa gdeeeeeeeebbbeeeeee bbc faaf caa gdeeeeeeebbbeeeeeee bbb aaac caa gdddddddbbbdddddddd gbb aaa caa cbbb bbc aaa caa cbbb bbb gaaa caa cbbb gbb faaf caa bbbb bbc aaacfaa bbbb bbb aaafaa bbbb cbb aaaaa bbbb bbb gaaaa bbbc cbbb caaa bbbc cbbb faa bbbc cbbb bbbg bbbc gbbbg bbbc gbbbg bbbg gbbbg bbbg cbbb bbbg cbbb bbb cbbb gbbb bbbb gbbb bbbb cbbb bbbb cbbb bbbb cbbb bbbc bbbc bbbc bbbc bbbc bbbc bbbc bbbg gbbbg bbbg gbbbg bbb gbbbg gbbb cbbb gbbbcbbb cbbbbb cbbb cb ``` <!-- end of image --> Let's see if area A yields any clues. <!-- image --> ```palette Key,Color ,#fefefeff a,#c3873aff b,#e2dc67ff c,#eee5b6ff d,#ddbc90ff e,#e9e48dff f,#cfa35cff g,#f6f2ddff ``` ```image cebe bbbbb ebbbbc cbbbbe gbbbbb ebbbbg cbbbbe gbbbbb ebbbbg cbbbbe gbbbbb ebbbbg cbbbbc gbbbbb bbbbbg cbbbbc gbbbbb bbbbbg ebbbbc df gbbbbe faad bbbbbg gfaaaacebbbbc gaaaaaacbbbbe caaaaaabbbbbg daaaaabbbbbc daaaafbbbbe faaaabbbbbg gaaaabbbbbc gaaafbbbbe caaabbbbb daabbbbbc fafbbbbe fabbbbb gabbbbbc cfbbbbbg dbbbbbf bbbbbff cbbbbfad gbbbbbaac bbbbbfaag cbbbbfaaag gbbbbbaaaf bbbbbaaaad cbbbbfaaaad gbbbbbaaaaac bbbbbaaaaaag ebbbbeaaaaaf gbbbbedaaaaaf bbbbbgfaaaaad ebbbbcgfaaaaac gbbbbe gaaaaaac bbbbbg caaaaaag ebbbbc daaaaaf cbbbbe daaaaaf bbbbb faaaaad ebbbbc gaaaaaac cbbbbe gaaaaaag bbbbb caaaaafg ebbbbc daaaaaf cbbbbe faaaaad gbbbbb faaaaad ebbbbg gaaaaaac cbbbbe caaaaaag gbbbbb daaaaaf ebbbbg daaaaaf cbbbbe faaaaa gbbbbb gfaaaa bbbbbg gaaaa cbbbbc caaa ``` <!-- end of image --> Gotcha! I've found 1 intersection hiding in area A! I'm ready to analyze the next area. Eureka! Let's inspect this close up of area B <!-- image --> ```palette Key,Color ,#fefefeff a,#c38739ff b,#e3dd6aff c,#ede0bcff d,#e1c79aff e,#ca9652ff f,#d4aa73ff g,#f7f1e2ff ``` ```image f aeg aaec aaaad aaaaaf aaaaaafg faaaaaaeg daaaaaaac caaaaaaad geaaaaaafg faaaaaaeg daaaaaaac caaaaaaad geaaaaaaf gfaaaaaaeg daaaaaaac caaaaaaad geaaaaaaf gfaaaaaaeg faaaaaaec daaaaaaad ceaaaaaad geaaaaaafg faaaaaaeg daaaaaaac caaaaaaad geaaaaaf faaaeg daag cc cg cbbg cbbbb cbbbbbb dbbbbbbc dbbbbbbc bbbbbbbc bbbbbbbg gbbbbbbbg gbbbbbbbg gbbbbbbbg gbbbbbbbg ``` <!-- end of image --> The evidence suggests that this is not an intersection point in area B. Answer: A: 1; B: 0; 1 + 0 = 1 It was tricky, but I finally found one single intersection in the image.

<!-- image --> ```palette Key,Color ,#fefefeff a,#c38739ff b,#e3dd67ff c,#efe5beff d,#dfc097ff e,#eae590ff f,#d0a264ff g,#f7f3e1ff ``` ```image g bbb cbb bbc bbb cbb gaa bbg daaag bbb daaaac ebb daaaaaf bbg daa aaaa d bbb daa aaaa faaebb faa daaac caaabbg faa caaad faabbe faa aaaa aabbb faa aaaa aabb faa faaag abbe aaa caaad gbbb aaa gaaaf dbbf aaa aaaa bbfd aaf faaag bbbac aaf daaac gbbaa aaf gaaaf bbfaa aaf aaaa bbbaaa aaf faaa gbbdaaf aaf daaac bbcfaad aad gaaaf bbb aaag aad aaaa cbb aaa aad aaaa bbc gaaa aad faaag bbb caaa aad caaad cbb faad aac aaaf bbc aaac aac aaaa bbb aaag aac faaag cbb aaa aac caaad bbg gaaa aag gaaaf bbb daaf aag aaaa ebb faad aag faaag bbg aaag aag daaac bbe aaa aa gaaa ebb gaaa aa ag bbg caaa aa bbe daaf aa ebb aaac aa bg gbb aaag gaa bbb bbe aaa gaa bbbc ebb gaaa gaa bbbg gbb daaf caa gbbbg bbe faad caa gbbbg bbb aaac caa cbbb gbb aaa caa cbbb bbc aaa daa ebbb bbb caaa daa ebbb gbb daaf daa ebbb bbc faaddaa bbbb bbb aaafaa bbbb cbb aaaaa bbbe bbb gaaaa bbbe cbbb caaa bbbe ebbb faf bbbc ebbe bbbc bbbe gbbbg bbbc gbbbg bbbc gbbb bbbg cbbb bbb cbbb bbb ebbb gbbb ebbb gbbb ebbb cbbb bbbb ebbb bbbe ebbe bbbe ebbe bbbe bbbc bbbc bbbc bbbc bbbg gbbbg bbbg gbbbg bbb gbbbg gbbb cbbb gbbbcbbb cbbbbb cbbb ce ``` <!-- end of image -->

The hunt for intersections begins! Let's analyze this image closely. These regions highlight areas that look suspicious. Lines seem to converge within them. <!-- image --> ```palette Key,Color ,#fefefeff a,#e6a2b7ff b,#666f81ff c,#f2f1efff d,#e8cbd5ff e,#7f8893ff f,#b0d6b0ff g,#9bbca1ff ``` ```image a aaac c aaaad dbg aaaaa cbbbg daaaa bbbe daaaa bbbb caaaac ebbb aaaad gbbbc aaaaa dbbbd daaaa cbbbg caaaac bbbe aaaad bbbb aaaaa ebbb daaaa gbbbc caaaa dbbbd aaaac cbbbg aaaad bbbe aaaaa bbbb daaaa ebbb caaaac gbbbc aaaad dbbbd aaaaa cbbbg daaaa cbbbe caaaac dbbbb aaaac gbbbb aaaadcccccccccccccccccccccc ebbbe aaaaaffffffffffffffffffffgc bbbbg daaaaffffffffffffffffffffccbbbbd gaaaafffffffffffffffffffdbbbbc gfaaaaaffffffffffffffffebbbb cd gffaaaaaffffffffffffffbbbbe aaac gfffaaaaaffffffffffffbbbbg aaa gfffffaaaaffffffffffbbbbd daad gffffffaaaafffffffgbbbbgc aaa gfffffffaaaaaffffebbbbffc caaa gffffffffaaaafffebbbbfffc aaac gfffffffffaaaffbbbbeffffc aaa gfffffffffaaafbbbbgfffffc daad gfffffffffaaabbbbfffffffc aaa gfffffffffaebbbbffffffffc caaa gfffffffffebbbbfffffffffc aaac gffffffffbbbbeffffffffffc aaa gfffffffbbbbaaffffffffffc daad gfffffgbbbbaaaffffffffffc aaa gffffgbbbbfaaaffffffffffc caaa gfffebbbbffaaaffffffffffc aaac gffbbbbefffaaaffffffffffc aaa gfbbbbgffffaaaffffffffffc aaad gbbbbffffffaaaffffffffffc aaa fbbbbfffffffaaaffffffffffc daaa ebbbbffffffffaaaffffffffffc aaa bbbbefffffffffaaaffffffffffc aaa bbbbeffffffffffaaaffffffffffc aaad cbbbbcgffffffffffaaaffffffffffc aaa fbbbb gffffffffffaaaffffffffffc daad ebbbb gfffffffffffaafffffffffgc aaa bbbbe cccccccccccdaadccccccccc caaa bbbbf caad aaac cbbbbc aad aaa dbbbb aaa daad gbbbb aaa aaa ebbbe aaa caaa bbbbf aaa aaac cbbbbd aaa aaa dbbbb aaa daad gbbbb aaa aaa ebbbe aaa caaa bbbbg aaa aaac cbbbbd daa aaa dbbbbc daac daad gbbbb daac aaa ebbbe caad caaa bbbbg caad aaac cbbbbd caad aaa dbbbbc aaa daad bbbb aaa aaa dbe aaadc daaa d aaaaaaaadc aaa daaaaaaaaaaaadc aaa cdaaaaaaaaaaaaad cdaaaaaaaa cdaad ``` <!-- end of image --> Eureka! Let's inspect this close up of area A <!-- image --> ```palette Key,Color ,#fefefeff a,#e6a1b7ff b,#666f81ff c,#f1e8ecff d,#c9ccd2ff e,#858897ff f,#efc3d1ff g,#a5a6b2ff ``` ```image aaaac aaaaac aaaaaaf aaaaaaaf aaaaaaaaf caaaaaaaaac faaaaaaaac faaaaaaaaf caaaaaaaaf ce caaaaaaaaac ceb faaaaaaaac dbbb faaaaaaaaf dbbbb faaaaaaaaf gbbbbb caaaaaaaaa cebbbbbb caaaaaaaaac cebbbbbbb faaaaaaaac dbbbbbbbbe faaaaaaaaf dbbbbbbbbg caaaaaaaaf gbbbbbbbbd caaaaaaaaf ebbbbbbbbd faaaaaaf cebbbbbbbec faaaaaa dbbbbbbbbec aaaaaa dbbbbbbbbg aaaaaa gbbbbbbbbd faaaaacgbbbbbbbbd faaaaaebbbbbbbec faaaabbbbbbbbec faagbbbbbbbbg faebbbbbbbbg febbbbbbbbd cebbbbbbbec cbbbbbbbbec dbbbbbbbbe gbbbbbbbbef gbbbbbbbbgaf cebbbbbbbbaaaf cebbbbbbbeaaaaa dbbbbbbbbgaaaaaa gbbbbbbbbg aaaaaa gbbbbbbbbd faaaaa cebbbbbbbbc faaaaa cebbbbbbbec faaaaac dbbbbbbbbg faaaaac dbbbbbbbbg faaaaac gbbbbbbbbd faaaaac cebbbbbbbbd caaaaac cebbbbbbbec caaaaaf bbbbbbbbe caaaaaf bbbbbbbg caaaaaf bbbbbbd caaaaaf bbbbbd aaaaaf bbbec aaaaaf bbec aaaaaa bg aaaaaa d aaaaaa faaaaa faaaaa faaaaac faaaaac faaaaac caaaaac ``` <!-- end of image --> Yes! I knew it! There's 1 intersection right here in area A! Answer: A: 1; 1 = 1 It was tricky, but I finally found one single intersection in the image.

<!-- image --> ```palette Key,Color ,#fefefeff a,#e7a1b7ff b,#666f81ff c,#f4e7ecff d,#d0d3d8ff e,#808695ff f,#efc3d0ff g,#a6a9b4ff ``` ```image a faac c aaaac dbg aaaaf bbbg faaaa bbbe caaaa bbbb aaaac ebbb aaaaf gbbbc aaaaa dbbbd faaaa bbbg caaaac bbbe aaaaf bbbb aaaaa ebbb faaaa gbbbc caaaa dbbbd aaaac bbbg aaaaf bbbe aaaaa bbbb faaaa ebbb caaaac gbbbc aaaaf dbbbd aaaaa cbbbg faaaa cbbbe caaaa dbbbb aaaac gbbbb aaaaf ebbbe faaaa bbbbg faaaa cbbbbd caaaac dbbbb aaaaf gbbbb cf aaaaa ebbbe aaac faaaa bbbbg aaa caaaac cbbbbd faaf aaaac dbbbbc aaa aaaaf gbbbb caaa faaa ebbbe aaac aaa bbbbg aaa faacbbbbd faaf faabbbbc aaa febbbb caaa ebbbe aaac bbbbe aaa bbbbgf faaf cbbbbaaa aaa gbbbb aaa caaa ebbbb aaa aaa bbbbg aaa aaa bbbbd aaa faaf cbbbbc aaa aaa dbbbb aaa caaa ebbbb aaa aaa bbbbe aaa aaa bbbbd aaa aaac cbbbbc faa aaa dbbbb faac faaf ebbbb caac aaa bbbbe caaf aaa bbbbg caaf aaac cbbbbc aaf aaa dbbbb aaa faaf gbbbb aaa aaa ebbbe aaa caaa bbbbg aaa aaac cbbbbd aaa aaa dbbbb aaa faaf gbbbb aaa aaa ebbbe aaa caaa bbbbg aaa aaac cbbbbd faa aaa dbbbb faac faaf gbbbb faac aaa ebbbe caac caaa bbbbg caaf aaac cbbbbd aaf aaa dbbbbc aaa faaf bbbb aaa aaa dbe aaafc caaa d aaaaaaaafc aaa faaaaaaaaaaaafc aaa cfaaaaaaaaaaaaac cfaaaaaaaa cfaaf ``` <!-- end of image -->

I'm analyzing this image to identify any points where lines intersect. These areas seem to enclose narrow spaces where lines might be close. <!-- image --> ```palette Key,Color ,#fefefeff a,#531e03ff b,#bd7b58ff c,#e4d1c8ff d,#7e5a42ff e,#b2d7b1ff f,#bfa48cff g,#97c896ff ``` ```image c cbbbc fbbbbbb bbbbbbbbbc cbbbbb bbbbbf bbbbbf cbbbbb bbbbbc bbbbbc cbbbbb fbbbbb bbbbbf cbbbbbc bbbbb bbbbbf fbbbbb cbbbbb bbbbbf bbbbbfgggggggggggggggggggg cbbbbb fbbbbbeeeeeeeeeeeeeegeeee fbbbbb bbbbbfeeeeeeeeeeedaaeee bbbbbc gbbbbbbeeeeeeeeeeaaaaee cbbbbb gefbbbbfeeeeeeeeaaaaeee fbbbbb geeebbbbeeeeeeedaaageee bbbbbc geeeebbbbeeeeegaaadeeee cbbbbb geeeegbbbbeeeeaaaaeeeee fbbbbf aaf geeeeebbbbfeedaaageeeee bbbbbc aaaaaadf geeeeeebbbbegaaadeeeeee cbbbbb aaaaaaaaaadc geeeeeeebbbbaaaaeeeeeee bbbbbf aaaaaaaaaaaaaab geeeeeeefbbaaaaeeeeeeee bbbbbc caaa edaaaaaaaaaaadeeeeeeeebdaaadeeeeeeee cbbbbb baaa faaaaaaaaaaaafeeeeeaaaaeeeeeeeee bbbbbf aaad baaaaaaaaaaadgaaaabbeeeeeeee gggggggggggggggbbbbbc aaae cdaaaaaaaaaaaadbbfeeeeeee eeeeeeeeeeeeefbbbbb aaa gefaaaaaaaaabbbbeeeeeee eeeeeeeeeeeebbbbbf aaa geeeeedaaaaeebbbfeeeeee eeeeeeeeeeebbbbb faaa geeeeeeeeeeeebbbfeeeeee eeeeeeeeefbbbbb daaa geeeeeeeeeeeebbbfeeeeee eeeeeeeebbbbbfg aaaf geeeeeeeeeeeebbbfeeeeee eeeeeeebbbbbeeg aaac geeeeeeeeeeeefbbbeeeeee eeeeefbbbbbeeeg aaa geeeeeeeeeeeefbbbeeeeee eeeebbbbbfeeeeg caaa geeeeeeeeeeeefbbbeeeeee eegbbbbbeeeeeeg faaa geeeeeeeeeeeeebbbeeeeee efbbbbbeeeeeeeg daad geeeeeeeeeeeeebbbeeeeee eedaafeeeeeeeeg aaaf egggggggggggggbbbgggggg eeaaaeeeeeeeeeg aaa bbb eeaaadeeeeeeeeg aaa bbb eedaaaeeeeeeeeg caaa bbb eeeaaaeeeeeeeeg baaa bbbc eeeaaafeeeeeeeg aaab bbbc gggaaaaggggggge aaac bbbc caaa aaa bbbf aaa aaa fbbf aaad faaa fbbb faaa daad cbbb aaa aaaf cbbb aaaf aaa bbb daaa aaa bbb caaa caaa bbb aaac baaa bbb aaad aaad bbb faaa aaae bbb aaa aaaa bbbc aaaf aaaaa bbbc daaa caaaad bbbf aaa caaaab fbbf aaac faaaaf fbbb aaad daaaac cbbb faaa daaaa cbbb aaa aaaaa cbbb aaab aaaaa bbb baaa aaaaa bbb aaa aaaad bbb aaae caaaab bbb daaa faaaaf bbb caaa daaaac bbbc aaa daaaa bbbc aaad aaaaa bbbc faaa aaaaa bbbf aaa aaaaa fbbf aaaf aaaad fbbb daaa caaaab cbbb caaafaaaaf cbbb aaaaaaac bbb aaaaaa bbb faaaa bbb aaa bbb c bbb bbb ``` <!-- end of image --> I'm going to scrutinize area A for any signs of an intersection. <!-- image --> ```palette Key,Color ,#fefefeff a,#531d02ff b,#be7a57ff c,#dcbfb0ff d,#7d4b32ff e,#eee1daff f,#c99c85ff g,#996e58ff ``` ```image c efb ebbb cbbbb efbbbbb ebbbbbbb cbbbbbbbb efbbbbbbbbb cbbbbbbbbbbc fbbbbbbbbbbe efbbbbbbbbbf cbbbbbbbbbbc fbbbbbbbbbbe ebbbbbbbbbbf cbbbbbbbbbbc fbbbbbbbbbbe ebbbbbbbbbbf cbbbbbbbbbbc cbbbbbbbbbfe fbbbgdbbf egdaaadc aaaaaad daaaaaa faaaaaac eaaaaaag daaaaad gaaaaaae caaaaaaf aaaaaad gaaaaaa faaaaaac eaaaaaag ``` <!-- end of image --> This close-up reveals that there are no intersections in area A. Right then, let's explore the next spot. I'm analyzing this close-up of area B with precision. <!-- image --> ```palette Key,Color ,#fefefeff a,#531d02ff b,#be7a57ff c,#d4b6a7ff d,#72422aff e,#e8dad3ff f,#be937eff g,#8f6955ff ``` ```image bbbbc bbbbbfe bbbbbbbc ee bbbbbbbbf daf bbbbbbbbbbe gaaade cbbbbbbbbbbc caaaaaaf efbbbbbbbbbf daaaaaad cbbbbbbbbbc gaaaaaaae ebbbbbbbbbe caaaaaaaf fbbbbbbbbe eaaaaaaad cbbbbbbbf gaaaaaaae cbbbbbbbc faaaaaaaf fbbbbbbbe eaaaaaaag bbbbbbbb daaaaaaae ebbbbbbbf faaaaaaac cbbbbbbbc eaaaaaaag fbbbbbbbe daaaaaaae bbbbbbbb faaaaaaac ebbbbbbbf eaaaaaaag cbbbbbbbc daaaaaad fbbbbbbbgaaaaaaac bbbbbbgaaaaaaag ebbbbbaaaaaaad cbbbdaaaaaaae fe fbgaaaaaaaf aadgce ebaaaaaaad aaaaaadgc gaaaaaaaf aaaaaaaaaadfe caaaaaaadbc aaaaaaaaaaaaaagfeeaaaaaaadbbbe aaaaaaaaaaaaaaaaaaaaaaaaabbbbf aaaaaaaaaaaaaaaaaaaaaaaadbbbbbc cfdaaaaaaaaaaaaaaaaaaaadbbbbbbbe cgdaaaaaaaaaaaaaaaaefbbbbbbb ecgaaaaaaaaaaaac ebbbbbbbe efgaaaaaaag cbbbbbbe cfdaag ebbbbbbe bbbbbbc bbbbbbc bbbbbbc fbbbbbc fbbbbbf fbbbbbf cbbbbbf cbbbbbb cbbbbbb ebbbbbb ebbbbbbe ebbbbbbe ebbbbbbe bbbbbbe bbbbbbc bbbbbbc ``` <!-- end of image --> Oh my, look at that! It's 1 intersection in area B! Answer: A: 0; B: 1; 0 + 1 = 1 After careful examination, I conclude that there is one intersection.

<!-- image --> ```palette Key,Color ,#fefefeff a,#531d02ff b,#be7a57ff c,#d8beb1ff d,#784b35ff e,#ebdfd9ff f,#c59b86ff g,#967564ff ``` ```image c ebbbc fbbbbbb bbbbbbbbbe cbbbbb bbbbbf bbbbbf cbbbbb bbbbbe bbbbbc cbbbbb fbbbbb bbbbbf ebbbbbe ebbbbbe bbbbbf cbbbbb cbbbbb bbbbbc bbbbbc ebbbbb fbbbbb c fbbbbb ebbbbbe gad bbbbbc bbbbbf eaaad ebbbbb ebbbbc aaaa fbbbbf bbbb daaae bbbbbc bbbb eaaad ebbbbb ebbbf aaaa fbbbbf eaaf fbbbe daaae bbbbbe aaaaaadc bbbb eaaag cbbbbb aaaaaaaaaade bbbbaaaa fbbbbf aaaaaaaaaaaaaag ebbaaaa bbbbbe eaaa cdaaaaaaaaaaaf fdaaag cbbbbb gaaa faaaaaaaaaaadc aaaa bbbbbf aaag gaaaaaaaaaaageaaaabb bbbbbe aaac edaaaaaaaaaaaadbbf cbbbbb aaa cdaaaaaaaabbbb bbbbbc aaa faaaa bbbe ebbbbbe caaa bbbc cbbbbb gaad bbbc bbbbbc aaag fbbf ebbbbb aaae fbbb fbbbbb aaa cbbb bbbbbc eaaa ebbb ebbbbb faaa ebbb cbbbbf daad bbb gaac aaaf bbb aaa aaa bbb aaag aaa bbb gaaa caaa bbb aaa gaaa bbbe aaac aaag bbbe daaa aaac bbbc caaa aaa fbbf aaae aaa fbbf aaag faaa cbbb faaa daad cbbb aaa aaaf ebbb aaaf aaae ebbb daaa aaa bbb eaaa eaaa bbb aaae gaaa bbb aaad aaag bbb faaa aaac bbb aaa aaaa bbbe aaaf aaaad bbbc gaaa eaaaad bbbc eaaa caaaag fbbf aaac faaaac fbbf aaad gaaaae cbbb caaa daaaa ebbb aaa aaaaa ebbb aaag aaaaa bbb gaaa aaaaa bbb aaa eaaaad bbb aaac caaaag bbb daaa faaaac bbb caaa gaaaae bbbe aaae daaaae bbbe aaag aaaaa bbbc faaa aaaaa bbbf aaa aaaaa fbbf aaaf eaaaad cbbb daaa caaaag cbbb eaaafaaaac ebbb aaaaaaae ebbb aaaaaae bbb faaaa bbb aaa bbb e bbb bbb ``` <!-- end of image -->

This image seems promising for intersection detection. Could these regions be concealing intersection points? Let's find out. <!-- image --> ```palette Key,Color ,#fefefeff a,#d6cc22ff b,#558828ff c,#edeab0ff d,#96c894ff e,#78a355ff f,#b1d7b0ff g,#d2d562ff ``` ```image cg aaac aaa gaaa aaac aaa gaaa aaac aaa gaaa aaa aaa gaag aaa caaa aaag aaa caaa aaag aaa caaa aaac aaa caaa aaac aaa gaaa aaac aaa dfffffffffffffffgaaafffd dfffffffffffffffaaaffffd dfffffffffffffffaaaffffd dffffffffffffffgaaaffffd dffffffffffffffaaafffffd dffffffffffffffaaafffffd ddddddddddddddddddddddddddd dfffffffffffffaaaafffffd fffffffffffffffffffffffffff dfffffffffffffaaaffffffd fffffffffffffffffffffffffff dfffffffffffffaaaffffffd fffffffffffffffffffffffffff dffffffffffffaaagffffffd fffffffffffffffffffffffffff dffffffffffffaaafffffffd fffffffffffffffffffffffffff dfffffffffffgaaafffffffd fffffffffffffffffffffffffff cdbdffffffffffaaagfffffffd fffffffffffffffffffffffffff febbbbbbbbbeffffffffaaaffffffffd fffffffffffffffffffffffffff cdebbbbbbbbbbbbbbbbbbdffffgaaaffffffffd ffffffffffffffffffffffdebbbbbbbbbbbbbbbbbbeebbbbbbbeffaaagffffffffd ffffffffffffffffdebbbbbbbbbbbbbbbbbbdf dfdbbbbbbbeaaafffffffffd fffffffffdebbbbbbbbbbbbbbbbbbedc dffffebbbbeaaafffffffffd fffdebbbbbbbbbbbbbbbbbbedff dffffffebbaaaebefffffffd febbbbbbbbbbbbbbbbbbedffffffff dffffffffdaaabbbbbdffffd cdebbbbbbbbbbbbbbbbbeedffffffffffffff dffffffffgaaabbbbbbbeffd bbbbbbbbbbbbbbedfffffffffffffffffffff dffffffffaaagfdbbbbbbbed bbbbbbbbdffffffffffffffffffffffffffff dffffffffaaafffffebbbbbbbf eed fffffffaaagffffffffffffffff dfffffffgaaafffffffebbbbbbbd ffffffgaaaaaaagffffffffffff dfffffffaaaffffffffffdbbbbbbbd ffffffaaaaaaaaaaaaagfffffff dfffffffaaaffffffffffffddbbbb fffffaaaagaaaaaaaaaaaaagfff dffffffgaaaffffffffffffd fbb fffffaaaffffffgaaaaaaaaaagf dffffffaaafffffffffffffd ffffaaaaffffffffffgaaaaaaaa dffffffaaafffffffffffffd fffgaaafffffffffffffffgaaaaa dfffffaaaafffffffffffffd fffaaagfffffffffffffffffgaaaa dfffffaaaffffffffffffffd ddaaaadddddddddddddddddddgaaaa dfffffaaaffffffffffffffd caaa caaaac dffffaaagffffffffffffffd aaag aaaag dffffaaafffffffffffffffd gaaa aaaag dfffgaaafffffffffffffffd aaac aaaaa dfffaaagfffffffffffffffd aaaa aaaaa dfffaaaffffffffffffffffd caaa gaaaa fddgaaaddddddddddddddddf aaag caaaa aaac aaaa caaaac aaa caaa aaaag caaa aaaa aaaag aaac gaaa aaaaa aaa aaac gaaaagaaa aaaa gaaaaaac caaa caaaaa aaag caaaa gaaa aa aaac aaaa caaa aaag gaa ``` <!-- end of image --> I'm eager to see what's happening in this magnified view of area A. <!-- image --> ```palette Key,Color ,#fefefeff a,#d7cc21ff b,#558828ff c,#ebe696ff d,#b3caa0ff e,#84a964ff f,#e9edd1ff g,#e0d858ff ``` ```image fd ffdeebbbb fddeebbbbbbbbbb fddebbbbbbbbbbbbbbbbb ffdeebbbbbbbbbbbbbbbbbbbbbbb fddeebbbbbbbbbbbbbbbbbbbbbbbbbbbbb ffddebbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb fddeebbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbeddf fddeebbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbeeddf bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbeedff bbbbbbbbbbbbbbbbbbbbbbbbbbbbeddf bbbbbbbbbbbbbbbbbbbbbeeddf bbbbbbbbbbbbbbbeedff bbbbbbbbeeddf bbeeddf f ccf faaaaagccf gaaaaaaaaaagcf caaaaaaaaaaaaaaagcf faaaaaaaaaaaaaaaaaaaagcf gaaaaaaaaaaaaaaaaaaaaaaaagcf faaaaaaaaaaaaaaaaaaaaaaaaaaaaaggcf aaaaaaacccgaaaaaaaaaaaaaaaaaaaaaaaagcf caaaaaag fcgaaaaaaaaaaaaaaaaaaaaaaaac faaaaaaaf fcgaaaaaaaaaaaaaaaaaaaaag gaaaaaac fcgaaaaaaaaaaaaaaaaaag caaaaaaa fcggaaaaaaaaaaaaaa aaaaaaaf fcgaaaaaaaaaa gaaaaaag fcgaaaaaa faaaaaaaf fgaaaa gaaaaaac gaaa ``` <!-- end of image --> This close-up reveals that there are no intersections in area A. Time for a closer look at another area. I'm analyzing this close-up of area B with precision. <!-- image --> ```palette Key,Color ,#fefefeff a,#d6cc22ff b,#558828ff c,#ebe592ff d,#a7c18fff e,#7aa04bff f,#eaecc8ff g,#e2da62ff ``` ```image faaaaaaf gaaaaaa aaaaaag faaaaaaf gaaaaaa aaaaaac caaaaaaf gaaaaaa aaaaaac caaaaaaf gaaaaag faaaaaac caaaaaa gaaaaag faaaaaac caaaaaa aaaaaag faaaaaac caaaaaa aaaaaag faaaaaaf gaaaaaa aaaaaag faaaaaaf gaaaaaa eedf aaaaaag bbbbed faaaaaaf bbbbbbbdf gaaaaaa bbbbbbbbbed aaaaaac bbbbbbbbbbbbdf caaaaaaf bbbbbbbbbbbbbbef gaaaaaa ddbbbbbbbbbbbbbbed aaaaaac debbbbbbbbbbbbbbdf caaaaaaf febbbbbbbbbbbbbbeaaaaaag fdbbbbbbbbbbbbbaaaaaac debbbbbbbbbeaaaaaaf fdbbbbbbbaaaaaaaed debbbbaaaaaaebbbdf febeaaaaaabbbbbbed faaaaaaabbbbbbbbbdf faaaaaaebbbbbbbbbbbef caaaaaabbbbbbbbbbbbbbed aaaaaag debbbbbbbbbbbbbbdf faaaaaaf febbbbbbbbbbbbbbed gaaaaaa fdbbbbbbbbbbbbbb aaaaaag debbbbbbbbbbb faaaaaaf fdbbbbbbbbb gaaaaaa debbbbbb aaaaaag febbbb faaaaaaf fdbb gaaaaaa d aaaaaac caaaaaaf gaaaaaa aaaaaac caaaaaaf gaaaaag faaaaaac caaaaaa gaaaaag faaaaaac caaaaaa aaaaaag faaaaaac caaaaaa aaaaaag faaaaaaf gaaaaaa aaaaaag faaaaaaf gaaaaaa aaaaaag faaaaaaf gaaaaaa aaaaaac ``` <!-- end of image --> The lines cross each other within area B, forming 1 intersection. Answer: A: 0; B: 1; 0 + 1 = 1 My investigation reveals that there is exactly one intersection in this image.

<!-- image --> ```palette Key,Color ,#fefefeff a,#d7cc21ff b,#558828ff c,#eae48cff d,#a4bf8dff e,#7da252ff f,#eaeccaff g,#e0d756ff ``` ```image cg aaac aaa caaa aaaf aaa gaaa aaaf aaa gaag aaaf faaa gaag aaa faaa aaag aaa faaa aaac aaa caaa aaac aaa caaa aaac aaa caaa aaaf aaa gaaa aaaf aaa gaag aaaf faaa gaag aaa faaa aaag aaa faaa fdef aaac debbbbbbbbbd aaa fdebbbbbbbbbbbbbbbbbbf caaa fdbbbbbbbbbbbbbbbbbbedbbbbbbbd aaac debbbbbbbbbbbbbbbbbbdf fbbbbbbbeaaa fdebbbbbbbbbbbbbbbbbedf ebbbbeaaa fdbbbbbbbbbbbbbbbbbbed dbbaaaebd fdebbbbbbbbbbbbbbbbbbdf faaabbbbbf fdebbbbbbbbbbbbbbbbbedf caaabbbbbbbd bbbbbbbbbbbbbbed aaaf fbbbbbbbe bbbbbbbbdf aaa ebbbbbbbf eedf aaac gaaa dbbbbbbbd caaaaaaagf aaaf fbbbbbbbd aaaaaaaaaaaagf aaa dbbbb aaaafgaaaaaaaaaaaac gaag fbb faaaf fgaaaaaaaaaag aaaf aaaa fcaaaaaaaa faaa caaa caaaaa gaag aaac gaaaa aaa aaaa caaaaf faaa faaa faaaaf aaag aaag aaaac aaa gaaa aaaag faaa aaaf aaaaa aaac aaaa aaaaa aaa caaa gaaaa caaa aaac caaaaf aaac aaaa faaaaf aaa faaaf aaaac caaa aaag aaaag aaac gaaa aaaaa aaa aaac gaaaacaaa aaaa gaaaaaaf faaa caaaaa aaag faaaa gaaa aa aaaf aaaa caaa aaac gaa f ``` <!-- end of image -->

I'm curious to see if this image contains any intersection points. My next step is to analyze the details within each area. <!-- image --> ```palette Key,Color ,#fefefeff a,#08f5a9ff b,#d9f6acff c,#91fad8ff d,#ebfaeaff e,#45f3b6ff f,#b0d7b0ff g,#90d09dff ``` ```image db dbbbb dbbbbbbb dbbbbbbbbbd dbbbbbbbbbd dbbbbbbbbbd dbbbbbbbbbd dac dbbbbbbbbbd aaa dbbbbbbbbbd aaad dbbbbbbbbbd eaaac dbbbbbbbbd aaaaa bbbbbbd daaaaa bbbbd aaaaaa bbb aaaaaad bbbb caaecaac bbb aaaddaae d dbbb aaa aaa aaa bbb eaae aaa gggggggaaaagggggfbbbggg aaa aaa dffffffaaaaafffffbbbffffd daaa caac dfffffaaaaaafffffbbbffffd eaac daae dffffeaaaaaaffffbbbfffffd aaa aaa dfffeaaageaagfffbbbfffffd caaa aaa dffgaaaefgaaeffbbbffffffd aaad aaa dfgaaaeffgaaeffbbbffffffd aaa eaac dgaaaaffffaaafbbbfffffffd caae caae daaaafffffaaafbbbfffffffd aaa aaa aaaaffffffaaabbbbfffffffd aaa aaa aaaafffffffaaabbbffffffffd eaac aaa aaaaffffffffaaabbbffffffffd aaa eaaceaaagffffffffeaafbfffffffffd daaa caaaaaacfffffffffeaaebfffffffffd aaac aaaaacdfffffffffgaaeffffffffffd aaa aaaae dffffffffffaaaffffffffffd caae aaae dfffffffffbaaaffffffffffd aaad caa dfffffffffbaaaffffffffffd aaa dffffffffbbaaaffffffffffd eaae dffffffffbbaaaffffffffffd aaa dfffffffbbbeaagfffffffffd daaa dfffffffbbbeaaefffffffffd eaac dffffffbbbfgaaefffffffffd aaa dffffffbbbffaaafffffffffd caaa dfffffbbbbffaaafffffffffd aaad dfffffbbbfffaaafffffffffd aaa dffffbbbbfffaaafffffffffd caae dffffbbbffffaaaeffffffffd aaa dfffbbbbffffeaaaaaagffffd aaa dfffbbbffffffaaaaaaaaaegd eaac ggfbbbggggggggeaaaaaaaaaac aaa bbb deaaaaaaaaaac daaa dbbb caaaaaaaaaaed aaac bbbd caaaaaaaaaacd aaa dbbb deaaaaaaaaaac caae bbbd caaaaaaaaaaed aaad bbb caaaaaaaaaaed aaa bbbd deaaaaaaaaaad eaae bbb ceaaaaaa aaa bbbd caaa daaa bbb d eaac bbbb aaa bbb ca bbbb bbb dbbb bbb dbbb bbbd dbbb bbbd dbbbbb dbbbbbbd dbbbbbbd dbbbbbbd bbbbbbbd bbbbbbb bbbbbbb dbbbbbbb dbbbbbbb dbbbbbbd bbbbbbbd bbbbbd dbb ``` <!-- end of image --> Time to investigate area A up close. <!-- image --> ```palette Key,Color ,#fefefeff a,#08f5a9ff b,#d9f7acff c,#6af8c5ff d,#cbfcecff e,#3af7b7ff f,#ecfad6ff g,#99fad9ff ``` ```image gaaaaaaag fbbbbbb gaaaaaaaag bbbbbbf daaaaaaaaac fbbbbbb daaaaaaaaaac bbbbbbf daaaaaaaaaaae fbbbbbb eaaaaaaaaaaaa bbbbbbf eaaaaaaaaaaaaa fbbbbbb caaaaaaadeaaaaad bbbbbbb caaaaaaag caaaaad bbbbbbf gaaaaaaag caaaaag fbbbbbb gaaaaaaac gaaaaac bbbbbbf daaaaaaac daaaaac fbbbbbb daaaaaaae daaaaae bbbbbbf daaaaaaae aaaaaa fbbbbbb eaaaaaaed aaaaaa bbbbbbf eaaaaaaad eaaaaad fbbbbbb caaaaaaad caaaaad bbbbbbf caaaaaaag caaaaagfbbbbbb aaaaaaag gaaaaacbbbbbbf aaaaaac daaaaacbbbbbb aaaaac daaaaaebbbbbf aaaae aaaaaabbbbb aaae aaaaaabbbbb aae eaaaaabbbbf aad caaaaagbbb ad caaaaacbbf d gaaaaacbb gaaaaaebf daaaaaeb aaaaaaf faaaaaa beaaaaad fbeaaaaad bbcaaaaag fbbcaaaaag bbbcaaaaac fbbbbaaaaae bbbbbaaaaae fbbbbbaaaaaa fbbbbbeaaaaa bbbbbbeaaaaad fbbbbbbcaaaaag bbbbbbfgaaaaag fbbbbbb gaaaaac bbbbbbf daaaaae fbbbbbb daaaaae bbbbbbf aaaaaa fbbbbbb eaaaaa bbbbbbf eaaaaad fbbbbbb caaaaag bbbbbbf gaaaaag fbbbbbb gaaaaac bbbbbbb daaaaac fbbbbbbf daaaaae fbbbbbb aaaaaacd bbbbbbf aaaaaaaaaegd fbbbbbb eaaaaaaaaaaaacgd bbbbbbf caaaaaaaaaaaaaaaecd fbbbbbb eaaaaaaaaaaaaaaaaaaegd bbbbbbf geaaaaaaaaaaaaaaaaaaa ``` <!-- end of image --> The evidence is clear: there's 1 intersection in area A. Answer: A: 1; 1 = 1 There's one and only one intersection present in the image.

<!-- image --> ```palette Key,Color ,#fefefeff a,#08f5a9ff b,#d9f7acff c,#6ff9cbff d,#d3fcefff e,#3cf7baff f,#effbdeff g,#a1fbdcff ``` ```image fb fbbbb fbbbbbbb fbbbbbbbbbf fbbbbbbbbbf fbbbbbbbbbf fbbbbbbbbbf dac fbbbbbbbbbf aaa fbbbbbbbbbf aaad bbbbbbbbbf eaaac fbbbbbbbbf aaaaa bbbbbbf daaaaa bbbbf aaaaaa bbb aaaaaad bbbb gaaecaag bbb aaaddaae d fbbb aaa aaa aae bbb caac aaa aaaa fbbb aaa aaa aaaaa bbb daaa caag aaaaaa fbbb eaag daae eaaaaaa bbbf aaa aaa caaagcaag fbbb gaaa aaa gaaac gaac bbbf aaad aaa daaae daae bbb aaa caag aaae aaa bbbf caae gaae aaaa aaa bbb aaa aaa aaaa aaabbbf aaa aaa aaaa aaabbb eaac aaa aaaa aaabbb aaa eaageaaad eaagb daaa gaaaaaag gaacb aaag aaaaac daae aaa aaaae faaa gaae aaae baaa aaad gaa fbaaa aaa bbaaa caac fbbaaa aaa bbbeaad daaa bbbcaag eaag bbbfdaae aaa bbb aaa gaaa bbbf aaa aaad bbb aaa aaa bbbb aaa caae bbb aaac aaa fbbb eaaaaaag aaa bbb daaaaaaaaaed eaac fbbb caaaaaaaaaac aaa bbb deaaaaaaaaaag daaa fbbb gaaaaaaaaaaed aaag bbbf caaaaaaaaaac aaa fbbb deaaaaaaaaaag gaae bbbf geaaaaaaaaaed aaad bbb caaaaaaaaaacd aaa bbbf deaaaaaaaaaad caac bbb geaaaaaa aaa bbbf caaa daaa bbb eaag bbbb aaa bbb ca fbbb bbb fbbb bbb fbbb bbb fbbb bbbf bbbbb fbbbbbbf fbbbbbbf fbbbbbbf bbbbbbbf bbbbbbb bbbbbbb fbbbbbbb fbbbbbbf fbbbbbbf fbbbbbbf bbbbbf fbb ``` <!-- end of image -->

The hunt for intersections begins! Let's analyze this image closely. It's crucial to examine these regions more closely. <!-- image --> ```palette Key,Color ,#fefefeff a,#d1727aff b,#ecbcbdff c,#db5854ff d,#b1d7b1ff e,#d19a92ff f,#f3efecff g,#96c995ff ``` ```image fddddddddddddddddddddddd fddddddddddddddddddddddd fddddddddddddddddddddddd fdddddddddddddddddeaeddd fddddddddddddddeaaaaaddd fdddddddddddeaaaaaeddddd fddddddddeaaccaedddddddd fdddddaaaaaaccaddddddddd fddaaaaaadddcccddddddddd faaaaaaddddddcccddddddddd aaaaaddddddddecccddddddddd aafddddddddddccacddddddddd aafddddddddddccecedddddddd babfddddddddddccdcadddddddd aa fdddddddddecadccdddddddd aa fdddddddddacddccdddddddd aa gggggggggccggccgggggggg fae cc ecb eaf fca bce aa ecb cc aa cc cc fae cc cc cb bab cc acf fccb aa bcb bcb fcce aa cc fca fcce aa cc cc cca bab cc cc cca eaf bce cc cca aa acf ecb ccc aa cc bce ccc fae cc cc ccc bab fca cc ccc aa ecb cc baf ccc aa cc acf aaaeggggcccggggggggggggggggggggggggggggggggggg aa cc bcb aaaaaddddaccddddddddddddddddddddddddddddddddddf bab cc fca aadaaaedddaccdddddddddddddddddddddddddddddddddf eaf bce cc aadddaaadddaccddddddddddddddddddddddddddddddddf aa acf cc faeddddaaaeddaccdddddddddddddddddddddddddddddddf aa cc cc bagddddddaaaddeccddddddddddddddddddddddddddddddf fae cc ecf eaddddddddaaaadeccdddddddddddddddddddddddddddddf bab fca bce aaddddddddddaaadeccedddddddddddddddddddddddddddf aa fce ab aadddddddddddaaaaecceddddddddddddddddddddddddddf aa bcb aadddddddddddddaaaeccedddddddddddddddddddddddddf aa bcb aaddddddddddddddeaaacceddddddddddddddddddddddddfbab ecf faeddddddddddddddddaaaccadddddddddddddddddddddddfeaf acf babdddddddddddddddddeaaccaddddddddddddddddddddddfaa ac eafdddddddddddddddddddaaccadddddddddddddddddddddfaa cc aafddddddddddddddddddddeaccaddddddddddddddddddddfae cc aafddddddddddddddddddddddacccdddddddddddddddddddeab cc aafdddddddddddddddddddddddecccddddddddddddddddddaa cc aafdddddddddddddddddddddddddccceddddddddddddddddaa cc faefddddddddddddddddddddddddddcccadddddddddddddddaa cc babfdddddddddddddddddddddddddddcccaeddddddddddddeab cc eaffddddddddddddddddddddddddddddcccaadddddddddddaaf cc aa fdddddddddddddddddddddddddddddcccaaedddddddddaa ca aa fddddddddddddddddddddddddddddddaccaaaddddddddaa fce aa fdddddddddddddddddddddddddddddddaccaaaeddddddae bce aa fddddddddddddddddddddddddddddddddacceaaaddddeab bcb aa fdddddddddddddddddddddddddddddddddaccdaaaeddaaf ecb feb fddddddddddddddddddddddddddddddddddeccdeaaadaaf ecf fdddddddddddddddddddddddddddddddddddeccddaaaaaf acf fddddddddddddddddddddddddddddddddddddecceddaaef cc fdddddddddddddddddddddddddddddddddddddecceddedf cc fdddddddddddddddddddddddddddddddddddddddccedddf cc ggggggggggggggggggggggggggggggggggggggggccagg cc fcce cc fcca cc cca cc cca cc ccc cc ccc fca ccc fce ccc bcb ccc bcb ccc ecb acc acf acc ac accf cc eccfcc ecccc bccc bcc ff ``` <!-- end of image --> Let's see what secrets area A holds. <!-- image --> ```palette Key,Color ,#fefefeff a,#d1707aff b,#e3a2a6ff c,#db5955ff d,#f2d2d4ff e,#dc888dff f,#f8eaebff g,#ebbbbdff ``` ```image aaaaed fcccccb aaaaaabf fcccccb aaaaaaaad faccccb aaaaaaaaabf facccce aaadbaaaaaad facccce aaaf deaaaaabf fecccce aaa baaaaaad ecccce aae deaaaaabf eccccaf aab baaaaaag eccccaf aab deaaaaaef eccccaf aag gaaaaaag bccccaf aad feaaaaaef bcccccf aaf gaaaaaag bcccccf aa feaaaaaef gcccccd ae gaaaaaag gcccccd ae feaaaaaef gcccccd ab gaaaaaag dcccccd ag feaaaaaefdcccccg ad gaaaaaagdcccccg af feaaaaaegcccccg af gaaaaaabcccccb a fbaaaaaacccccb e gaaaaaacccccb b fbaaaaacccccb g daaaaaccccce g fbaaaaccccce d daaaaccccce f fbaaaccccce daaacccccaf fbaacccccaf deacccccaf baccccccf deccccccd bccccccb dacccccef ecccccag bcccccaef gcccccaag dcccccaaef dcccccaaag dcccccaaaef fccccccaaag fccccccaaaef f facccccaaaag d facccccaaaaed g facccccaaaaab e faccccaaaaaaed a eccccaaaaaaab fa eccccaeaaaaaed ga eccccagaaaaaab ba eccccafbaaaaaed ea bccccafdaaaaaabf faa bcccccffbaaaaaad daa bcccccf daaaaaabfgaa gcccccd fbaaaaaaeaa gcccccd deaaaaaaa gcccccd baaaaaa gcccccd deaaaa dcccccg baaa dcccccg fgf dcccccg dcccccg ``` <!-- end of image --> I observe 1 intersection inside area A. I'm ready to analyze the next area. I'm determined to find out if an intersection exists in area B. <!-- image --> ```palette Key,Color ,#fefefeff a,#d1707aff b,#e6a7aaff c,#db5854ff d,#ecbfc2ff e,#dd8d92ff f,#f9ecedff g,#f3d8daff ``` ```image gb gbaaag gbaaaaaab gbaaaaaaaaaa gbaaaaaaaaaaedf fdbaaaaaaaaaaedf fdeaaacccaaaaedf fdeaaaaaccccaedf fdeaaaaaaaaccccb fdeaaaaaaaaaaecccce fdeaaaaaaaaaabg dcccca gdeaaaaaaaaaabg bccccc gbeaaaaaaaaaabg acccccg aaaaaaaaaaebg ccccccd aaaaaaaebg gccccccb aaaaedf bcccccce aedf eccccccc f ccccacccf gcccaecccg dcccbbcccb ecccdgccce acccffccca fccca cccc dccce ecccg bcccd bcccd acccg dcccb ``` <!-- end of image --> Darn it! This close-up doesn't show any intersections in area B. Answer: A: 1; B: 0; 1 + 0 = 1 The image features one single intersection point.

<!-- image --> ```palette Key,Color ,#fefefeff a,#d0707bff b,#e9adafff c,#dc5854ff d,#f0cbccff e,#e09093ff f,#f8e8e9ff g,#e17572ff ``` ```image bad baaaaa eaaaaad feaaccad feaaaaacce feaaaaad ccc faaaaaaf ccc aaaaef bccc aaf ccgcf aa ccbcb bad ccfcg aa dce cc aa gcf cc aa cc cc dab cc ecd eaf fcg dce aa ecd cc aa cc cc fae cc cc cb bad cc gcf fccb aa bcb bcb fcce aa gc fcg fcce aa cc cc ccg dab cc cc ccg eaf dce cc ccg aa gcf ecd ccg aa cc dce ccc fae cc cc ccc bad fcg cc ccc aa ecd cc ba ccc aa cc gc aaab gcc aa cc bcb aaaaaf gcc dab cc fcg aa aaae gcc eaf bcb cc ae daaaf ecc aa gcf cc dab eaae eccf aa cc cc bad faaaf bccf fae cc ecd ea eaae bccf bad fcg dce aa faaafdccd aa dce gb aa eaaedccd aa dcb aa faaadccb aa bcd aa eaaaccb dab ecd fae faaacce eaf gcf bad eaacce aa gc eaf faaccg aa cc aa baccg fae cc aa accc bad cc aa bccc aa cc aa cccd aa cc fae ccca aa cc dab cccab dab cc baf cccaa eaf cc aa gccaab aa cg aa gccaaa aa fce aa gccaaab fae dce aa eccdaaa bad bcb aa eccfaaab aa bcd feb bccfdaaafaa ecf bccd aaaaa gc dccd daab cc dccd d cc fccb cc fccb cc fcce cc cce cc ccg cc ccg cc ccg cc ccc fcg ccc fce ccc dcb ccc bcb gcc ecd gcc ecf gcc gc ecc cc eccfcc bcccc bccc dcc ff ``` <!-- end of image -->

Time to put on my detective hat and find those intersection points! These regions highlight areas that look suspicious. Lines seem to converge within them. <!-- image --> ```palette Key,Color ,#fefefeff a,#5d17b3ff b,#721f21ff c,#8e6cc1ff d,#9dbe98ff e,#d8c4d8ff f,#96635fff g,#b1d7b1ff ``` ```image e bb fbfb eb bb bd bd bb eb fb fb ebe bb bf bf bb ebe db fb be bb bb bf fb ebe eb fb bf bb bb bf fb ebe be fb bf bb fb bf eb be bd db bb bb fb bf ebe be bf db bb bb db bf be be bb db fb bb eb bf bf bg bb gb fb fb be bb bf bd fb eb eb fb bd bb gddddbbddddddddd bd dgggfbgggggggggg ddbdgggggggggggggggg dggdbdgggggggggg ggfbgggggggggggggggg dggbfcdggggggggg gggbbggggggggggggggg dgbbgaaacggggggg ggggbfgggggggggggggg dfbggagcaaadgggg ggggdbdggggggggggggg dbdggaggggaaacgg gggggfbggggggggggggg bbggcaggggggdaaae ggggggbbgggggggggggg fgggcagggggggggcaac gggggggbfggggggggggg dgggacgggggggggg eaaac gggggggdbdgggggggggg dgggacgggggggggg caaae ggggggggfbgggggggggg dgggaggggggggggg aaac gggggggggbbggggggggg dgggaggggggggggg eaaae ggggggggggbfgggggggg dgggaggggggggggg caac ggggggggggdbdggggggg dggcaggggggggggg eaaae gggggggggggfbggadggg dggcaggggggggggg caac ggggggggggggbbaagggg dggacggggggggggg eaaac ggggggggggggdbbggggg dggacggggggggggg caaae gggggggggggcacbdgggg dggagggggggggggg aaac ggggggggggcadgfbgggg dggagggggggggggg eaaae gggggggggaadgggbgggg dgdagggggggggggg caac ggggggggaagggggggggg gdcadddddddddddd eaaae gggggggaaggggggggggg ca caac ggggggaagggggggggggg ac eaaac gggggaaggggggggggggg ae caaae ggggaagggggggggggggg a aaac gggaaggggggggggggggg a eaaacacgggggggggggggggg ea aacggggggggggggggggg ca gggggggggggggggggggg ca gggggggggggggggggggg ac gggggggggggggggggggg ae gggggggggggggggggggg a dddddddddddddddddddd a ea ca ac ac ae ``` <!-- end of image --> Here's a close-up of the area A. <!-- image --> ```palette Key,Color ,#fefefeff a,#5b14b3ff b,#711e20ff c,#8550c6ff d,#be9799ff e,#dac9e5ff f,#935355ff g,#b08edaff ``` ```image dbbf ebbb fbbe fbbd dbbf ebbbe fbbd dbbf gge ebbb eaaacg bbbe gaaaaaage fbbd caacaaaaacg dbbf cac gcaaaaace ebbbe aac egaaaaacg fbbd aag gcaaaaace dbbf eaag egaaaaaage bbf gaae ecaaaaa bbe gaa gaaa dd caa ec cac aac aag eaag gaae gaa caa cac aac aag eaag gaae gaa caa cac aac eaag eaae gaae gaa caa aac aag eaag eaae ``` <!-- end of image --> My analysis shows that the lines in area A do not cross. Okay, let's direct our attention to the next zone. Let's see what secrets area B holds. <!-- image --> ```palette Key,Color ,#fefefeff a,#5c15b3ff b,#711d20ff c,#8753c7ff d,#af8080ff e,#e6dae8ff f,#8a454bff g,#c5a9c8ff ``` ```image fbbd ebbbg gbbbe dbbf fbbd ebbbg gbbbe dbbf fbbd efbbg ebbbe dbbf fbbd fbbg ebbbe gbbf dbbd fbbg ebbbe gbbf dbbd fbbg ebbbe gbbf dbbd fbbg ebbbe gbbf ce dbbd caae fbbgecaace ebbbaaac gbbbac efbbf gaabbbd gaaagbbbe gaaag gbbfe caaae dbbf caaae fbbg caaae efg ecaace ecaac eaaac eaaac gaaac gaaag gaaag caaag caaae caaae caaae ecaace g eaaac aacgaaac aaaaaac gcaaag egg ``` <!-- end of image --> As I suspected, there's 1 intersection within area B. Answer: A: 0; B: 1; 0 + 1 = 1 I've found a single intersection point in the image.

<!-- image --> ```palette Key,Color ,#fefefeff a,#5c15b4ff b,#721f21ff c,#8a57c8ff d,#c19d9dff e,#e2d4e2ff f,#995c5fff g,#b696dcff ``` ```image e bb fbfb db bb bd bd bb ebe fb fb ebe bb bf bd bb ebe db fb bd bb bb bf fb ebe ebe fb bd bb bb bf db ebe be fb bf bb fb bf db ebe bd db bb bb fb bf ebe ebe bf db bb bb db bf bd bd bb db fb bb ebe bf bd bd bb db db fb be bb bf bd fb db db fb bd bb bb bd fb ebe ebe fb bfge bb bb aaac bd db a gaaae ebe bd a caac fb bb ga gaaag bb d ca caac bf ac eaaag ebe ag gaaae fb a eaaac bb a gaaae bf ea caac ebe ga gaaag fb ae ca caac bbac ac eaaag ebf ag gaaae gagbe a eaaac cae db a gaaae cae b ea caac aa ga eaaag aa ca caac aa ac eaaag aa ae gaaae aa a eaaac eac a gaaagac ea cag ga cc ag ae a a ea ga cc ag ae ``` <!-- end of image -->

I'm on the case! Let's uncover any intersections hidden in this image. I need to zoom in on these areas to get a better look. <!-- image --> ```palette Key,Color ,#fefefeff a,#e6474fff b,#e0c5e4ff c,#ea7a7fff d,#f2eff0ff e,#b1d7b1ff f,#96c995ff g,#f3acb0ff ``` ```image ddd bbbbbbbbbbbbbbddd dddbbbbbbbbbbbbbbbbddd dddbbbbbbbbbbbbbbbddd dddbbbbbbbbb bb dcaa b dcaaacb bd dcaaacb b dcaaacb ddbddddddddgaaacbddddddd dfeebeeeeeeeaceeeeeeeeeef deeebeeeeeeeaeeeeeeeeeeef deeeebeeeeeeaeeeeeeeeeeef deeeebeeeeeeaeeeeeeeeeeef deeeebbeeeeeaeeeeeeeeeeef deeeeebeeeeeaeeeeeeeeeeef deeeeebbeeeeaeeeeeeeeeeef deeeeeebeeeeaeeeeeeeeeeef deeeeeebeeeeaeeeeeeeeeeef deeeeeeebeeeaeeeeeeeeeeef deeeeeeebeeeaeeeeeeeeeeef deeeeeeeebeeaeeeeeeeeeeef deeeeeeeebeeaeeeeeeeeeeef deeeeeeeebbeaeeeeeeeeeeef deeeeeeeeebeaeeeeeeeeeeef deeeeeeeeebbaeeeeeeeeeeef deeeeeeeeeebaeeeeeeeeeeef deeeeeeeeeebceeeeeeeeeeef deeeeeeeeeeebeeeeeeeeeeef deeeeeeeeeeebeeeeeeeeeeef deeeeeeeeeeecbeeeeeeeeeef cd deeeeeeeeeeeabeeeeeeeeeef gaad deeeeeeeeeeeabbeeeeeeeeef gaab deeeeeeeeeeeaebeeeeeeeeef gaab deeeeeeeeeeeaebbeeeeeeeef baag deeeeeeeeeeeaeebeeeeeeeef baag deeeeeeeeeeeaeebbeeeeeeef daag deeeeeeeeeeeaeeebeeeeeeef daac deeeeeeeeeeeaeeebeeeeeeef aac deeeeeeeeeeeaeeeebeeeeeef cac deeeeeeeeeeeaeeeebeeeeeef caa deeeeeeeeeeeaeeeebbeeeeef caad deeeeeeeeeeeaeeeeebeeeeef caad deeeeeeeeeeeaeeeeebbeeeef gaad deeeeeeeeeeeaeeeeeebeeeef gaab deeeeeeeeeeeaeeeeeebeeeef gaag deeeeeeeeeeeaeeeeeeebeeef baag deeeeeeeeeeeaeeeeeeebeeef daag dfffffffffffafffffffbeffe daac ba db daac ba b aac ba bd cac ga db caa ga b caad ga b gaad ga bb gaab ga b gaab gc b baag gc bb baaggc b daac b dd bd db b bd db b bd db b bd db b b bb b b bb b b ``` <!-- end of image --> I'm now examining the contents of area A in detail. <!-- image --> ```palette Key,Color ,#fefefeff a,#e6464eff b,#dec1e7ff c,#f1a8afff d,#f6eaf2ff e,#f8d1d3ff f,#ea7077ff g,#e8d5efff ``` ```image gbb aaaafce dbbd aac gbg daae dbbd daae bbg daae dbb daae bbg daae gbb daad bbd daad gbb eaad dbbd eaad gbg eaad dbbd eaad bbg eaad dbb eaad bbg eaa gbb eaa bbd eaa gbb eaa dbbd eaa gbg eaa dbbd caa bbg caa dbb caa bbg caa gbb caa bbd caf gbb caf dbbd caf gbg caf dbbdcaf bbgcaf dbbcaf bbcaf gbbaf bbff gbbf bbc bbb cbbd fcbg ffbb fabbg facbb facbbg facgbb fac bbd fac gbb fac dbbd fac gbg fac dbbd fac bbg fac dbb fac bbg fac gbb fac bbd aac gbb aac dbbd aac gbg aac dbbd aac bbg aae dbb aae bbg aae gbb aae bbd aae gbb aae dbbd aae gbg daae dbbd daae bbg daae dbb daae bbd daae gbg daad dbb daad bbd eaad gbg ``` <!-- end of image --> Success! This area contains 1 intersection point! Answer: A: 1; 1 = 1 After careful examination, I conclude that there is one intersection.

<!-- image --> ```palette Key,Color ,#fefefeff a,#e6464eff b,#dfc3e8ff c,#ee8d93ff d,#f2e3f0ff e,#f8ced0ff f,#ea6c73ff g,#f3aeb1ff ``` ```image dd bbbbbbbbbbbbbdddd dddbbbbbbbbbbbbbbddd ddddbbbbbbbbbbbbbdddd dddbbbbbbbb bb dcaa b dcaaafe bd dcaaafe b dcaaafe bd gaaafe db ag b ae db ae b ad db ad b ad bd a b a bd a b a b a db a b a db a b a bda ba bc b bd fb fd ab caad adb gaae a b gaae a bb eaag a b eaag a bd daac a b daac a bd aaf a db faf a b faf a db caa a b caad a bb gaad da b gaae da bd eaae da db eaag da b daag ea bd daac ea db aac ea b faf ea bd faf ea db faa ga b caad ga b caad gf db gaae gf b gaae gf b eaag gf bd eaagcf b daaf b dd bd db b bd db b bd db b bd db b b db b b bd b b ``` <!-- end of image -->

This is the image I'm working with. The goal is to count the intersections. These regions highlight areas that look suspicious. Lines seem to converge within them. <!-- image --> ```palette Key,Color ,#fefefeff a,#4f3ec9ff b,#ef7339ff c,#bfb9ebff d,#eba177ff e,#7f7ad0ff f,#f0eeeaff g,#afd6afff ``` ```image c cac aaa a aa ca ac ae fa a ea ca ae ae faf af ea fa ae ee ac af ca fa aa ea ac ac ca fa ea ea ae af ac faf aa a ea ca ea ae ac ac ac aa a ca ca ea aa af ac ac ae a ca ea ca ea faf ggggggggggggggggaeggggg ae ae fggggggggggggggggaggggggf faf aa d fgggggggggggggggeaggggggf ea ca bb fgggggggggggggggaeggggggf ae ac dbf fgggggggggggggggagggggggf ac aa fbd fggggggggggggggeagggggggf ca ca bb fggggggggggggggaegggggggf aa af dbffggggggggggggggaggggggggf ac ae fbdgggggggggggggeaggggggggf ca ea bbggggggggggggaeggggggggf ea faf fbbgggggggggggagggggggggf ae ae fgdbdgggggggggagggggggggf faf aa fgggbbgggggggaegggggggggf ea ca fggggbbggggggaggggggggggf aeac fgggggdbdggggaggggggggggf aa fgggggggbbggaaggggggggggf fggggggggbbgagggggggggggf fgggggggggdbagggggggggggf fggggggggggaabggggggggggf fggggggggggagbbgggggggggf fggggggggggaggbbdgggggggf fgggggggggeaggggbbggggggf fgggggggggaggggggbbgggggf fgggggggggagggggggbbggggf fggggggggeaggggggggdbdggf fggggggggaeggggggggggbbgf fggggggggaggggggggggggbbf c fgggggggeagggggggggggggdbd ae fgggggggaeggggggggggggggfbb fa fgggggggagggggggggggggggf bbf ea fggggggeagggggggggggggggf dbd ac fggggggaegggggggggggggggf fbb ca fggggggaggggggggggggggggf bbf ae fgggggeaggggggggggggggggf dbd fa fgggggaeggggggggggggggggf fbb aa fgggggagggggggggggggggggf bb af ffffcafffffffffffffffff dbf ea ae fbd ac a bb ca ca bbf ae ae dbd af a fbb ea ca bbf acae dbd caaf fbb aa bbf fc dbd fbbbbf fdbbbbf fdbbbbf fdbbbbf fdbbbbf fdbb ``` <!-- end of image --> Here's a close-up of the area A. <!-- image --> ```palette Key,Color ,#fefefeff a,#4e3dc9ff b,#f07238ff c,#b2abe7ff d,#f3976eff e,#7f70d3ff f,#ebe1eaff g,#f8c4abff ``` ```image eae faac caaf eae faac caaf eae faac caaf eaa faac caaf eaa aae caaf eaa aae d caac bbf eaa bbbg aae gbbbd caac fbbbbf eaa dbbbg aae gbbbd faac fbbbdf eaa dbbbg aae gbbbd faac gbbbdf caaf fdbbbg aae gbbbg faac gbbbdf caaf fdbbbg aae dbbbg faac gbbbd caaf fdbbbeae dbbaac geaad eaabbf faaebbbg caafgbbbd eaa fbbbdf faac fdbbbg caaf gbbbd eaa gbbbdf aae fdbbbg caaf dbbbg eaa gbbbdf aae fdbbbf caac dbbbg eaa gbbbd aae fbbbbf caac dbbbg eaa gbbbd aae fbbb caac db eaa g aae faac eaa aae faac caaf aae faac caaf eae faac caaf eae faac caaf eaa ``` <!-- end of image --> I can confirm that 1 intersection exists in area A. Answer: A: 1; 1 = 1 There's only one, but is an intersection after all.

<!-- image --> ```palette Key,Color ,#fefefeff a,#4f3ec9ff b,#f07339ff c,#b3ace7ff d,#f5a078ff e,#8175d8ff f,#d9d5f3ff g,#fad6c5ff ``` ```image c caf aaa a aa fa ac ae fa a ea fa ae ae af a ea fa ae ee af af ca fa aa ea ac af fa a ea ea ae af af af aa a ea fa ea ae ac ac af aa a ca ca ea aa af ac ac ae a fa ea ca ea fa ac ae ae a fa aa d ca ea fa bb ac ae ac dbg a af aa gbd ca ca ca bb ae aa af dbg a ac ae gbd ca fa ea bb ae ea fa bbg a ae ae gbd fa fa aa bb ae ea fa bb a aeac dbd fa aa gbb ae bb af dba eab afbb a dbg ea gbd af bb a bbg ea gbd ac bb a bbg c ea dbd ae ac bb a a bb ea ca dbd af ac gbb ca a bb ae ca dbg fa ac gbb aa a bb af ca dbg ea ae gbd ac a bb fa ca bbg ae ae gbd a a bb ea fa bbg acae dbd caa bb aa bb c dbd gbbbbg gdbbbbg gdbbbbg gdbbbbg gdbbbbg gdbb ``` <!-- end of image -->

I'm on the case! Let's uncover any intersections hidden in this image. I have a hunch that these areas might contain the intersections we're looking for. <!-- image --> ```palette Key,Color ,#fefefeff a,#abf983ff b,#2eb404ff c,#d7fbc5ff d,#88fc4aff e,#b0d7b0ff f,#69c84dff g,#95cc91ff ``` ```image dc dda dda add add cdd dd ddc dda dda add geeeeeeeeeeeeeeeeeeeadd eeeeeeeeeeeeeeeeeeegdde eeeeeeeeeeeeeeeeeeeddee eeeeeeeeeeeeeeeeeeddaee cfbbeeeeeeeeeeeeeeeeddaeee gbbbbbbbfeeeeeeeeeeeeedddeeee ebbbbbbfc gbbbeeeeeeeeeeedddeeeee cfbbbbbbe eebbbfeeeeeeeeaddeeeeee fbbbbbbg eeegbbbeeeeeeeddeeeeeee gbbbbbbfc eeeeebbbfeeeeddeeeeeeee cfbbbbbbe eeeeeefbbbeeddaeeeeeeee fbbbbbbg eeeeeeeebbbfdaeeeeeeeee gbbbbbbfc eeeeeeeeefbbbeeeeeeeeee cfbbbbbbe eeeeeeeeeddbbbgeeeeeeee ggggggggggggcfbbbbbbg eeeeeeeeaddefbbbeeeeeee eeeeeeeeefbbbbbbfc eeeeeeeeddeeeebbbgeeeee eeeeegbbbbbbfe eeeeeeeddeeeeeefbbbeeee eegbbbbbbfee eeeeeeeddeeeeeeeebbbgee eeebbfeeeeee eeeeeeeddeeeeeeeeefbbfe eeeddeeeeeee eeeeeeeddeeeeeeeeeegbbbc eeeddeeeeeee eeeeeeeddeeeeeeeeeeeebbbf eeeddeeeeeee eeeeeeedaeeeeeeeeeeeeegbbb eeeddeeeeeee eeeeeeadaeeeeeeeeeeeeee bbbf eeeddeeeeeee eeeeeeddeeeeeeeeeeeeeee cbbb eeeddeeeeeee eeeeeeddeeeeeeeeeeeeeee bbbg eeeadeeeeeee ggggggddggggggggggggggg ebbb eeeadaeeeeee dd b eeeedaeeeeee dd eeeeddeeeeee dd eeeeddeeeeee da eeeeddeeeeee cda ggggddgggggg adc dd ad ad dd adc dd cda dd da dd dd dd dd da dd cdc dd adc dd ad adc dd cdc dd da dd dd dd dd ac dd dd dddc cda dd ddddda cdc dd cda addda adc ad cdc addda dd cdc ad cdddd dd cda dd cdddd dd da dd cddddc dd dd dd ddddc dd dd dd dddda da dd dd addda cda dd da addda cdc adcda adddd ad adadc cdddd dd cddd cddddc dd ddd ddddc dd ddd ddddc dd ddd addda dd ddd addda da ddd addddcda dda cddddc ada cdd cdc c ``` <!-- end of image --> I'm now examining the contents of area A in detail. <!-- image --> ```palette Key,Color ,#fefefeff a,#a3f67aff b,#2db403ff c,#c1f4a8ff d,#88fd4aff e,#81d168ff f,#5ac935ff g,#defad1ff ``` ```image ce gafbbb gcebbbbbbb cefbbbbbbbbbb gafbbbbbbbbbbbbec cbbbbbbbbbbbbfag gbbbbbbbbfec fbbbbecg fffa ddda ddda addd addd cdddg cdddg gdddc gdddc ddda ddda dddd addd adddg cdddg cdddc gdddc gddda ddda dddd addd addd cdddg cdddg gdddc ``` <!-- end of image --> Area A doesn't meet the criteria for an intersection. Let's shift our focus to the next area. Let's zoom in on area B to get a clearer view. <!-- image --> ```palette Key,Color ,#fefefeff a,#a4fc76ff b,#2db403ff c,#dff9d4ff d,#88fc4aff e,#bdf4a3ff f,#59c636ff g,#8fd77aff ``` ```image addd edddd edddde cdddda cdddda addddc addddc addddc gc edddde bbg cdddde bbbfe cdddda bbbbbg cdddda gbbbbbfc addddc ebbbbbbg addddc gbbbbbfc eddddc ebbbbbbg edddde cfbbbbbfc cdddda ebbbbbbg cdddda cfbbbbbfc cdddda ebbbbbbe addddc cfbbbbbfc addddc gbbbbbbe eddddc cfbbbbbfcedddde gbbbbbbfddda cfbbbbbfda gbbbbbbe dbbbbbbg addfbbbbbfe eddddafbbbbbg edddde gbbbbbfc cdddda ebbbbbbg cdddda gbbbbbfc adddd ebbbbbbg ddddc cfbbbbbfc cddde ebbbbbbg cddde cfbbbbbfc edddc ebbbbbbg edddc cfbbbbbfc adddc gbbbbbbe addd cfbbbbb dddd gbbbb ddda cfbb ddda gb cddde c cddde edddc edddc addd addd dddd ddda ``` <!-- end of image --> Bingo! This close-up reveals 1 intersection in area B! Answer: A: 0; B: 1; 0 + 1 = 1 There's only one, but is an intersection after all.

<!-- image --> ```palette Key,Color ,#fefefeff a,#9af26fff b,#2db403ff c,#cff9bbff d,#88fc49ff e,#b4f792ff f,#60c740ff g,#e9fcdfff ``` ```image dg dde dda add edd cdd gddg ddc dde dda add edd gdd ddg ddc cfbb dde abbbbbbba dda ebbbbbbfc cbbb add cfbbbbbbe bbba cdd gabbbbbba ebbb gdd ebbbbbbfg bbbe ddg cfbbbbbbe ebbb ddc gabbbbbba bbbfde ebbbbbbfg abbb cfbbbbbfc adbbbc gfbbbbbba cdd abbf ebbbbbbfg gdd gbbbc cfbbbbbfc ddg fbbf cbbbbbba dd gbbbg bbfg dd fbbf da dd gbbbg dd da fbbf dd gde cbbbg dd cdc fbba dd edg cbbb ad dd bbba edg dd ebbb cdc dd b gde dd da dd dd da dd cde dd edc dd ad ad dd edc dd gde dd da dd dd dd dd gde dd cdc dd edg ad ad edg dd cdc dd gde dd dd dd dd ec da dd dddc gde dd ddddde cdc dd gde addde edg edg cdc eddda ad cdc edg cdddd dd gde dd cddddg dd da dd gddddg dd dd dd gddddc dd dd dd addde da dd dd addde gde dd da eddda cdc adgde eddda edg ededc cddddg dd cdddg gddddg dd ddd gddddc dd ddd ddddc dd ddd addde dd ddd eddda da ddd edddacde ada cddddc ede cdd cdc c ``` <!-- end of image -->

Based on a first glance, I suspect there could be intersection regions here. I have a hunch that these areas might contain the intersections we're looking for. <!-- image --> ```palette Key,Color ,#fefefeff a,#f2e25dff b,#ddf5d4ff c,#dde186ff d,#b1d7b1ff e,#f1f8eeff f,#96ca95ff g,#c8e6c2ff ``` ```image e ebb bbb ebbe bbb ebbe bbb ebbe bb bbb bbbe ebbe bbbb bbb ebbbb ebbe dfffffffffffffffbbbbbffffffffffffffffffffffffffffffffffbbb fddddddddddddddgbbgbbgdddddddddddddddddddddddddddddddddbbb fddddddddddddddbbbdbbbddddddddddddddddddddddddddddddddbbbe fddddddddddddddbbgdgbbddddddddddddddddddddddddddddddddbbge fddddcaaddddddbbbdddbbgddddddddddddddddddddddddddddddbbbde fddddaaacdddddbbgdddbbbddddddddddddddddddddddddddddddbbgde fdddcaaaaddddbbbddddbbbdddddddddddddddddddddddddddddbbbdde fdddaaaaaadddbbbddddgbbdddddddddddddddddddddddddddddbbgdde fddaaadaaaddbbbddddddbbgdddddddddddddddddddddddddddbbbddde b fddaaaddaaadbbbddddddbbbdddddddddddddddddddddddddddbbbddde caa fdaaadddcaagbbdddddddbbbddddddddddddddddddddddddddbbbdddde aaa fdaaaddddaabbbdddddddgbbddddddddddddddddddddddddddbbbdddde aaae faaaddddddcbbdddddddddbbgddddddddddddddddddddddddbbbdddddeeaaa faacddddddbbbcddddddddbbbddddddddddddddddddddddddbbbdddddeaaa aaaddddddgbbcaddddddddgbbdddddddddddddddddddddddgbbddddddcaab baacddddddbbbaaaddddddddbbdddddddddddddddddddddddbbbddddddaaa aaadddddddbbgaaaddddddddbbgdddddddddddddddddddddgbbddddddaaae caacddddddbbbddaaadddddddbbbdddddddddddddddddddddbbbddddddaac aaadddddddbbgddcaacddddddgbbddddddddddddddddddddgbbddddddaaa caafddddddbbbddddaaadddddddbbgdddddddddddddddddddbbbdddddcaab aaafddddddbbbdddddaaaddddddbbbddddddddddddddddddgbbddddddaaae caaefdddddgbbddddddaaaddddddbbbddddddddddddddddddbbbdddddaaade aaa fdddddbbbdddddddaaadddddgbbdddddddddddddddddgbbgdddddaacde aaa fddddgbbddddddddcaacdddddbbgddddddddddddddddbbbdddddaaadde eaac fddddbbbdddddddddaaadddddbbbdddddddddddddddgbbgddddcaacdde aaa fdddgbbgddddddddddaaaddddbbbdddddddddddddddbbbdddddaaaddde eaac fdddbbbdddddddddddcaacdddgbbddddddddddddddgbbgddddaaadddde aaa fdddbbgddddddddddddaaaddddbbgdddddddddddddbbbddddcaacdddde baab fddbbbddddddddddddddaacdddbbbddddddddddddgbbgddddaaaddddde aaa fddbbgddddddddddddddaaadddgbbddddddddddddbbbddddcaadddddde caab fdbbbddddddddddddddddaaadddbbddddddddddddbbgddddaaadddddde aaa fdbbbddddddddddddddddcaacddbbgddddddddddbbbddddaaaddddddde caae fgbbddddddddddddddddddaaaddbbbddddddddddbbgdddcaacddddddde aaa fbbbdddddddddddddddddddaaadgbbdddddddddbbbddddaaadddddddde aaa dbbddddddddddddddddddddaaaddbbdddddddddbbgdddaaaddddddddde aaa bbbdddddddddddddddddddddaaadbbbdddddddbbbddddaaaddddddddde aaa ebbgdddddddddddddddddddddcaacbbbdddddddbbgdddaaadddddddddde eaac bbbdddddddddddddddddddddddaaagbbddddddbbbdddcaacdddddddddde aaa ebbgddddddddddddddddddddddddaaabbgdddddbbbdddaaaddddddddddde eaac bbbdddddddddddddddddddddddddcaabbbddddbbbdddaaadddddddddddde b aaa bbgddddddddddddddddddddddddddaabbbddddbbbdddaaadddddddddddde baabbaab bbbfdddddddddddddddddddddddddddacbbdddbbbdddaaaddddddddddddde aaaaaaa bbbfdddddddddddddddddddddddddddaabbgddbbbddcaacddddddddddddde baaaab bbb fddddddddddddddddddddddddddddabbbdgbbdddaaadddddddddddddde caa bbb fddddddddddddddddddddddddddddabbbdbbbddaaaddddddddddddddde ebb fddddddddddddddddddddddddddddacbbbbbdddaaaddddddddddddddde bbb fddddddddddddddddddddddddddddcabbbbbddaaadddddddddddddddde ebbe fddddddddddddddddddddddddddddcabbbbddcaacdddddddddddddddde bbb fdddddddddddddddddddddddddddddagbbbddaaaddddddddddddddddde ebbe fdddddddddddddddddddddddddddddaabbddaaadddddddddddddddddde bbb fdddddddddddddddddddddddddddddaaggddaaadddddddddddddddddde bbe fdddddddddddddddddddddddddddddaacddaaaddddddddddddddddddde bbb fdddddddddddddddddddddddddddddaaadcaacddddddddddddddddddde bbb fdddddddddddddddddddddddddddddaaadaaadddddddddddddddddddde bbb fdddddddddddddddddddddddddddddcaaaaaddddddddddddddddddddde bbb fdddddddddddddddddddddddddddddcaaaaaddddddddddddddddddddde ebb fddddddddddddddddddddddddddddddaaaadddddddddddddddddddddde bbb fddddddddddddddddddddddddddddddaaacdddddddddddddddddddddfe ebbe eeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeaaaeeeeeeeeeeeeeeeeeeeeeee bbb aa ebbe bbb bbe bbb bbb bbb bbbbb ebbbbbb bbbbb be ``` <!-- end of image --> Let's get to the bottom of what's happening inside area A. <!-- image --> ```palette Key,Color ,#fefefeff a,#f2e35cff b,#ddf6d5ff c,#f4e87cff d,#f5eea1ff e,#e9f8e4ff f,#faf5cbff g,#f7fbf0ff ``` ```image ebbbbbbbbbbg gbbb bbbbbebbbbbe ebbb gbbbbbgebbbbe gbbbb bbbbbb gbbbbb ebbbb gbbbbbg bbbbbg gbbbbb ebbbbb bbbbbe ebbbbb gbbbbbe ebbbbe bbbbbe dacf ebbbbb gbbbbb ebbbbbg daaaaf gbbbbbe bbbbbg bbbbbe gaaaaac ebbbbb ebbbbe ebbbbbg daaaaaad bbbbbe ebbbbb bbbbbe gaaaaaaaag ebbbbbg gbbbbb ebbbbbg daaaaaaaac bbbbbe bbbbbg bbbbbe faaaaaaaaaa gbbbbbg ebbbbe ebbbbbg caaaaaaaaaa bbbbbe gbbbbb bbbbbe faaaaaddaaaad gbbbbbg gbbbbbg ebbbbbg caaaaag caaaag bbbbbb bbbbbg bbbbbe faaaaad faaaac gbbbbbg ebbbbe gbbbbbg caaaaag daaaaf ebbbbb gbbbbb bbbbbb gaaaaac faaaafbbbbb bbbbbe bbbbbb daaaaaf caaabbbbbe ebbbbe gbbbbbg gaaaaac faadbbbbbg gbbbbb bbbbbb daaaaaf aabbbbbe bbbbbg gbbbbbg gaaaaac adbbbbbg ebbbbe bbbbbb daaaaag fbbbbbb ebbbbb gbbbbbe faaaaad gbbbbbcf gbbbbb ebbbbb caaaaag bbbbbbac bbbbbg gbbbbbe faaaaad bbbbbcaad ebbbbe ebbbbb caaaaag bbbbbaaaag ebbbbb gbbbbbe aaaaad gbbbbdaaaac gbbbbbg ebbbbb aaaaa ebbbbdaaaaaf bbbbbg gbbbbbe f aaaaf bbbbegaaaaaag ebbbbe ebbbbb ga aaac ebbbb faaaaad gbbbbb bbbbbe da aaaf bbbbe caaaaaf bbbbbg bbbbb faa aac ebbbbg faaaaac bbbbbe bbbbe caa aaf bbbbe daaaaad ebbbbe ebbbbg faaa ac gbbbbg gaaaaaag gbbbbb bbbbe gaaaa ag bbbbb faaaaac bbbbbg ebbbbg daaaa d gbbbbg caaaaaf bbbbbe bbbbe faaaaa g ebbbb gaaaaac ebbbbb ebbbbg caaaaa gbbbbb daaaaad gbbbbb bbbbe daaaaad ebbbbb caaaaag bbbbbg ebbbbg gaaaaaag bbbbbe faaaaac ebbbbe bbbbe daaaaaf ebbbbb daaaaaf ebbbbb ebbbbg faaaaac bbbbbe gaaaaaag gbbbbb bbbbb caaaaag ebbbbbg faaaaad bbbbbg gbbbbb daaaaad bbbbbe caaaaaf ebbbbe bbbbbb gaaaaac gbbbbbg faaaaac gbbbbb gbbbbbg caaaaaf bbbbbb daaaaad bbbbbg bbbbbb faaaaac gbbbbbg gaaaaaag bbbbbe gbbbbbg caaaaag ebbbbb faaaaac ebbbbe bbbbbb daaaaad gbbbbbg caaaaaf gbbbbb gbbbbbg gaaaaac ebbbbb gaaaaac bbbbb bbbbbb caaaaaf gbbbbbe daaaaad bbbbb gbbbbbg faaaaac ebbbbb caaaaag ebbbb ebbbbb caaaaag bbbbbe faaaaac gbbbb gbbbbbe daaaaad bbbbbe gaaaaaag ebbbe gbbbbbe caaaaaf gbbbbbg faaaaad ebbbb ebbbbb faaaaad bbbbbe caaaaaf gbbbb gbbbbbe gaaaaaag gbbbbbg faaaaac bbbbg ebbbbb daaaaad bbbbbb daaaaad ebbbe gbbbbbe aaaaac gbbbbbg gaaaaaag gbbbb ebbbbb aaaaaf ebbbbb faaaaac gbbbbg gbbbbbe faaaad gbbbbbe caaaaaf bbbbe ebbbbb gaaaaag ebbbbb gaaaaac ebbbe bbbbbe daaaad bbbbbe daaaaad gbbbb ebbbbbg faaaac ebbbbb caaaaag bbbbg bbbbbe caaaaf bbbbbe faaaaac bbbbe ebbbbbg faaaad ebbbbbg daaaaaf ebbbe bbbbbe gaaaaag bbbbbe gaaaaaaggbbbb ebbbbbg daaaaf bbbbbg faaaaad bbbbg bbbbbe faaaaa bbbbb caaaaafbbbbe ebbbbbg caaaaa bbbbg faaaaacbbbbb bbbbbe faaaaad bbbb daaaaabbbbb ebbbbbg gaaaaaag bbbe gaaaaabbbbbg bbbbbb daaaaaf bbb faaaabbbbbe gbbbbbg faaaaac bbe caaadbbbbb bbbbbb caaaaag bb gaaacbbbbbg gbbbbbg daaaaad be daaabbbbbg bbbbbb gaaaaaag bg caadbbbbe gbbbbbg daaaaaf e faacbbbbb bbbbbb faaaaac g daabbbbbg gbbbbbg caaaaag gaabbbbbe bbbbbb daaaaad aadbbbbe gbbbbbe gaaaaacg cacbbbbb ebbbbb caaaaaf faabbbbbg gbbbbbe faaaaac faabbbbbe ebbbbb caaaaag gaadbbbbbgbbbbbe daaaaad aacbbbbbebbbbb gaaaaac caabbbbbbbbbbe caaaaaf caadbbbbbbbbb faaaaac daadbbbbbbbbe caaaaag daacbbbbbbbb daaaaad faaadbbbbbbg caaaaaf gaaacbbbbbe faaaaad aaaabbbbbg gaaaaaag caaadbbbe daaaaad caaaafeg gaaaaac daaaad caaaaaf daaaac faaaaad faaaac gaaaaaag faaaaa daaaaad gaaaaag faaaaac aaaaag caaaaaf caaaaffaaaaad caaaadaaaaaag daaaaaaaaaaf daaaaaaaaac faaaaaaaaaf faaaaaaaad gaaaaaaaag aaaaaaaf ``` <!-- end of image --> I am surprised, so clear, 1 intersection has appeared in area A. Answer: A: 1; 1 = 1 There's one and only one intersection present in the image.

<!-- image --> ```palette Key,Color ,#fefefeff a,#f3e35cff b,#ddf6d5ff c,#f3e87eff d,#f7efa8ff e,#e8f8e3ff f,#f9f5caff g,#f7fbefff ``` ```image g ebb bbb ebbg bbb gbbg bbb gbbg bb bbb ebbe gbbg bbbb bbb ebbbb gbbe bbbbbg bbb gbbgbbe gbbe bbb bbb bbb gbbg ebb bbe daa bbb bbg bbb aaad bbe bbb bbe caaaa bbb bbb bbb aaaaac bbe gbb bbe caagcaag ebb bbg bbb f aaa aaa bbb bbb bbb daa aaa daafbb bbb bbb aaa gaac aabbb gbb bbb aaag aaa gcbbg bbe ebb gaac faad bbbf bbb bbb aaa aaa gbbca ebb ebb daad faad bbbaac gbb bbb aaa aaa bbeaaag bbe ebb aaag daaf bbb aaa bbb bbb faac aaa bbe daad ebb ebb aaa caag bbb aaa bbg bbb daaf aaa bbb gaac bbe ebbg aaa caag ebb caag bbb bbb aaag aaa bbb aaa gbb gbbg faac aaa ebbg daad bbg bbb aaa gaac bbb aaa bbb gbbg caaf aaa gbbg gaaa bbb bbb aaa faad bbb caaf gbb gbbg aaa aaa gbbe aaa bbe bbb faac faad bbb faac bbb gbbg aaa aaa bbe aaag ebb bbb caaf daaf bbb aaa gbb gbbe gaaa aaa bbb daad bbe bbb aaa caag ebb aaa bbb bbe faad aaa bbb gaac ebb bbb aaa caag ebb caag bbg bbe caaf aaa bbb aaa bbe bbb gaaa aaa gbbg daadbbb bbe aaa gaac bbb aaaebb bbb daad aaa gbbe gaaabbg bbe aaa faad bbb caabbb bbb caag d aaa bbe aabbb bbb gaaa faaffaad bbb facbb bbb aaa aaaaaaa bbb aabbe bbb daad faaaaf ebb abbb ebb aaa daa bbb abbb bbb caag ebb acbbebb gaac bbb cabbbbb aaa gbbg dabbbb daad bbb fadbbb aaa gbbg aabbg aaag bbb aafg gaac bbe aac aaa bbb aaa daad bbe aaa aaa bbb caaaaag bbb daaaac ebb faaaa bbb aaaf gbbg aaa bbb aag gbbg bbb bbe bbb bbe bbb bbbbb gbbbbbb bbbbe be ``` <!-- end of image -->

Time to put on my detective hat and find those intersection points! These spots mark what I'd call 'danger zones' - areas where intersections are more likely. <!-- image --> ```palette Key,Color ,#fefefeff a,#468b1bff b,#00248bff c,#92c189ff d,#6e88b4ff e,#edf4eeff f,#b1d7b1ff g,#264d83ff ``` ```image aa faaae aaaa dgaaaceeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee baaaaffffffffffffffffffffffffffffffffe ebaaaafffffffffffffffffffffffffffffffe ggaaacffffffffffffffffffffffffffffffe ebaaaaffffffffffffffffffffffffffffffe edbaaaafffffffffffffffffffffffffffffe efbaaaacffffffffffffffffffffffffffffe effbaaaaffffffffffffffffffffffffffffe effdgaaaafffffffffffffffffffffffffffe efffbaaaafffffffffffffffffffffffffffe effffbaaaaffffffffffffffffffffffffffe effffggaaacfffffffffffffffffffffffffe f efffffbaaaafffffffffffffffffffffffffe ebbb efffffcbaaaaffffffffffffffffffffffffe dbbbbbf effffffbaaaacfffffffffffffffffffffffe egbbbbbbbg efffffffbaaaafffffffffffffffffffffffe dbbbbbbbbd efffffffdgaaaaffffffffffffffffffffffe egbbbbbbbbe effffffffbaaaaffffffffffffffffffffffe dbbbbbbbbd efffffffffbaaaafffffffffffffffffffffe egbbbbbbbbe efffffffffggaaacffffffffffffffffffffe fbbbbbbbbd effffffffffbaaaaffffffffffffffffffffe gbbbbbbbbf effffffffffcbaaaafffffffffffffffffffe fbbbbbbbbd efffffffffffgaaaacffffffffffffffffffe dbbbbbbbbf effffffffffffbaaaaffffffffffffffffffe fbbbbbbbbg effffffffffffdgaaaafffffffffffffffffe dbbbbbbbbf efffffffffffffbaaaafffffffffffffffffe ebbbbbbbbge effffffffffffffbaaaaffffffffffffffffe dbbbbbbbbd effffffffffffffggaaacfffffffffffffffe ebbbbbbbbge efffffffffffffffbaaaafffffffffffffffe dbbbbbbbbd effffffffffffffffbaaaafffffffffffffcgbbbbbbbge effffffffffffffffgaaaacffffffffffdbbbbbbbbd efffffffffffffffffbaaaaffffffffgbbbbbbbbe efffffffffffffffffdgaaaaffffdbbbbbbbbd effffffffffffffffffbaaaaffgbbbbbbbbce efffffffffffffffffffbaaaabbbbbbbgfffe efffffffffffffffffffdgaaagbbbbdfffffe effffffffffffffffffffbaaaabgffffffffe efffffffffffffffffffffbaaaafffffffffe effffffffffffffffffffffaaaacffffffffe efffffffffffffffffffffffaaaaffffffffe efffffffffffffffffffffffcaaaafffffffe effffffffffffffffffffffffaaaafffffffe efffffffffffffffffffffffffaaaaffffffe efffffffffffffffffffffffffcaaacfffffe effffffffffffffffffffffffffaaaafffffe efffffffffffffffffffffffffffaaaaffffe efffffffffffffffffffffffffffaaaacfffe effffffffffffffffffffffffffffaaaafffe effffffffffffffffffffffffffffcaaaaffe ecccccccccccccccccccccccccccccaaaacce aaaa faaac cc aaaa caaa eaaaa caaaaac caaaf caaaaaaa aaaa caaaaaaae eaaaa caaaaaaae aaaae caaaaaaae aaaa faaaaaaae faaac faaaaaaae aaaa faaaaaaae eaaaa faaaaaaae caaaf faaaaaaae aaaa faaaaaaae eaaaa aaaaaaae aaaae caaaaae aaaa aaaaf faaac caaae aaaa aaaa aaaa faaae caaaf aaaa aaaa eaaaf eaaaa aaaa aaaaeaaac aaaaaaa faaaaac aaaaa aaaa caa ``` <!-- end of image --> I'm going to scrutinize area A for any signs of an intersection. <!-- image --> ```palette Key,Color ,#fefefeff a,#458a1aff b,#04288bff c,#76a957ff d,#556db1ff e,#d2dddaff f,#a2baaeff g,#225851ff ``` ```image aaaaaaae aaaaaaac gaaaaaaaf baaaaaaaae bbaaaaaaac dbgaaaaaaaf ebbaaaaaaaa dbgaaaaaaac bbgaaaaaaae ebbaaaaaaac dbgaaaaaaaf bbaaaaaaaae fbbaaaaaaac dbgaaaaaaaf ebbaaaaaaaa dbgaaaaaaac bbgaaaaaaae ebbaaaaaaaa dbgaaaaaaaf bbaaaaaaaae fbbaaaaaaac dbgaaaaaaaf ebbaaaaaaaa fbgaaaaaaac bbgaaaaaaae ebbaaaaaaaa dbgaaaaaaaf bbaaaaaaaae fbbaaaaaaac dbgaaaaaaaf ebbaaaaaaaa fbgaaaaaaac dbgaaaaaaae ebbaaaaaaaa dbgaaaaaaaf bbaaaaaaaae fbbaaaaaaac dbgaaaaaaaf ebbaaaaaaaae fbgaaaaaaac dbgaaaaaaae ebbaaaaaaaa dbgaaaaaaaf bbaaaaaaaae ebbaaaaaaac dbgaaaaaaaf bbaaaaaaaae fbgaaaaaaac dbgaaaaaaae ebbaaaaaaaa dbgaaaaaaac bbaaaaaaaae ebbaaaaaaac dbgaaaaaaaf bbaaaaaaaae fbgaaaaaaac dbgaaaaaaaf ebbaaaaaaaa fbgaaaaaaac ed bbaaaaaaaae fbbb ebbaaaaaaac edbbbbb dbgaaaaaaaf fbbbbbbbb bbaaaaaaaae edbbbbbbbbbb fbbaaaaaaac fdbbbbbbbbbbbb dbgaaaaaaaf edbbbbbbbbbbbbbbb ebbaaaaaaaa fdbbbbbbbbbbbbbbbbd fbgaaaaaaacdbbbbbbbbbbbbbbbbbf dbgaaaaaaabbbbbbbbbbbbbbbde ebbaaaaaaaabbbbbbbbbbbbf dbgaaaaaaagbbbbbbbbde bbaaaaaaaabbbbbbf ebbaaaaaaagbbde dbgaaaaaaade ebbaaaaaaaa edgaaaaaaac caaaaaaae eaaaaaaac faaaaaaaf caaaaaaae eaaaaaaac caaaaaaaf aaaaaaaa faaaaaaac caaaaaaae eaaaaaaac faaaaaaaf caaaaaaae eaaaaaaac caaaaaaaf aaaaaaaa faaaaaaac caaaaaaae eaaaaaaac faaaaaaaf caaaaaaae eaaaaaaac caaaaaaaf ``` <!-- end of image --> Gotcha! I've found 1 intersection hiding in area A! Answer: A: 1; 1 = 1 One intersection, that's it, but I found it.

<!-- image --> ```palette Key,Color ,#fefefeff a,#458b1aff b,#00248bff c,#83b166ff d,#7185beff e,#d8e1deff f,#afc8aaff g,#254b84ff ``` ```image aa faaae aaaa dgaaac baaaa ebaaaa ggaaaf baaaa ebaaaa baaaae baaaa dgaaac baaaa baaaa ggaaaf f baaaa ebbb ebaaaa dbbbbbe gaaaae egbbbbbbbg baaaa dbbbbbbbbd dgaaac gbbbbbbbbe baaaa dbbbbbbbbd baaaa gbbbbbbbbe dgaaaf fbbbbbbbbd baaaa gbbbbbbbbe ebaaaa fbbbbbbbbd gaaaae dbbbbbbbbf baaaa ebbbbbbbbg fgaaac dbbbbbbbbf baaaa ebbbbbbbbg baaaa dbbbbbbbbd dgaaaf ebbbbbbbbg baaaa dbbbbbbbbd ebaaaa egbbbbbbbge gaaaae dbbbbbbbbd baaaa gbbbbbbbbe fgaaac dbbbbbbbbd baaaa gbbbbbbbbe baaaabbbbbbbd dgaaagbbbbe baaaabd ebaaaa caaae aaaa eaaac aaaa aaaa faaaf aaaa aaaa caaae aaaa eaaac aaaae aaaa faaac cc aaaa caaa aaaa caaaaac caaaf caaaaaaa aaaa faaaaaaa eaaac faaaaaaa aaaae faaaaaaa aaaa faaaaaaa faaac faaaaaaae aaaa faaaaaaae aaaa faaaaaaae caaaf faaaaaaae aaaa faaaaaaae eaaac aaaaaaae aaaae caaaaae aaaa aaaae faaac faaa aaaa aaaa aaaa eaaae caaaf aaaa aaaa eaaaf eaaaa aaaa aaaaeaaaf aaaaaaa faaaaac aaaaa aaaa caa ``` <!-- end of image -->

I'm optimistic that I'll find some intersections in this image. My next step is to analyze the details within each area. <!-- image --> ```palette Key,Color ,#fefefeff a,#c11cdaff b,#a73035ff c,#dc84eaff d,#bb7471ff e,#c8a4aeff f,#f2ebf1ff g,#afd6afff ``` ```image f caa aaa faac aaa aaa caaf d aaa dbb aac bbbbf caa dbbbf aaa dbbbe faac ebbbe fffffffffffffffffffffff aaa fbbbdfgggggggggggggggggggggggg aaa fbbbbggggggggggggggeaaaaacegg caaf bbbbgggggggggggggaaaaaaaaaaaaaccf aaa bbbbggggggggggggaaaaaaaaaaaaaaaaaaaaacf aac bbbbggggggggggaaaggggggeecaaaaaaaaaaaaaaaaacc caa fbbbbgggggggggaaagggggggg fccaaaaaaaaaaaaaaaf aaa fgdbbbegggggggaaegggggggg fcaaaaaaaaa faac fggdbbbdgggggaaaggggggggg faaa aaa fgggebbbdggggaaaggggggggg faac aaa fgggggbbbbggeaaeggggggggg aaa caaf fggggggbbbbgaaagggggggggg caaf aaa fgggggggbbbbaaagggggggggg aaa aac fggggggggbbbbaggggggggggg aaa caa fgggggggggbbbbggggggggggg faac aaa fggggggggggbbbbeggggggggg aaa faac fgggggggggaaabbbdgggggggg caaf aaa fgggggggggaaaebbbdggggggg aaa aaa fggggggggeaaeggbbbbgggggg aaa faaf fggggggggaaaggggbbbbggggg faac aaa fggggggggaaagggggbbbbgggg aaa aaa fgggggggeaagggggggbbbbggg caaf caa fgggggggaaaggggggggbbbbgg aaa aaa fgggggggaaagggggggggdbbbd aaa faac fggggggcaagggggggggggdbbbe faac aaa fggggggaaaggggggggggggebbbd aaa aaa fggggggaaeggggggggggggggbbbd caacaaf fgggggaaaggggggggggggggggbbbb aaaaa fgggggaaagggggggggggggggg bbbb aaaaa ffffcaaffffffffffffffff bbbb faaaf fbe aaa bbbbf aaa dbbbf aaa dbbbf faf bbbbe caaf ebbbe fbbbb aaa ebbbd dbbbd aac fbbbd bbbbe caa fbbbb fbbbb aaa bbbb dbbbb faac bbbb bbbbe aaa bbbbf fbbbbf aaa dbbbf dbbbb caaf ebbbe bbbbe aaa ebbbe fbbbbf aac fbbbd dbbbb caa fbbbb bbbbe aaa bbbbbbbbbbbf aac bbbbbbbbb caa dddddde aaa faac aaa aaa caaf aaa aac caa aaa faac aaa aaa faaf aaa aaa caaf aaa aac caa aaa faac aaa caa ``` <!-- end of image --> Let's put area A under the microscope. <!-- image --> ```palette Key,Color ,#fefefeff a,#c11adbff b,#a72f34ff c,#e5a0efff d,#b95365ff e,#d59da1ff f,#efd6e4ff g,#d25be4ff ``` ```image cggggccf f caaaaaaaaaaggccf bf aaaaaaaaaaaaaaaaa bbf faaaaaaaaaaaaaaaaa bbbe gaaaaaaaaaaaaaaaaa bbbbe aaaaagggaaaaaaaaaa bbbbbe caaaaaf fccggaaa bbbbbbd gaaaaa f dbbbbbbd aaaaac dbbbbbbdf caaaaaf dbbbbbbbf gaaaag ebbbbbbbf faaaaac ebbbbbbbe caaaaa ebbbbbbbe aaaaag fbbbbbbbe faaaaac fbbbbbbbd gaaaaa fdbbbbbbd aaaaag fdbbbbbbdf caaaaaf dbbbbbbbf gaaaag ebbbbbbbf aaaaac ebbbbbbbecaaaaa ebbbbbbbdaaaag fbbbbbbbdaaac fbbbbbbbdaa fdbbbbbbbg fdbbbbbbdf dbbbbbbbf adbbbbbbbf caadbbbbbbbe gaaadbbbbbbbe faaaaaebbbbbbbe caaaaa fbbbbbbbd aaaaag fdbbbbbbd faaaaac fdbbbbbbdf gaaaaa dbbbbbbdf aaaaag dbbbbbbbf caaaaaf ebbbbbbbe gaaaaa ebbbbbbbe aaaaac ebbbbbbbe caaaaaf fbbbbbbbd gaaaag fbbbbbbbd faaaaac fdbbbbbbdf caaaaa dbbbbbbd aaaaag dbbbbbb faaaaac ebbbbb gaaaaa ebbbb aaaaag ebbb caaaaaf fbb gaaaag fb aaaaac f caaaaa gaaaag faaaaac ``` <!-- end of image --> Bingo! This close-up reveals 1 intersection in area A! Answer: A: 1; 1 = 1 My investigation reveals that there is exactly one intersection in this image.

<!-- image --> ```palette Key,Color ,#fefefeff a,#c119daff b,#a72f34ff c,#e08decff d,#c06b6fff e,#dbaaacff f,#f0d3edff g,#cd49e2ff ``` ```image f caa aaa faac gaa aaa caaf d aaa dbb aag bbbb caa dbbbf aaa dbbbe faac ebbbe gaa fbbbd aaa bbbb caaaagcc faaf bbbb aaaaaaaaaaaaagcf aaa bbbb aaggaaaaaaaaaaaaaaaagcf aag bbbb gaa fcgaaaaaaaaaaaaaaaagcf caa dbbbf aaa fcgaaaaaaaaaaaaaaa aaa dbbbe faac fcgaaaaaaaa aac ebbbe gaa faaa gaa fbbbd aaa aac aaa fbbbd caaf aaa faaf bbbb aaa caaf aaa bbbbaag aaa aag bbbba gaa caa dbbbf aac aaa bbbbf aaa aac gaabbbe caaf gaa aaafbbbd aaa aaa faaf fbbbd gaa faaf aaa bbbb aac aaa aag bbbb aaa aag caaf bbbb caaf caa aaa dbbbf aaa aaa aag dbbbf gaa aac caa ebbbe aac gaa aaa fbbbd aaa aaa aac fbbbd caacaaf gaa bbbb aaaaa aaa bbbb gaaag faaf bbbb aaa fbe aaa bbbb aaa dbbbf aag dbbbf faf bbbbe caa ebbbe fbbbb aaa ebbbd dbbbd aac fbbbd bbbbe gaa bbbb fbbbb aaa bbbb dbbbd faac bbbb bbbbe gaa bbbb fbbbb aaa dbbbf dbbbb caaf ebbbe bbbbe aaa ebbbe fbbbb aag fbbbd dbbbb caa bbbb bbbbe aaa bbbbbbbbbbb aac bbbbbbbbb gaa dddddde aaa faaf aaa aag caaf aaa aag caa aaa aac gaa aaa faaf aaa aag caa aaa aac gaa aaa faac gaa caa ``` <!-- end of image -->

I'm examining this image closely. My goal: find any and all intersections. There are 1 areas where the lines seem to converge. We should take a closer look at area A. <!-- image --> ```palette Key,Color ,#fefefeff a,#87636eff b,#714fceff c,#591d32ff d,#a996bcff e,#ded6edff f,#b1d6b1ff g,#95c896ff ``` ```image be bdd beeb be b be b be b be b be b be b be be be dd be ed be eb be b be b be b be b be b be be be de be dd be eb be eb be b be b be b be b be be be be be be be be be ac be ccd be ca c be c cd be cd c be c ecffffcaffffffffffffffffgbe acc cgfffffcffffffffffffffffbe c ca dcgfffffcaffffffffffffffbg aa ca c gffffffcfffffffffffffbfg c cd aa gffffffcaffffffffffdbffg aa cf c gfffffffcfffffffffdbfffg c ce cd gfffffffcafffffffbbffffg dc ece ec gffffffffcffffffbbfffffg c ec ce gffffffffcaffffbbffffffg fc fc dc gfffffffffcfffbbfffffffg ce dc c gfffffffffcafbdffffffffg ec ac ac gffffffffffcbdfffffffffg ce ac c gffffffffffbaffffffffffg ec cc ca gfffffffffbfcffffffffffg cf ca c gfffffffdbffcafffffffffg c ca cd gffffffdbffffcfffffffffg cd cd ec gfffffdbfffffcaffffffffg c cf ce gffffbbfffffffcffffffffg aa ce dc gfffbbffffffffcafffffffg c ce c gffbbffffffffffcfffffffg aa ec gfbbfffffffffffcaffffffg c ec gbdfffffffffffffcffffffg aa dc bdffffffffffffffcafffffg c ac bgffffffffffffffffcfffffg dc ac ebegffffffffffffffffcaffffg c ac eb c dc ca db aa ce ca db c ec cd bb aa ce c bb c ec bb aa cf bd c c bd aa cd c c aa ad c c aca c ``` <!-- end of image --> Could this be where the intersection is hiding, in area A? <!-- image --> ```palette Key,Color ,#fefefeff a,#723e52ff b,#7250cfff c,#56172dff d,#c4b2d1ff e,#e7e1f1ff f,#9880dcff g,#9f7c8aff ``` ```image gca dcc ccd acg cg dcc ce acg f g dcce fb acg ebbb dcce ebbbe acg ebbbe dcce ebbfe acg dbbf dcce dbbf acg dbbf dcce fbbd acg fbbd dcce fbbd acg efbbe dcce ebbbe acg ebbbe dcce ebbbe acg ebbf dcce dbbf acg dbbf dccefbbf acbbbd dbbbd fbbg efbbace ebbbeacg ebbbe dcce ebbfe acg dbbf dcce dbbf acg dbbf dcce fbbd acg fbbd dcce fbbd acg fbbe dcce ebbbe acg ebbbe dcce ebbbe acg ebbf dcce dbbf acg dbbf dcce dbbf acg fbbd dcce fbbd acg bbd dcce be acg e dcce ``` <!-- end of image --> The evidence is clear: there's 1 intersection in area A. Answer: A: 1; 1 = 1 I have found one intersection!

<!-- image --> ```palette Key,Color ,#fefefeff a,#754154ff b,#704dcfff c,#56162dff d,#bba2abff e,#ded5edff f,#a08adfff g,#977180ff ``` ```image be bff beeb be b be b be b be b be b be b be be be ff be ef be eb be b be b be b be b be b be be be fe be ff be ef be eb be b be b be b be b be be be be be be be be be gc be cad be ag c be c ad be cd c be a ec ad be aca ce c be c ca dc ad ebe gg cg c c ebe c cd aa ag eb ga cd c c fb c ce cd ag fb da ec ec c fb c ec ce ag bb dc dc dc c bf ce dc c ag bf ec gc ga cbf ce ac c bg ec aa ag ebec cd ca c eb ag c cg cd eb c ad cd ec fb ag c cd ce fb c ag ce dc bb ag c ce c bb c gg ec bf ag c ec bf c ga dc be ag c gc be c da gc ebe ag c aa eb c dc ca fb ag ce cg fb c ec cg fb ag ce c bb c ec bf ag cd bf c c bf ag cd c c gg ag c c gcg c ``` <!-- end of image -->

This is the image I'm working with. The goal is to count the intersections. These spots mark what I'd call 'danger zones' - areas where intersections are more likely. <!-- image --> ```palette Key,Color ,#fefefeff a,#476879ff b,#7b9a05ff c,#819ba2ff d,#b2d7b2ff e,#042952ff f,#96b347ff g,#99c894ff ``` ```image c ee eee e ee e ee de ea ce ea ce ea ae ec ea dec ec ded ec ded ed ced e ce e ae e ae e ae dc de ee eed de ee eae ce ee e ae ae ee ce ee aa ee ea ea ea ee ed ed ec ea e ce ed ea gggggggggggggaeggggggeegggggggggggggggggggggecd ea dddddddddddddeadddddddeeddddddddddddddddddddedg ec dddddddddddddegddddddddeadddddddddddddddddddedg dec dddddddddddddeddddddddddecddddddddddddddddddedg dec ddddddddddddaeddddddddddcegddddddddddddddddgedg ded ddddddddddddeadddddddddddaeddddddddddddddddcedg ced ddddddddddddegddddddddddddeedddddddddddddddcedg ce dddfddddddddeddddddddddddddeeddddddddddddddaedg ae dddbbfdddddaedddddddddddddddeadddddddddddddaedg ae ddddgbbfdddeadddddddddddddddcegddddddddddddeadg ae ddddddgbbfdegddddddddddddddddaeddddddddddddeadg ee ddddddddgbbaddddddddddddddddddeedddddddddddecdg ee ddddddddddabbfdddddddddddddddddeeddddddddddecdg ee ddddddddddeafbbfddddddddddddddddeadddddddddeddg ee ddddddddddegddfbbgddddddddddddddgecddddddddeddg e ddddddddddedddddfbbgdddddddddddddaeddddddddeddg dddddddddaedddddddfbbgddddddddddddeedddddddeddg dddddddddeadddddddddfbbgdddddddddddeedddddgeddg dddddddddeddddddddddddfbbgddddddddddeaddddceddg ddddddddgeddddddddddddddfbbgddddddddgecdddaeddg ddddddddaeddddddddddddddddfbbgdddddddcegddaeddg ddddddddeaddddddddddddddddddfbbdddddddaegdeaddg ddddddddedddddddddddddddddddddbbbddddddaeaeaddg dddddddgedddddddddddddddddddddddbbbdddddceeaddg gggggggaegggggggggggggggggggggggggbbbgggggecggd ec bbb e bbb e bbf ae bbf ec bbf e bbf e bbf ae bbf ec dbbf e dbbg de dbbg ae dbbg ec dbbd e dbd de gb ae fb ec bb a bb bd bf gb bf bd bd fb db bd gb fb fb b bb fb bb b bf bb bg b bbf db ``` <!-- end of image --> This is a magnified view of the region A. <!-- image --> ```palette Key,Color ,#fefefeff a,#314f6fff b,#7d9b08ff c,#a7b3c2ff d,#dce2d5ff e,#022751ff f,#aec166ff g,#6b8097ff ``` ```image geed aeeg ceed aee daeec gee eeg deeed gee ceec ceea gee geed geea aea aee aeeg aea eeg aeec eeg ceec deeed eeg geed ceeed deeg aea geea deec eeg geeg ceec ceec aeec ceec geed deeec ceed aea ceeed geed fd eeg ceea gee dbbfd ceec geeg gee fbbbbfd geed aeeg aea dfbbbbfd aea deeec aea dfbbbbf eeg deeed aea dbbbbbf ceec ceea eeg dbbbbbf geed geea eeg dbbbbbfaea aeeg deec dbbbbbag aeec deec dbbbbbf deeed ceec gbbbbbf ceead ceed aeabbbbbf geea ceed eeg fbbbbbf aeeg gee ceec fbbbbbd aeec gee geed fbbbbbd deeec gea aea fbbbbbd ceeed aea eeg fbbbbbd geea aea ceec fbbbbbd geeg eeg geed fbbbbfd aeeg eeg aea dfbbbbfd deeec deeg deeg dfbbbbfd deeed deec ceec dfbbbbfd ceea ceec gee dfbbbbfd geea ceec aea dfbbbbfd aeeg ceed deeg dfbbbbfd daeec geed ceec dfbbbbfd deeed gee gee dfbbbbfd ceead gee aea dfbbbbfd geea aea deeg dfbbbbfd aeead aea ceec dfbbbbf aeeec eeg gee dbbbbbf geeeg eeg aea dbbbbbf ceeeaeeg deeg dbbbbbf ceeeeec ceec dbbbbbf daeeec ``` <!-- end of image --> Gotcha! I've found 1 intersection hiding in area A! Answer: A: 1; 1 = 1 My investigation reveals that there is exactly one intersection in this image.

<!-- image --> ```palette Key,Color ,#fefefeff a,#2b4a6aff b,#7d9b08ff c,#90a0b2ff d,#d5dccfff e,#022751ff f,#afc167ff g,#5c748dff ``` ```image c ee eee e ea e ea de ea ce eg ge eg ga dec ag dec eg dec ec ced ed ced e ged e ge e ae e ae dc de ae eed ce ee ege ce ee e ae ge ee ce ee aa ee eg eg eg ea ed ded ec ea e ce ed ea ce ae ed eg eg ee e deg ed ea e dec e ec e dec ce ced e ced eg ge de ced ed ee ce ced f e ea ge ge bbf ce ec ga ge dbbf eg ded ag ae dbbf ed ge ec ae dbba ae ec ae gbbf ea ed ee egfbbd eg e ee ed fbbd ded e e e fbbd ce e ge fbbd ae e eg fbbd ee de e fbbd eg ce e fbbd ec ce ge fbbd ce ge eg fbb ged aa e bbb geceg de bbb deec ge bbb ed eg bbb e bbb de bbb ge bbb ec bbf e dbbf de dbbf ge dbbf ec dbbf e dbbf de dbbf ge dbbf ec dbbd e fbd de fb ge fb ec bb g bb bd bb fb bf bd dbd fb dbd bd fb fb bb bd bb bb bb b bf bb bf b dbbb db ``` <!-- end of image -->

I'm on the case! Let's uncover any intersections hidden in this image. I wonder what's going on inside those areas? Perhaps intersections are hiding there. <!-- image --> ```palette Key,Color ,#fefefeff a,#edf5eeff b,#20b87eff c,#c2d1bbff d,#92cb99ff e,#b1d7b1ff f,#d1e7daff g,#52c596ff ``` ```image g gbbf abbb bbbf gbbb bbb bbbe ebbb bbba bbbg fbbb bbbf gbbg abbb bbbe adddddddddddddddddddgbbbde aeeeeeeeeeeeeeeeeeeebbbeed aeeeeeeeeeeeeeeeeeebbbgeed aeeeeeeeeeeeeeeeeedbbbeeed aeeeeeeeeeeeeeeeeebbbeeeed aeeeeeeeecceeeeeebbbgeeeed aeeeeeeeccceeeeedbbbeeeeed aeeeeeeecccceeeebbbdeeeeed aeeeeeeecccceeegbbbeeeeeed aeeeeeecccccceebbbeeeeeeed aeeeeeecccccccbbbgeeeeeeed aeeeeeecccecccbbbeeeeeeeed aeeeeeecceeeccebeeeeeeeeed aeeeeeccceeecccgeeeeeeeeed aeeeeeccceedgccceeeeeeeeed aeeeeeccceebbccceeeeeeeeed aeeeeccceegbbbccceeeeeeeed aeeeeccceebbbecccceeeeeeed aeeeecccebbbdeeccceeeeeeed aeeeecccgbbbeeecccceeeeeed aeeecccebbbeeeeeccceeeeeed aeeecccbbbgeeeeeeccceeeeed aeeccccbbbeeeeeeeccceeeeed accccccgbbeeeeeeeeeccceeeed fcccccccdbbgeeeeeeeeecccceeed fccccccccedbbbeeeeeeeeeeeccceeed accccccccaeeebbbdeeeeeeeeeeecccceed acccccccca aeegbbbeeeeeeeeeeeeeccceed fcccccccf aeebbbeeeeeeeeeeeeeeeccced fcccccccf aebbbgeeeeeeeeeeeeeeeccced acccccccca agbbbeeeeeeeeeeeeeeeeecccd acccccccca abbbeeeeeeeeeeeeeeeeeecccc fcccccccf bbbgeeeeeeeeeeeeeeeeeeeccca fcccccccf fbbbeeeeeeeeeeeeeeeeeeeeeccc acccccccc gbbbddddddddddddddddddddddcccf acccccccca fbbbbg ccc fcccccccf gbbbbe fccc fcccccccf ebbbbb ccca acccccccc bbbbbf ccc acccccccca dbbbbg cccc fcccccccf abbbbba ccc fcccccccf gbbbbd accc cccccc fbbbbb ccca acca bbbbbf c dbbbbg abbbbba gbbbbd fbbbbb bbbbbe ebbbbg abbbbbf gbbbbg fbbbbb bbbbbe ebbbbb bbbbbf gbbbbg fbbbbba gbbbbe ebbbbb bbbbbf dbbbbg abbbbba gbbbbd fbbbbb bbbbf fbg a ``` <!-- end of image --> I wonder what we'll find inside area A? <!-- image --> ```palette Key,Color ,#fefefeff a,#eaf2ecff b,#1fb87eff c,#c3d1bbff d,#74cfabff e,#a0dec5ff f,#d3e3d5ff g,#45c393ff ``` ```image gbbbbbg dbbbbbba fbbbbbbe gbbbbbg ebbbbbbf abbbbbbd dbbbbbga ebbbbbbe agbbbbbd dbbbbbba aa fbbbbbbe cccf gbbbbbg fccccf ebbbbbbf cccccca abbbbbbd accccccf gbbbbbg fccccccca ebbbbbbf ccccccccc abbbbbbd ccccccccca dbbbbbba acccccccccc fbbbbbbe fccccccccccf gbbbbbg cccccccccccca dbbbbbba acccccffcccccffbbbbbbe fcccccaaccccccdbbbbbg fccccc fcccccebbbbbf cccccf ccccccdbbbd acccccf fccccccbbga fccccca ccccccdbe cccccc fccccccd acccccf decccccf accccca fbgcccccca fccccc gbbdcccccc cccccc ebbbbcccccca acccccf abbbbbdcccccc fccccca gbbbbbgccccccf cccccc ebbbbbbfacccccc cccccf abbbbbbd ccccccf accccca dbbbbbba acccccca fccccca fbbbbbbe fcccccf cccccc gbbbbbg acccccca acccccf dbbbbbba fcccccc fcccccafbbbbbbe ccccccf fccccc gbbbbbg acccccc cccccfebbbbbbf ccccccf acccccfbbbbbbd acccccca fcccccdbbbbbga fcccccf afcccccccbbbbbbe acccccca afcccccccccdbbbbbd fcccccc cccccccccccgbbbbba cccccca ccccccccccebbbbbe fcccccc cccccccccdbbbbbg ccccccf ccccccfaebbbbbbf acccccca cccfa abbbbbbd fcccccf fa gbbbbbg acccccca ebbbbbbf fcccccc abbbbbbd cccccca dbbbbbba fcccccc fbbbbbbe ccccccf gbbbbbg acccccca dbbbbbba fcccccc fbbbbbbe accccccf gbbbbbg fcccccc ebbbbbbf ccccccf abbbbbbd acccccc dbbbbbga fccccc bbbbbbe ccccc bbbbbd acccc bbbbba fccc bbbbe accc ``` <!-- end of image --> I observe 1 intersection inside area A. Answer: A: 1; 1 = 1 The final count is: one intersection.

<!-- image --> ```palette Key,Color ,#fefefeff a,#e9f3ecff b,#1fb87eff c,#c3d1bbff d,#72d1acff e,#a2e1c9ff f,#d4e5d7ff g,#45c393ff ``` ```image g gbbf abbb bbbf dbbb bbb bbbe ebbb bbba gbbd fbbb bbbf gbbg abbb bbbe dbbb bbb bbbd ebbb bbba cf gbbg ccca abbb cccc bbbf cccca dbbb fccccc bbb cccfccfbbbe ccc cccbbb accf fcccba ccc cccd ccc fgccc ccc bbccca fcca gbbgccc ccc abbb cccf ccc bbbe ccc accfdbbb fccc ccc bbb ccc cccbbbd accc accccbbb ccca ccccccgbba ccc fcccccccdbbg cccf fcccccccf abbb ccc acccccccc bbbf fccc acccccccca dbbb ccc fcccccccf bbb accc fcccccccf bbbe cccf acccccccc ebbb ccc acccccccca bbba fccc fcccccccf gbbd ccca fcccccccf fbbb accc acccccccc dbbbf cccf acccccccca abbbbg ccc fcccccccf gbbbbe fccc fcccccccf ebbbbb ccca acccccccc bbbbbf ccc acccccccca dbbbbg fccc fccccccca abbbbba ccc fcccccccf gbbbbd accc cccccc ebbbbb ccca acca bbbbbe c dbbbbg abbbbba gbbbbd fbbbbb bbbbbe ebbbbg abbbbba dbbbbd fbbbbb gbbbbe ebbbbg bbbbbf dbbbbd abbbbba gbbbbe ebbbbb bbbbbf dbbbbg abbbbba gbbbbd ebbbbb bbbbe fbg a ``` <!-- end of image -->