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oliveirabruno01

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intersection-count-pixmap-CoT

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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,#d9f6aeff b,#2c10d5ff c,#7169d4ff d,#b1d7b2ff e,#b1ec5fff f,#a0cda0ff g,#eef4efff ``` ```image a e e e e ge aa aa eg eg e e e fffffffffffffefffff fddddddddddddeddddd fddddddddddddeddddd fdddddddddddfeddddd fdddddddddddeeddddd fdddddddddddefddddd fdddddddddddedddddd fdddddddddddedddddd fdddddddddddedddddd fdddddddddddedddddd fdddddddddddedddddd fdddddddddddedddddd fdddddddddddedddddd fddddddddddfedddddd fddddddddddeedddddd fddddddddddefdddddd fddddddddddeddddddd fddddddddddecbbdddd fdddddddddcbbfddddd fddddddfbbceddddddd fddddcbbfddeddddddd fdfbbcdddddeddddddd cbbfdddddddeddddddd gbbcdddddddddfeddddddd cbbd fdddddddddeeddddddd bbc fdddddddddefddddddd gbc fdddddddddedddddddd gfffffffffffffffffffffffg bb fdddddddddedddddddd gfdddddddddddddddddddddfg gbc fdddddddddedddddddd gfdddddddddddddddddddddfg bb fdddddddddedddddddd g gfdddddddddddddddddddddfg dbc fdddddddddedddddddd eea gfdddddddddddddddddddddfg bb fdddddddddedddddddd eea gfdddddddddddddddddddddfg dbc fdddddddddedddddddd eea gfdddddddddddddddddddddfg bb fddddddddfedddddddd eea gfdddddddddddddddddddddfg dbc fddddddddeedddddddd eea gfdddddddddddddddddddddfg bb fddddddddefdddddddd eea gfdddddddddddddddddddddfcbd fffffffffefffffffff eea gfdddddddddddddddddddddbb gggggggggeggggggggg eeagfdddddddddddddddddddcbcg e eeeddddddddddddddddddbbdfg e geeeddddddddddddddcbcddfg e gfdeeedddddddddddbbddddfg e gfdddeeedddddddcbfdddddfg e gfdddddeeeddddbbdddddddfg ge gfdddddddeeecbfddddddddfg aa gfdddddddddbbedddddddddfg aa gfdddddddcbfdeeedddddddfg eg gfddddddbbdddddeeedddddfg e gfddddcbfddddddddeeedddfg e gfddfbbddddddddddddeeedfg e gfdcbfdddddddddddddddeeeg e gfbbdddddddddddddddddddeee e cbfddddddddddddddddddddfgaee e gbcfdddddddddddddddddddddfg aee ge cbggfdddddddddddddddddddddfg aee aa gbc gfdddddddddddddddddddddfg aee aa bbg gfdddddddddddddddddddddfg aee eg gbc gfdddddddddddddddddddddfg aee e bbg gfdddddddddddddddddddddfg aee e gbc gfdddddddddddddddddddddfg aee e bb gfdddddddddddddddddddddfg aee e gbc gfdddddddddddddddddddddfg aee e bb gfdddddddddddddddddddddfg aee e dbc gfffffffffffffffffffffffg aee ge c ggggggggggggggggggggggg aee aa aeeaa aeg ``` <!-- end of image --> Eureka! Let's inspect this close up of area A <!-- image --> ```palette Key,Color ,#fefefeff a,#cbf38fff b,#290cd6ff c,#9082e8ff d,#eff6e6ff e,#aeec53ff f,#5942dfff g,#cac3f4ff ``` ```image c gfb cbbb a gfbbfd eea cbbbg aeeea gfbbfd daeeea cbbbg daeeea gfbbc daeeea cbbbg daeeead gfbbc daeeead cbbbg daeeead gfbbc daeeead cbbfg daeeead gfbbc daeeeadcbbfg daeebbbc cbbbead gbbbcaeeead cbbfg daeeead gbbbc daeeead dfbbfg daeeead gbbbc daeeead dfbbfg daeeead gbbbc daeeead dfbbfg daeeead gbbbc daeeead dfbbfg daeee cbbbc dae dfbbfd d cbbbc fbbfd bbc fd ``` <!-- end of image --> There's no doubt about it - I see 1 intersection in area A. Moving on to the next area. Let's see if area B yields any clues. <!-- image --> ```palette Key,Color ,#fefefeff a,#cbf390ff b,#290cd6ff c,#968ae6ff d,#e5f8c9ff e,#b1ee55ff f,#5f4cd9ff g,#cec8f5ff ``` ```image aed eed ee ee dee dea dea dea aea aed aed eed ee ee ee dee dea dea aea aed aed eed ee ee ee dee dea dea aea aed aed eed ee ee gcbc eegfbbbf dfbbbbfg gfbbbbc cbbbbfc gfbbbbcaea cfbbbfg aed gfbbbbcg aed cfbbbfc eed gcbbbbcg ee cfbbbfc ee gcbbbbfg ee bbbfc dee bfg dea dea aea aed aed aed eed ee ee dee dea dea aea aed aed aed eed ee ee dee dea dea aea aea aed aed ``` <!-- end of image --> I've cracked the case! This area contains 1 intersection. Answer: A: 1; B: 1; 1 + 1 = 2 The image features two intersection points.

<!-- image --> ```palette Key,Color ,#fefefeff a,#c7f287ff b,#2b0ed6ff c,#9283eaff d,#dff7baff e,#b1ee55ff f,#624ce1ff g,#cec7f5ff ``` ```image d e e e e e da ad ad e e e e e e e da ad ad e e e e e e e da dd ad e egbb fbb gbbce fbbg e gbbc e cbbg e gbbf da cbbg da fbf ad gbc e bb e gbc e bb e gbc e eed bb e eed gbc e eed bb da eed cbc da eed bb ad eed cbc e eed bb e aed cbg e aed bb e aed cbg e aed bb e aed cbg e aea bb da aeacbg da bba ad fbg aea ed bf aea e fbg aea e bf aea e fbg aea e gbf aea e fbg aea e gbf aea da fb dea da gbf dea ad fb dea ad gbf dea e fb dee e gbc dee e bb dee e gbc dee e bb dee e gbc dee e f dee da deead ded ``` <!-- end of image -->

I'm analyzing this image to identify any points where lines intersect. These zones are intriguing. I bet there's something interesting happening within them. <!-- image --> ```palette Key,Color ,#fefefeff a,#e28227ff b,#c9353aff c,#f1c5a5ff d,#f2f4ecff e,#cfa171ff f,#b1d7b1ff g,#97c995ff ``` ```image caa daa dggggggggggggggggggggggggggggggggggggad daa dffffffffffffffffffffffffffffffffffeaaa daa dfffffffffffffffffffffffffffffffffaaaa aa dfffffffffffffffffffffffffffffffeaaaeg aa dffffffffffffffffffffffffffffffaaaaffg aa dfffffffffffffffffffffffffffffaaaefffg aa dfffffffffffffffffffffffffffaaaafffffg aa dffffffffffffffffffffffffffaaaeffffffg aa dffffffffffffffffffffffffeaaaffffffffg aa dfffffffffffffffffffffffaaaafffffffffg aa dfffffffffffffffffffffeaaagffffffffffg aad dffffffffffffffffffffaaaaffffffffffffg aad dffffffffffffffffffeaaaefffffffffffffgd aad dfffffffffffffffffaaaafffffffffffeebbbe aac dffffffffffffffffaaaefffffffebbbbbbbbbb aac dffffffffffffffaaaaffffebbbbbbbbbbbefg aac dfffffffffffffaaaeebbbbbbbbbbbeffffffg dddeaeddddddddddd dfffffffffffeabbbbbbbbbbbefffffffffffg fffeaeffffffffffgd dfffffffebbbbbbbbbbbeffffffffffffffffg fffeaafffffffffffd dffebbbbbbbbbbbefffffffffffffffffffffg fffeaafffffffffffd cbbbbbbbbbbbaafffffffffffffffffffffffffg fffeaafffffffffffd cbbbbbbbbbbegeaaaeffffffffffffffffffffffffffg fffeaafffffffffffd cbbbbbbbbbbecffffaaaaffffffffffffffffffffffffffffg ffffaafffffffffffd dcbbbbbbbbbbed dffffaaefffffffffffffffffffffffffffffg ffffaafffffffffffd dcbbbbbbbbbbed dfffaaaffffffffffffffffffffffffffffffg ffffaafffffffffffdcbbbbbbbbbbed dfffaafffffffffffffffffffffffffffffffg ffffaafffffffebbbbbbbbbbed dfffaafffffffffffffffffffffffffffffffg ffffaaffffffbbbbbbbed dffaaefffffffffffffffffffffffffffffffg ffffaafffffbbbeffd dffaaffffffffffffffffffffffffffffffffg ffffaaffffbbbffffd dffaaffffffffffffffffffffffffffffffffg ffffaafffbbbfffffd dfaaeffffffffffffffffffffffffffffffffg ffffaaffbbbffffffd dfaafffffffffffffffffffffffffffffffffg ffffaafbbbfffffffd dgaafffffffffffffffffffffffffffffffffg ffffaaebbefffffffd daaefffffffffffffffffffffffffffffffffg ffffaabbeffffffffd daaffffffffffffffffffffffffffffffffffg ffffabbbfffffffffd caaffffffffffffffffffffffffffffffffffg ffffbbbffffffffffd aaeffffffffffffffffffffffffffffffffffg fffbbbeffffffffffd aafffffffffffffffffffffffffffffffffffg ffbbbaeffffffffffd daadddddddddddddddddddddddddddddddddddd fffbaaeffffffffffd aae ffffeaeffffffffffd aa ffffeaeffffffffffd caa ffffeaaffffffffffd aae ffffeaaffffffffffd aa ffffeaaffffffffffd caa ffffgaaffffffffffd aae fffffaaffffffffffd aa fffffaaffffffffffd caa fffffaaffffffffffd aac fffffaaffffffffffd aa fffffaaffffffffffd caa fffffaaffffffffffd aac fffffaaffffffffffd aa fffffaaffffffffffd caa fffffaaffffffffffd aac gggggaaggggggggggd aa aad caa aad aac aad aa aac caa aac aac aac aa eae caa eae aac cae aa caa caa caa aac caa aa daa caa daa daac aa caaaaa aa deaaaaaaed aa caaaaaaac aa caaaaaaac aa deaaaaaaed aa caaaaaaac aa deaaaaaaed aaaaaaaac aaaaad dc ``` <!-- end of image --> Let's see if area A yields any clues. <!-- image --> ```palette Key,Color ,#fefefeff a,#e28126ff b,#ca3237ff c,#ecb18aff d,#f8e5dbff e,#d86a6eff f,#e9a05bff g,#f2cab1ff ``` ```image faaac faaac caaaf caaaf caaaf caaaf gaaaf gaaaa gaaaa gaaaa gaaaa daaaa daaaad daaaad daaaad aaaad aaaag aaaag dgce aaaag gcebbbbb aaaag dbbbbbbbbb faaac dbbbbbbbbbb faaac ebbbbbbbbbe faaac ebbbbbecgd faaac ebbbbbd faaaf cbbbbbd caaaf gbbbbbg caaaf gbbbbbc caaaf dbbbbbe caaaf dbbbbbe gaaaa ebbbbe gaaaa ebbbbbd gaaaa ebbbbbd gaaaacbbbbbg daaaabbbbbg daaabbbbbc daabbbbbe dabbbbbe dbbbbbe ebbbbbd ebbbbbc cbbbbbag gbbbbbaag bbbbbbaag debbbaaac eefaaac faaac faaac caaaf caaaf caaaf caaaf gaaaf gaaaa gaaaa gaaaa gaaaa daaaa daaaad daaaad daaaad aaaad aaaag aaaag aaaag aaaag faaac faaac faaac faaac faaaf caaaf caaaf caaaf caaaf gaaaa gaaaa ``` <!-- end of image --> Yes! I knew it! There's 1 intersection right here in area A! Let's move forward and inspect another region. Let's see if area B yields any clues. <!-- image --> ```palette Key,Color ,#fefefeff a,#e28126ff b,#ca3237ff c,#eaa992ff d,#f9e9e0ff e,#d96b6dff f,#e99f5aff g,#f1cab8ff ``` ```image c dfa caaa dfaaaa gaaaaaa dfaaaaaaf gaaaaaaag faaaaaafd gaaaaaaag caaaaaafd dfaaaaaac caaaaaafd dfaaaaaac gaaaaaaag dfaaaaaafd gaaaaaaag faaaaaafd gaaaaaaag caaaaaafd dfaaaaaac caaaaaafd dfaaaaaac gaaaaaaag dfaaaaaafd gaaaaaaag faaaaaafd gce gaaaaaaag gcebbbbb caaaaaafd dgcebbbbbbbbbb dfaaaaaac dgcebbbbbbbbbbbbbbb caaaaaafd dgcebbbbbbbbbbbbbbbbbbbe dfaaaaaac dgcebbbbbbbbbbbbbbbbbbbecgd gaaaaaaag dgcebbbbbbbbbbbbbbbbbbbecgd dfaaaaaafdgcebbbbbbbbbbbbbbbbbbbecgd gaaaaaabebbbbbbbbbbbbbbbbbbbecgd faabbbbbbbbbbbbbbbbbbbbbecgd dgebbbbbbbbbbbbbbbbbbbbecgd dgcebbbbbbbbbbbbbbbbbbbecgd dgcebbbbbbbbbbbbbbbbbbbecgd dgcebbbbbbbbbbbbbbbbbbbecgd dgcebbbbbbbbbbbbbbbbbbbbegd bbbbbbbbbbbbbbbbbbbaaaag bbbbbbbbbbbbeeeaaaaaafd bbbbbbbeecg gaaaaaaag bbeecg faaaaaafd g daaaaaaag faaaaafd daaaaac caaaad faaaf daaaag caaaad faaaf daaaag caaaad faaaf daaaag caaaa faaaf daaaag caaaa faaaf daaaag caaaa faaaf daaaag caaaa faaaf daaaag caaaa aaaaf daaaag caaaa aaaaf aaaag aaaa ``` <!-- end of image --> I've cracked the case! This area contains 1 intersection. Answer: A: 1; B: 1; 1 + 1 = 2 I can confirm there's two intersections in there.

<!-- image --> ```palette Key,Color ,#fefefeff a,#e38126ff b,#ca3137ff c,#ecb392ff d,#f9e7dcff e,#d86a6eff f,#eaa25eff g,#f2cdb6ff ``` ```image gaa daa ad daa caaa aa aaaa aa gaaag aa aaaa aa daaac aa faaa aa daaaf aa faaad aa aaaf aa caaad aa aaaa aad gaaag d aad aaaa gebbbe aag daaac gebbbbbbbbb aag faaa gebbbbbbbbbeg fac daaafgebbbbbbbbbeg fac fabbbbbbbbbbeg faf gebbbbbbbbbeg caf gebbbbbbbbbeg caf cebbbbbbbbbbaa gaa cebbbbbbbbbeggaaag gaa cebbbbbbbbbed aaaa daa cebbbbbbbbbed daac daa cebbbbbbbbbed faf aa dcbbbbbbbbbbcd aad aa cbbbbbbbbbbcd daa aa dbbbbbbbcd faf aa bbbcd aa aa bbb daa aa bbb faf aa bbb aa aa ebbd daa aacbbg aaf aabbc aa abbe daa bbb aaf bbbg aa bbbac daa efac aaf faf aa caf gaa caf aac gaa aa gaa gaa daa aac daa aa aa gaa aa aac aa aa aa gaa aa aac aa aa aa gaa aa aac aa aa aa gaa aad aac aad aa aag gaa aag aac fac aa fac gaa faf aac caf aa caf caa gaa aag gaa aa daa caa daa daag aa gaaaaa aa faaaaaafd aa gaaaaaaac aa caaaaaaag aa dfaaaaaac aa gaaaaaaag aa dfaaaaaafd aaaaaaaac aaaafd dc ``` <!-- end of image -->

I'm curious to see if this image contains any intersection points. There are 1 regions I'd like to highlight in the image. <!-- image --> ```palette Key,Color ,#fefefeff a,#26fae4ff b,#a77758ff c,#6ef0d8ff d,#b1d7b2ff e,#b1a182ff f,#e9f6f0ff g,#a2cfa2ff ``` ```image aa faaf aaaa aaaa caaaac aacfaa faa aac aaa caa aaf aaf caa aaa aac faa faa aac aaa caa fffffffffffffffffffffffffffffaaffffffffaaffffffffffffffffff ggggggggggggggggggggggggggggcaaggggggggaaagggggggggggggggggf gdddddddddddddddddddddddddddaacdddddddddaaddddddddddddddddgf gdddddddddddddddddddddddddddaaddddddddddaacdddddddddddddddgf fbb gddddddddddddddddddddddddddaaaddddddddddcaadddddddddddddddgf ebbbb gddddddddddddddddddddddddddaaddddddddddddaadddddddddddddddgf bbbbbbb gdddddddddddddddddddddddddcaaddddddddddddaaaddddddddddddddgfbbbe dbbe gdddddddddddddddddddddddddaacdddddddddddddaaddddddddddddddgbbbf dbbe gdddddddddddddddddddddddddaaddddddddddddddaacddddddddddddebbb ebbe gddddddddddddddddddddddddaaaddddddddddddddcaadddddddddddbbbb ebbe gddddddddddddddddddddddddaaddddddddddddddddaacdddddddddbbbef ebbd gdddddddddddddddddddddddcaaddddddddddddddddaaaddddddddbbbegf ebbd gdddddddddddddddddddddddaacdddddddddddddddddaaddddddebbbddgf bbbf gdddddddddddddddddddddddaaddddddddddddddddddaaaddddebbbdddgf bbbf gddddddddddddddddddddddaaaddddddddddddddddddcaadddbbbbddddgf bbbf gddddddddddddddddddddddaaddddddddddddddddddddaacdbbbedddddgf bbbf gdddddddddddddddddddddcaaddddddddddddddddddddcaabbbgddddddgf bbb gdddddddddddddddddddddaacdddddddddddddddddddddaabbddddddddgf bbb gdddddddddddddddddddddaadddddddddddddddddddddbaaadddddddddgf bbb gddddddddddddddddddddaaaddddddddddddddddddddbbeaadddddddddgf bbb gddddddddddddddddddddaadddddddddddddddddddgbbbgaacddddddddgf fbbb gdddddddddddddddddddcaaddddddddddddddddddebbbddcaaddddddddgf fbbb gdddddddddddddddddddaacdddddddddddddddddbbbbddddaaddddddddgf fbbb gdddddddddddddddddddaadddddddddddddddddbbbedddddaaadddddddgf fbe gddddddddddddddddddaaaddddddddddddddddbbbedddddddaadddddddgf f gddddddddddddddddddaadddddddddddddddebbbdddddddddaacddddddgf gdddddddddddddddddcaaddddddddddddddebbbddddddddddcaaddddddgf gdddddddddddddddddaacdddddddddddddbbbbddddddddddddaaddddddgf gdddddddddddddddddaadddddddddddddbbbedddddddddddddaaadddddgf gddddddddddddddddaaadddddddddddgbbbgdddddddddddddddaadddddgf gddddddddddddddddaadddddddddddebbbdddddddddddddddddaacddddgf gdddddddddddddddcaaddddddddddbbbbddddddddddddddddddcaaddddgf gdddddddddddddddaacdddddddddbbbeddddddddddddddddddddaacdddgf gdddddddddddddddaaddddddddgbbbgdddddddddddddddddddddaaadddgf a gddddddddddddddaaadddddddebbbddddddddddddddddddddddddaadddgf caa gddddddddddddddaadddddddbbbbdddddddddddddddddddddddddaaaddgf faaf gdddddddddddddcaaddddddbbbeddddddddddddddddddddddddddcaaddgf aaa gdddddddddddddaacdddddbbbeddddddddddddddddddddddddddddaacdgf aaa gdddddddddddddaaddddebbbddddddddddddddddddddddddddddddcaadgf caaf gddddddddddddaaadddebbbddddddddddddddddddddddddddddddddaadgf faac gddddddddddddaadddbbbbdddddddddddddddddddddddddddddddddaaagf aaa gdddddddddddcaaddbbbeddddddddddddddddddddddddddddddddddgaagf aaa gdddddddddddaacgbbbgddddddddddddddddddddddddddddddddddddaacf faaf gdddddddddddaaebbbddddddddddddddddddddddddddddddddddddddcaaf aac gddddddddddaaabbbddddddddddddddddddddddddddddddddddddddddaaf aaa gddddddddddaabbedddddddddddddddddddddddddddddddddddddddddaaa caaf gdddddddddcaabgdddddddddddddddddddddddddddddddddddddddddddaa faac gddbeddddeaagdddddddddddddddddddddddddddddddddddddddddddddaac aaa gdbbbeddbbaaddddddddddddddddddddddddddddddddddddddddddddddcaa aaa gddebbbbbaaaddddddddddddddddddddddddddddddddddddddddddddddgaaf faaf gdddebbbbaadddddddddddddddddddddddddddddddddddddddddddddddgaaa aac gddddebbcaadddddddddddddddddddddddddddddddddddddddddddddddgfaa aaa gdddddddaacdddddddddddddddddddddddddddddddddddddddddddddddgfaac caa gdddddddaaddddddddddddddddddddddddddddddddddddddddddddddddgfcaa faac gddddddaaaddddddddddddddddddddddddddddddddddddddddddddddddgf aaf aaa gddddddaadddddddddddddddddddddddddddddddddddddddddddddddddgf caa aaa gdddddcaadddddddddddddddddddddddddddddddddddddddddddddddddgf aa faaf gdddddaacdddddddddddddddddddddddddddddddddddddddddddddddddgf aacaac gdddddaaddddddddddddddddddddddddddddddddddddddddddddddddddgf faaaa gddddaaaddddddddddddddddddddddddddddddddddddddddddddddddddgf aaa gddddaadddddddddddddddddddddddddddddddddddddddddddddddddddgf cac gdddcaadddddddddddddddddddddddddddddddddddddddddddddddddddgf gdddaacdddddddddddddddddddddddddddddddddddddddddddddddddddgf gdddaaddddddddddddddddddddddddddddddddddddddddddddddddddddgf gddaaaddddddddddddddddddddddddddddddddddddddddddddddddddddgf gggaagggggggggggggggggggggggggggggggggggggggggggggggggggggg caa cc ``` <!-- end of image --> Let's see if area A yields any clues. <!-- image --> ```palette Key,Color ,#fefefeff a,#25fae5ff b,#a77758ff c,#8afcf0ff d,#e2d3c9ff e,#bd9f89ff f,#c2fdf7ff g,#5af6e4ff ``` ```image gaaa gaaaaf faaaa faaaac caaaa aaaaa faaaac aaaa gaaaa gaaaf faaaag faaac caaaaf aaaa aaaaa caaaf aaaac aaag aaaa gaaaf caaaf gaaa aaaa caaac faaac aaag d gaaa aaaaf db faaag aaaag dbb caaaf gaaaa bbb faaac aaaaa dbbbbb gaaa caaaa dbbbbbe faaaa faaaa ebbbbbe caaaa gaaa ebbbbbd aaaaa faaac bbbbbbb faaaac aaaa dbbbbbe gaaaa caaaf ebbbbbe aaaaf gaaaf dbbbbbbd aaaa faaac dbbbbbe faaac aaaa bbbbbb gaaa caaaf ebbbbbd faaag aaag ebbbbbd caaaf aaaaebbbbbd aaaa aaaagbbbe gaaa gaaaaeb faaag dbaaaaad caaaf dbbgaaaaf aaaa ebbbbaaaag faaaa ebbbbbgaaaa gaaaa dbbbbbbdcaaaa caaaaf dbbbbbe caaaf aaaaa ebbbbbd faaag faaaac ebbbbbd gaaa gaaaa dbbbbbbd faaac aaaag dbbbbbe aaaa aaaaf bbbbbb caaaf aaaa ebbbbbd faaag gaaa dbbbbbe faaac faaag ebbbbbe aaaa caaaf ebbbbbd aaaaf aaaa bbbbbbb aaaag faaac dbbbbbe gaaaaf gaaa dbbbbbe faaaac caaaf ebbbbbd caaaa aaaa dbbbbbbd aaaa faaaa bbbbbb gaaaf gaaaa ebbbbbe faaag faaaag ebbbbbd gaaa caaaaf dbbbbbbd caaac aaaaa dbbbbbe aaaa aaaa ebbbbbb faaag faaag bbbbbbd gaaa caaaf dbbbbbe faaac aaaa dbbbbbe aaaa faaac ebbbbbd aaaaf gaaa ebbbbbd aaaag faaag bbbbbbd gaaaaf aaaa ebbbbbe aaaaa faaac ebbbbbd caaaaf gaaa dbbbbbbd aaaag faaaa dbbbbbe gaaaa caaaa ebbbbbb faaaa aaaaa bbbbbbd aaaa gaaaa dbbbbbe aaag aaaag dbbbbbe gaaaf aaaaf ebbbbbd faaag aaaa ebbbbbd gaaa faaac dbbbbbb caaac gaaa dbbbbbe aaaa faaagebbbbbe caaa aaaabbbbbd aaa faaagbbbb aaa gaaabbbbe aaa faaagbbbd caa caaaebbd faa ee daaaabe ga ebbbb ebgaaaa a ebbbbe bbaaaag c ebbbbe dbbgaaaaf ebbbbedbbbaaaaa ebbbbbbbeaaaac ebbbbbbgaaaa bbbbbbaaaag dbbe aaaa faaac gaaa faaag caaaf aaaa faaac faaag caaaf aaaa faaaa gaaaa faaaag aaaaa aaaac aaaaf faaag caaaf aaaa faaac faaag caaaf aaaa ``` <!-- end of image --> Area A contains 2 intersections. Answer: A: 2; 2 = 2 After a long analysis, I found two intersections.

<!-- image --> ```palette Key,Color ,#fefefeff a,#25fae5ff b,#a77758ff c,#89fcf0ff d,#e2d2c8ff e,#c09e88ff f,#d5fdf9ff g,#46f9e6ff ``` ```image aa faaf aaaa aaaa caaaag aacfaa faa aac aag caa aaf aa caa aag aac faa faa aac aag caa aaf aaf caa aaa aac faa faa aac dbb aag caa ebbbb aaf aaf bbbbbbb caa gaa bbbe dbbe aac aa dbbbd dbbe faa aac dbbb ebbe aag caa ebbb ebbe aaf aaf bbbe ebbd caa gaa bbbd ebbd aac aa dbbb bbbd faa aag ebbb bbbd aag faa bbbe bbb aaf aac bbbd bbb caa caabbbd bbb aac aabb bbb faa baag bbb aag bbbaa bbb aaf bbbdaac bbb caa dbbb caa bbb aac ebbb aaf dbbb faa bbbe aag dbe aag bbbd faa d aaf dbbb aac caa ebbb caa aac bbbe aaf faa bbbd gaa aag dbbbd aa aaf ebbb aac caa bbbb caa aac bbbe aaf faa bbbd gaa a aag dbbb aa gaa aaf ebbb aag faaf caa bbbe faa aag aac bbbd aac aaa faa dbbb gaa caaf aag ebbb aa aac aaf bbbe aag aaa caa bbbd faa gaa aacdbbbd aac faaf faaebbb caa aag aaabbb aaf aaa aabbe aag caa caabd faa faac be daag aac aaa ebbe ebaa caa gaa ebbebbaag aaf faaf ebbbbaaf gaa aag ebbcaa aa aaa aac aac caa faa caa faac aag aaf aaa aaf gaa gaa caa aa caaf aac aagaag faa faaaa aag aaa aaf cac caa aac faa aag aaf caa gc ``` <!-- end of image -->

I'm analyzing this image to identify any points where lines intersect. Let's take a closer look at what's happening inside these zones. <!-- image --> ```palette Key,Color ,#fefefeff a,#8ff847ff b,#895d02ff c,#9bc693ff d,#b1d7b1ff e,#a19650ff f,#a3eb7aff g,#edf4e5ff ``` ```image ag aaag aaaa aaaa gaaaa gg gaaaa ebbg daaaf gbbbe faaaf bbbbb aaaad bbbbbb aaaag bbbbbbb aaaag cbbbcbbbg aaaa gbbbb bbbd aaaa bbbb ebbe gaaaa bbbb dbbb gaaaa ebbbd bbb daaaf dbbbe bbb faaaf bbbb bbbg aaaad bbbb bbbc aaaag bbbbg ebbe aaaag cbbbc gbbb aaaa gbbbb bbb aaaa bbbb bbb gaaaa bbbb bbbg gaaaa dcccccccccccccccccccccccccccbbbbcccccccccccccbbbeccccccccc daaaf cddddddddddddddddddddddddddcbbbedddddddddddddebbbddddddddd faaaf cddddddddddddddddddddddddddbbbbddddddddddddddcbbbddddddddd aaaad cdddddddddddddddddddddddddbbbbddddddddddddddddbbbdddfcdddd aaaagcddddddddddddddddddddddddbbbbdddddddddddddddddbbbdddaaaddd aaaacdddddddddddddddddddddddebbbedddddddddddddddddbbbcddaaaddd aaaaddddddddddddddddddddddcbbbbddddddddddddddddddbbbeddaaaddd aaaadddddddddddddddddddddbbbbdddddddddddddddddddebbbdfaaaddd gaaaadddddddddddddddddddbbbbddddddddddddddddddddcbbbdfaafddd gaaaadddddddddddddddddbbbbcdddddddddddddddddddddbbbdaaafddd faaaadddddddddddddddebbbeddddddddddddddddddddddbbbdaaadddd caaaafddddddddddddddbbbbdddddddddddddddddddddddbbbcaaadddd cdaaaafddddddddddddbbbbddddddddddddddddddddddddebbeaaadddd cddaaaadddddddddddbbbbdddddddddddddddddddddddddebbbaaadddd cdddaaaadddddddddbbbbcddddddddddddddddddddddddddbbbaafdddd cddddaaaadddddddbbbbedddddddddddddddddddddddddddbbbaacdddd cdddddaaaaddddebbbbbddddddddddddddddddddddddddddbbbaaddddd cddddddaaaaddbbbbbedddddddddddddddddddddddddddddbbbeaddddd cddddddfaaaabbbbbdddddddddddddddddddddddddddddddebbbaddddd cdddddddfaebbbbbddddddddddddddddddddddddddddddddcbbbaddddd cddddddddbbbbbeddddddddddddddddddddddddddddddddddbbbfddddd cdddddddbbbbbafddddddddddddddddddddddddddddddddddbbbdddddd cdddddebbbbbaaaddddddddddddddddddddddddddddddddddbbbdddddd cddddbbbbbedaaaadddddddddddddddddddddddddddddddddbbbeddddd cdddbbbbbddddaaaadddddddddddddddddddddddddddddddfebbbddddd cdebbbbbddddddaaaaddddddddddddddddddddddddddddddfabbbddddd cbbbbbeddddddddaaaadddddddddddddddddddddddddddddaabbbddddd bbbbbddddddddddfaaaaddddddddddddddddddddddddddddaabbbddddd dbbbbbddddddddddddfaaaadddddddddddddddddddddddddddaabbbcdddd ebbbbeddddddddddddddaaaafddddddddddddddddddddddddddaabbbedddd bbbbbdddddddddddddddddaaaafddddddddddddddddddddddddfaaebbbdddd dbbbbbcddddddddddddddddddaaaaddddddddddddddddddddddddaaafbbbdddd ebbbbc cdddddddddddddddddddaaaadddddddddddddddddddddddaaadbbbdddd bbbbbg cddddddddddddddddddddaaaaddddddddddddddddddddddaaadbbbdddd dbbbbb cdddddddddddddddddddddaaaadddddddddddddddddddddaaadbbbcddd ebbbbc cddddddddddddddddddddddaaaaddddddddddddddddddddaaadbbbeddd bbbbbg cddddddddddddddddddddddfaaaaddddddddddddddddddfaaadebbbddd dbbbbb cdddddddddddddddddddddddfaaaadddddddddddddddddaaafdcbbbddd ebbbbe cddddddddddddddddddddddddaaaafddddddddddddddddaaadddbbbddd bbbbbg cdddddddddddddddddddddddddaaaafdddddddddddddddaaadddbbbddd dbbbbb cddddddddddddddddddddddddddaaaadddddddddddddddaaadddbbbcdd ebbbbe cdddddddddddddddddddddddddddaaaadddddddddddddfaaaddddddddd bbbbbg cddddddddddddddddddddddddddddaaaaddddddddddddfaafddddddddd dbbbbb cdddddddddddddddddddddddddddddaaaadddddddddddaaafddddddddd ebbbbe cddddddddddddddddddddddddddddddaaaaddddddddddaaadddddddddd bbbbbg cddddddddddddddddddddddddddddddfaaaadddddddddaaadddddddddd gbbbbb cdddddddddddddddddddddddddddddddfaaaaddddddddaaadddddddddd ebbbbe cddddddddddddddddddddddddddddddddaaaafddddddfaaadddddddddd gbbbbg cdddddddddddddddddddddddddddddddddaaaafdddddaaafdddddddddd cbb ggggggggggggggggggggggggggggggggggaaaagggggaaaggggggggggg e aaaa aaa aaaa aaa gaaaa gaaa gaaaafaaf daaaaaad faaaaa faaaa aaaa aad ``` <!-- end of image --> This close-up of area A is like examining a piece of evidence. <!-- image --> ```palette Key,Color ,#fefefeff a,#8ff847ff b,#895c00ff c,#cebb96ff d,#e2f2ccff e,#968024ff f,#b7fa88ff g,#b09456ff ``` ```image ebbbbbbe bbbbbbc ebbbbbbbd ebbbbbc bbbbbbbc gbbbbbg cbbbbbbg cbbbbbe dbbbbbbe cbbbbbb gbbbbbbc bbbbbb cbbbbbbc ebbbbb fdd dbbbbbbg gbbbbb aaaafd dbbbbbbe cbbbbb daaaaad d ebbbbbbd cbbbbb daaaaa a gbbbbbbc dbbbbbd faaaaf af cbbbbbbb bbbbbc faaaaf aaf dbbbbbbbe ebbbbg aaaaaf aaaf ebbbbbbbd gbbbbg aaaaad aaaaf bbbbbbbd cbbbbb daaaaa aaaaad cbbbbbbg dbbbbbd faaaaf aaaaaad dbbbbbbe bbbbbc aaaaaf aaaaaaad ebbbbbbd ebbbbg aaaaad daaaaaaa gbbbbbbc gbbbbe daaaaad faaaaaaf cbbbbbbg cbbbbb daaaaa faaaaaaf dbbbbbbe dbbbbbdfaaaaa faaaaaaf ebbbbbed bbbbbcfaaaaa aaaaaaaf gbbbbbbd ebbbbcaaaaaa aaaaaaad cbbbbbbb gbbbbgaaaaaa aaaaaaaad cbbbbbbbg gbbbbeaaaaaa daaaaaaad bbbbbbbd dbbbbbaaaaaf faaaaaaa debbbbbbc bbbbbaaaaaf faaaaaaf cbbbbbbbc ebbbbeaaaad faaaaaaf gbbbbbbbg gbbbbeaaaad faaaaaaf debbbbbbbe cbbbbbaaaa aaaaaaaf cbbbbbbbbed cbbbbbaaaa aaaaaaad gbbbbbbbbg dbbbbbaaaf daaaaaaad debbbbbbbbc bbbbbaaaf daaaaaaad bbbbbbbbbe ebbbbeaad aaaaaaaagbbbbbbbbg gbbbbeaad faaaebbbbbbbbed cbbbbbaa faebbbbbbbbg dbbbbbaf debbbbbbbbc bbbbbef cbbbbbbbbbf bbbbbed gbbbbbbbbeaad bbbbbe dbbbbbbbbbaaaad bbbbbb cbbbbbbbbbaaaaaad bbbbbb gbbbbbbbbgdaaaaaaa bbbbbbd debbbbbbbbc faaaaaaa bbbbbbc gbbbbbbbbg faaaaaaaf debbbbbe debbbbbbbbc faaaaaaaf febbbbbb bbbbbbbbbd aaaaaaaa fabbbbbbd gbbbbbbbbg aaaaaaad aabbbbbbd debbbbbbbbc daaaaaaad aabbbbbbc cbbbbbbbbed daaaaaaad daaebbbbbg gbbbbbbbbg daaaaaaa daaebbbbbe bbbbbbbbc faaaaaaa faaebbbbbb bbbbbbed faaaaaaf faaabbbbbbd bbbbbg faaaaaaf aaaabbbbbbc bbbed aaaaaaaf daaaaebbbbbg bbg aaaaaaaad faaaaebbbbbe bc daaaaaaaa faaaagbbbbbb d daaaaaaad faaaafbbbbbb daaaaaaa aaaaadbbbbbb faaaaaaa daaaaadebbbbb faaaaaaf daaaaa gbbbbb faaaaaaf faaaaa cbbbbb faaaaaaf faaaaf cbbbbb aaaaaaaf aaaaaf dbbbbbd daaaaaaad daaaaad ebbbbg aaaaaaaad daaaaa gbbbbg daaaaaaaa faaaaf cbbbbe faaaaaaa faaaaf cbbbbb faaaaaaf aaaaad dbbbbbd faaaaaaf aaaaad bbbbbc faaaaaaf daaaaa ebbbbg aaaaaaaf faaaaa gbbbbg daaaaaaad faaaaa cbbbbb daaaaaaad aaaaaa dbbbbb daaaaaaa daaaaaa eggd aaaaaaaa daaaaaa faaaaaaaf faaaaaa faaaaaaaf faaaaaf faaaaaaa aaaaaaf aaaaaaaf aaaaaad daaaaaaad daaaaaa daaaaaaad daaaaaa daaaaaaad faaaaaf daaaaaaa faaaaaf faaaaaaf daaaaaad faaaaaaf daaaaaa aaaaaaaf faaaaaa aaaaaaaad faaaaaf daaaaaaaa aaaaaaf ``` <!-- end of image --> Aha! I've found 2 intersections inside area A! Answer: A: 2; 2 = 2 After a thorough search, I conclude that there are two intersections.

<!-- image --> ```palette Key,Color ,#fefefeff a,#8ff846ff b,#895c00ff c,#c3ad80ff d,#d6ebb5ff e,#9f8132ff f,#b1f97eff g,#ecf4ddff ``` ```image ag aaag aaaa aaaa gaaaa gg daaaa cbbg daaaf dbbbe faaaf bbbbb aaaad bbbbbb aaaag ebbbbbb aaaag cbbbcbbb aaaa gbbbe bbbc aaaa bbbb cbbe gaaaa bbbb dbbb daaaa ebbbd bbb daaaf dbbbe bbb faaaf bbbb bbbg aaaad bbbb bbbc aaaag ebbbg cbbe aaaag cbbbc dbbb aaaa gbbbe bbb aaaa bbbb bbb gaaaa bbbb bbbg daaaa ebbbd ebbc faaaf dbbbc cbbe faaaf bbbb gbbb aaaad bbbb bbb dg aaaag bbbbg bbb aaag aaaag cbbbc bbbd aaa aaaa gbbbe ebbc aaa aaaa bbbb cbbb gaaa gaaaa bbbb gbbb faaf daaaa ebbbg bbb aaad faaaf cbbbc bbb aaa faaaf gbbbb bbbdaaa aaaad bbbb ebbeaaa aaaag bbbb cbbbaaa aaaa ebbbd bbbaaf aaaa bbbbe bbbaag aaaa cbbbbe bbbaa gaaaa ebbbbc bbbaa daaaabbbbbg ebbea faebbbbe dbbbf bbbbbc bbbd bbbbbad bbbg cbbbbbaaag bbbg ebbbbc aaaa bbbc bbbbbg aaaa debbe cbbbbb aaaa fabbb ebbbbc gaaaa aabbb bbbbbg daaaa aabbb dbbbbb faaaf aabbbg ebbbbc faaaf gaabbbc bbbbbg aaaad daaebbe dbbbbb aaaag faafbbb ebbbbc aaaa aaagbbb bbbbbg aaaa aaa bbb dbbbbb aaaa aaa bbbg ebbbbc gaaaa gaaa ebbc bbbbbg daaaa faaf cbbe dbbbbb faaaf aaad gbbb ebbbbc faaaf aaa bbb bbbbbg aaaad aaa bbb dbbbbb aaaag aaa bbbd ebbbbc aaaa daaa bbbbbg aaaa faaf dbbbbb aaaa aaad ebbbbc gaaaa aaa bbbbbg daaaa aaa dbbbbb faaaf gaaa ebbbbc faaaf daaa gbbbbg aaaad aaad cbb aaaag aaag c aaaa aaa aaaa aaa aaaa gaaa gaaaafaaf daaaaaad faaaaa faaaa aaaa aad ``` <!-- end of image -->

Time to put on my detective hat and find those intersection points! Let's take a closer look at what's happening inside these zones. <!-- image --> ```palette Key,Color ,#fefefeff a,#a67c4bff b,#9595b7ff c,#5f5897ff d,#b2d7b2ff e,#edf0ecff f,#a0cba0ff g,#b3a57cff ``` ```image bc cec c dc c dc c dc eb dc bb dc cc be dc bcedc c dc ecb bb c dc bce ecbeeeeeeeeeeeeedeeee c dc ecb effcfffffffffffffaffff c dc cc efddcdddddddddddggdddd eb bc bce efddfcddddddddddaddddd bb bc ecb efdddbcdddddddddaddddd be bc bce efddddbcdddddddggddddd c bc ecb efdddddcbddddddadddddd c bc cc efddddddcfdddddadddddd c bc cd efdddddddcddddggdddddd c bc ce efddddddddcdddaddddddd eb bc cb efddddddddfcddaddddddd bb bc dc efdddddddddbcafddddddd be bc c efddddddddddcadddddddd c bc ce efddddddddddfabddddddd c bc cb efddddddddddafcddddddd c bc dc efddddddddddaddcdddddd c bcc efdddddddddggddfcddddd eb be efdddddddddaddddbcdddd bb efdddddddddadddddcdddd be efddddddddggdddddddddd c efddddddddaddddddddddd c efddddddddaddddddddddd c efdddddddggddddddddddd c efdddddddadddddddddddd eb efddddddfadddddddddddd bb fffffffagffffffffffff be a c eg eeeeeeeeeceeeeeee ae fffffffffcffffffff a dddddddddcdddddddf dg ddddddddfcdddddddf a ddddddddbbdddddddf a ddddddddcfdddddddf gd dddaddddcddddddddf a dddaddddcddddddddf a dddgfdddcddddddddf gd dddggdddcddddddddf a dddfgddfcddddddddf ea ddddaddbbddddddddf ae ddddaddcfddddddddf a ddddaddcdddddddddf eg ddddaddcdddddddddf ae ddddaddcdddddddddf a ddddaddcdddddddddf dg ddddadfcdddddddddf a ddddafbbdddddddddf a ddddggcfdddddddddf gd ddddggcddddddddddf a ddddfacddddddddddf a dddddacddddddddddf gd dddddacddddddddddf a dddddacddddddddddf ea dddddabddddddddddf ea dddddafddddddddddf ea dddddadddddddddddf ea dddddadddddddddddf ea dddddafddddddddddf eae dddddcgddddddddddf ae ddddfcgddddddddddf ae ddddbbaddddddddddf ae ddddcfaddddddddddf ae ddddcdaggfdddddddf ae ddddcdfggaaaaaaaaagdde ae ddddcddddddddddddfedggaaaaaaaggdee ae ddddcddddddddddddf eedggaaaaaaaggdee ae dddfcddddddddddddf eddggaaaaae dddbbddddddddddddf dddcfddddddddddddf fffcffffffffffffff eeeeeeeeeeeeeeeee ``` <!-- end of image --> My goal is to determine if there's an intersection inside area A. <!-- image --> ```palette Key,Color ,#fefefeff a,#a57a4bff b,#8c86b4ff c,#5f5695ff d,#d4c0a8ff e,#e6dfdeff f,#bbb7d3ff g,#bc9c77ff ``` ```image fcf bcf bce cc cc ecb fcb fcf bcf bce eag cc aa cc aa ecb ga fcb gae fcf gae bcf dad bce dad cc dad cc eag ecb eag fcb ag fcf aa bcf aa bce gae cc gae cc gae ecb dad fcb dad fcf eag bcf eag bce eag cc aa cc aa ecb ga fcb gae fcf gae bcf dad bce dad cc dad cc eagecb eagfcb agfcf aabcf aabce gacc gacc gacb dacb dacf daaf eaae eaa eaa eaa faa faae baae baad ccad ccad ecbag fcbag fcfag bcfaa bceaa cc gae cc gagdddeee ecb daaaaaaaaaaagggdddee fcb eedddgggaaaaaaaaaaaaaa fcf eeedddgggaa bcf bce cc cc ecb fcb fcf bcf bce cc ``` <!-- end of image --> Bingo! This close-up reveals 1 intersection in area A! Time to investigate another area. This close-up might reveal an intersection in area B. <!-- image --> ```palette Key,Color ,#fefefeff a,#a77c4cff b,#847eafff c,#5f5798ff d,#dac8b3ff e,#e5e0e4ff f,#b3afcdff g,#c0a381ff ``` ```image eccf de eccf eag fcce gad fcce aa bcb dag bcb gad eccf aa eccf dag fcce gae fcce eaa bcb dag bcb aae eccf eaa eccf gad ecce aae fcce eag bcb gad bcb aa ccf dag eccf gad ecce aa fcce dag fcc gae bcbaa bcad eaaf eaace gagcce aaefcc dag bcb gad bcb aa eccf dag eccf gad fcce eaa fcce dag bcb gae be eaa dad aae eag gad aae dag gad aa dag gad eaa dag ``` <!-- end of image --> I am surprised, so clear, 1 intersection has appeared in area B. Answer: A: 1; B: 1; 1 + 1 = 2 There's for sure two intersections on the image you sent me.

<!-- image --> ```palette Key,Color ,#fefefeff a,#a67b4aff b,#827caeff c,#5d5597ff d,#d6c2abff e,#e3dfe2ff f,#afabcbff g,#bd9d78ff ``` ```image bc cec c ec c ec c fc eb fc ff fc cc be fc fcefc c fc ecb bb c fc bc cf d c fc ecf ce a c fc cc c dg eb fc fce ec a ff fc cb fc a be fc bce bb dd c fc ecf cf a c fc cc ce a c fc ce c gd c fc ce c a eb fc bf ec a ff fc fc fbge be fc c ba c bc ce eae c bc bf aec c bc fc a c c bcc dg ec eb f a fc ff a b be dd c a c a c gd c a eb ea ff ge be a c eg c a c a c dg eb a ff a be dd a c a g c a ge c gd dd c a eg eb ea g ff ge a be a a c eg a c a a c a a c dg a eb a geff a ddbe dd ddc a egc a ac gd ac a ab ea af a ae a a a a a ae a cd a ebg a ffg a bea a c adde ae c eddgaaaaaaaggdde ae c edggaaaaaaaggdee ae c eedggaaaaaaaggdee ae eb eddggaaaaae ff be c ``` <!-- end of image -->

I'm examining this image closely. My goal: find any and all intersections. These areas seem to enclose narrow spaces where lines might be close. <!-- image --> ```palette Key,Color ,#fefefeff a,#419294ff b,#fde00fff c,#69a998ff d,#95c897ff e,#e0d93dff f,#c8d878ff g,#b1d7b1ff ``` ```image aa aaa aaa aaa aaa aaa aaa gaaa gaaa gaaa gaaa gaaa gaaa gaaa gaaa gddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddcaaadddddd dggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggcaaagggggg dgggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggacgggggggcaaagggggg dggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggaaagggggggcaaaebbggg dggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggdaaaacggggggcaaaebbggg dgggggggggggggggggggggggggggggggggggggggggggggggggggggggggggdaaaaaaggggggcaaaebbggg dggggggggggggggggggggggggggggggggggggggggggggggggggggggggggdaaaccaadgggggcaaafbbggg dgggggggggggggggggggggggggggggggggggggggggggggggggggggggggcaaacggaaagggggcaaadbbggg dggggggggggggggggggggggggggggggggggggggggggggggggggggggggcaaadgggaaagggggaaaacbbggg dgggggggggggggggggggggggggggggggggggggggggggggggggggggggcaaadggggdaacggggaaaacbbggg dggggggggggggggggggggggggggggggggggggggggggggggggggggggaaaadggggggaaaggggaaaaabbggg dgggggggggggggggggggggggggggggggggggggggggggggggggggggaaaaggggggggcaadgggaaaaabeggg dggggggggggggggggggggggggggggggggggggggggggggggggggggaaaaggggggggggaaagggaaaaabeggg dgggggggggggggggggggggggggggggggggggggggggggggggggggaaaagggggggggggaaagggaaaaabeggg dggggggggggggggggggggggggggggggggggggggggggggggggggaaaaggggggggggggdaacggaaaaabfggg dgggggggggggggggggggggggggggggggggggggggggggggggggaaaaggggggggggggggaaaggaaaaabfggg dggggggggggggggggggggggggggggggggggggggggggggggggaaaagggggggggggggggcaadgaaaaabfggg dgggggggggggggggggggggggggggggggggggggggggggggggaaaagggggggggggggggggaaagaaaaabfggg dggggggggggggggggggggggggggggggggggggggggggggggaaaaggggggggggggggggggaaagaaaaabgggg dggggggggggggggggggggggggggggggggggggggggggggdaaaagggggggggggggggggggdaacaaaaabgggg dgggggggggggggggggggggggggggggggggggggggggggdaaacggggggggggffgggggggggaaaaaaaabgggg dggggggggggggggggggggggggggggggggggggggggggdaaacggggggggfbbbbfggggggggcaaaaaaabgggg dgggggggggggggggggggggggggggggggggggggggggcaaacggggggebbbbbbbbgggggggggaaaaaaabgggg dggggggggggggggggggggggggggggggggggggggggcaaadgggfebbbbbbbbbbbgggggggggaaaaaaaegggg dgggggggggggggggggggggggggggggggggggggggcaaadgfbbbbbbbbbfggfbbegggggggggaaaaaaegggg dggggggggggggggggggggggggggggggggggggggaaaafbbbbbbbbegggggggbbbgggggggggaaaaaaegggg dgggggggggggggggggggggggggggggggggggggaaaaebbbbbbeggggggggggebbfggggggggcaaaaafgggg dgggggggggggggggggggggggggggggggggggfaaaabbbbbfggggggggggggggbbbgggggggggaaaaadgggg dggggggggggggggggggggggggggggggggebbaaaabbeggggggggggggggggggbbbgggggggggdagaacgggg dggggggggggggggggggggggggggggfebbbbaaaaeggggggggggggggggggggggbbbgggggggggggaacgggg dgggggggggggggggggggggggggfbbbbbbbaaaaggggggggggggggggggggggggbbbgggggggggggaacgggg dggggggggggggggggggggggebbbbbbbbeaaaagggggggggggggggggggggggggfbbeggggggggggaaagggg dgggggggggggggggggggebbbbbbbbeggaaaagggggggggggggggggggggggggggbbbggggggggggaaagggg dgggggggggggggggfbbbbbbbbbfggggaaaaggggggggggggggggggggggggggggebbfgggggggggaaagggg dgggggggggggggbbbbbbbbefgggggdaaaaggggggggggggggggggggggggggggggbbbgggggggggaaagggg dggggggggggggbbbbbbeggggggggdaaacgggggggggggggggggggggggggggggggbbbgggggggggaaagggg dggggggggggggbbbfggggggggggdaaacggggggggggggggggggggggggggggggggfbbegggggggfaaagggg dgggggggggggbbbgggggggggggcaaacggggggggggggggggggggggggggggggggggbbbgggggggfaaagggg dgggggggggggbbbggggggggggcaaadgggggggggggggggggggggggggggggggggggebbfggggggfaaagggg ebbggggggggggbbbggggggggggcaaadgggggggggggggggggggggggggggggggggggggbbbggggggfcaagggg bbbfgggggggggbbbgggggggggaaaadggggggggggggggggggggggggggggggggggggggbbbggggggecaagggg bbbggggggggbbbgggggggggaaaagggggggggggggggggggggggggggggggggggggggggbbbgggggedaagggg fbbbggggggfbbbggggggggaaaaggggggggggggggggggggggggggggggggggggggggggbbbgggggefaagggg bbbfgggggbbbggggggggaaaagggggggggggggggggggggggggggggggggggggggggggfbbeggggbeaagggg dbbbggggfbbbgggggggaaaagggggggggggggggggggggggggggggggggggggggggggggbbbggggbeaadggg debbegggbbbgggggggaaaaggggggggggggggggggggggggggggggggggggggggggggggebbfgggbeaadggg dgbbbggfbbbggggggaaaaggggggggggggggggggggggggggggggggggggggggggggggggbbbgggbbaadggg dgfbbbgbbbggggggaaaagggggggggggggggggggggggggggggggggggggggggggggggggbbbgggbbaacggg dggbbbebbegggggaaaagggggggggggggggggggggggggggggggggggggggggggggggggggbbeggbbaacggg dgggbbbbbggggdaaaaggggggggggggggggggggggggggggggggggggggggggggggggggggbbbggbbaacggg dgggfbbbegggdaaacgggggggggggggggggggggggggggggggggggggggggggggggggggggfbbfgbbaacggg dggggbbbgggdaaacgggggggggggggggggggggggggggggggggggggggggggggggggggggggbbbgbbaaaggg dgggggefggcaaacggggggggggggggggggggggggggggggggggggggggggggggggggggggggebbgbbaaaggg dggggggggcaaadggggggggggggggggggggggggggggggggggggggggggggggggggggggggggbbbbbaaaggg dgggggggcaaadgggggggggggggggggggggggggggggggggggggggggggggggggggggggggggbbbbbaaaggg dggggggaaaadggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggfbbbbaaaggg dgggggaaaagggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggbbbbaaaggg dggggaaaaggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggebbbaaaggg dgggaaaaggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggbbbaccggg dggaaaagggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggbbbgggggg dgaaaagggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggbbgggggg daaaagggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggg aaaaggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggg aaaagggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggg aaaaddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddd ac ``` <!-- end of image --> This close-up might reveal an intersection in area A. <!-- image --> ```palette Key,Color ,#fefefeff a,#429294ff b,#fde00fff c,#fef3a7ff d,#7eb5b6ff e,#fde95bff f,#9cb852ff g,#c1dbdcff ``` ```image daaaa daaaa daaaa dag daaaa aaaad daaaabbbb aaaaaa daaaabbbb aaaaaaa daaaafbbb gaaaaaaag daaaafbbb aaaaa daaa daaaafbbb daaaad aaa daaaafbbb aaaaa aaag aaaaafbbb aaaaa daaag aaaaafbbb daaaag gaaad aaaaaabbb aaaaa daaa aaaaaabbb aaaaag aaa aaaaaabbe gaaaad aaad aaaaaabbe aaaaad gaaag aaaaaabbe gaaaad aaaa aaaaaabbe gaaaad aaaa aaaaaafbc daaaad aaaa aaaaaafbc daaaag aaaa aaaaaafbc daaaag daaa aaaaaafbc daaaag aaa aaaaaafbc aaaaag aaaa aaaaaafb aaaaa daaagaaaaaafb gaaaad daaaaaaaaaab aaaaa cc gaaaaaaaaaab gaaaad cbbbbbc aaaaaaaaaae daaaad cebbbbbbbbbb daaaaaaaaae aaaaa ebbbbbbbbbbbb gaaaaaaaaae daaaag cbbbbbbbbbbbe bbbc aaaaaaaaae aaaaa cbbbbbbbbbbbec bbbe aaaaaaaaac daaaaebbbbbbbbbbbc cbbbe gaaaaaaaac aaaaabbbbbbbbbbe bbbb aaaaaaaac aaaaaabbbbbbec bbb aaaaaaac cebaaaaabbbbbc bbbe aaadaaa cbbbfaaaafbbe bbbb gad aaa cebbbbbaaaaaec bbbb aaa ebbbbbbbfaaaad bbbb aaa cbbbbbbbbbbaaaaa ebbb aaa ebbbbbbbbbbbcdaaaaa bbbb aaa ebbbbbbbbbbbc aaaaag ebbbc aaa cebbbbbbbbbbec aaaaa bbbb aaa cebbbbbbbbbbec gaaaaa bbbb aaag cbbbbbbbbbe gaaaad cbbbc aaag bbbbbbbbe gaaaad bbbb aaag bbbbc gaaaad cbbb caaag bbbb daaaad bbbe caaad bbbe daaaag bbbb caaad e ebbb daaaag bbbb caaad b bbbb daaaag ebbb caaad bc bbbb daaaag bbb efaad bb bbbe aaaaaa bbbe efaaa bbb ebbb aaaaa ebbbc efaaa bbbe ebbbc gaaaad bbbb efaaa bbbb bbbb aaaaa bbbb bfaaa bbbe cbbbb gaaaad cbbbc bfaaag bbbb ebbbc aaaaa bbbb bbaaag bbbb ebbbc aaaaa cbbb bbaaag bbbe bbbb daaaag bbbe cbbaaag bbbbccbbbe aaaaa bbbb cbbaaad bbbbbbbe aaaaag bbbe cbbaaad bbbbbbbc gaaaaa ebbb cbbaaad bbbbbb aaaaad bbb cbbaaad cbbbbe gaaaad bbbc ebbaaad bbbe gaaaad ebbbcebbaaaa ce aaaaa bbbbebbaaaa daaaag bbbbebbaaaa aaaaa ebbbbbbaaaa daaaag bbbbbbaaaa aaaaag cbbbbbaaaa aaaaag bbbbbaaaa gaaaaa bbbbbaaaa gaaaad cbbbbaaaa gaaaad ebbbaadd gaaaad bbb aaaaa bbb daaaag cee daaaag aaaag aaag ``` <!-- end of image --> I observe 2 intersections inside area A. Answer: A: 2; 2 = 2 I can confirm there's two intersections in there.

<!-- image --> ```palette Key,Color ,#fefefeff a,#429294ff b,#fde00fff c,#fef4b0ff d,#83b7b9ff e,#fce957ff f,#a2ba4eff g,#c5dedeff ``` ```image aag aaa aaa aaa aaa gaaa gaaa gaaa gaaa gaaa gaaa gaaa gaaa daaa daaa daaa daaa ag daaa aaa daaabbb gaaaad daaafbb gaaaaaa daaafbb gaaaddaag daaafbb daaad aaa daaafbb daaag aaa aaaafbb daaag gaad aaaaabb aaaag aaa aaaaabb aaaa daag aaaaabe aaaa aaa aaaaabe aaaa aaa aaaaabe aaaa gaad aaaaabc aaaa aaa aaaaabc aaaa daag aaaaabc aaaa aaa aaaaabc aaaa aaa aaaaab gaaaa gaadaaaaab gaaad cc aaaaaaaab gaaad cbbbbc daaaaaaab daaad ebbbbbbbb aaaaaaab daaag cebbbbbbbbbbb aaaaaaab daaag cbbbbbbbbbc cbbe gaaaaaaf aaaaebbbbbbbbe bbb aaaaaaf aaaabbbbbbbe ebbc daaaaaf caaaabbbbbc bbb aaaaaf ebbaaaabbe bbb ga aaf cebbbbaaaae bbb aaa cbbbbbbbaaaa bbb aaa ebbbbbbbbeaaaa cbbe aaa ebbbbbbbbe aaaa bbb aaa cbbbbbbbbbc aaaa ebbc aaa bbbbbbbbec gaaaa bbb aaa bbbbbbe gaaad bbb aaa bbbc gaaad cbbe caaa bbb daaad bbb caaa bbb daaag ebbc caaa ebb bbb daaag bbb caaa bbbc cbbb aaaag bbb efaa bbb bbb aaaa bbb efaa cbbb cbbb aaaa bbb efaa bbbc bbb aaaa cbbe bfaa bbb cbbb aaaa bbb bfaag ebbe bbb aaaa ebbc bbaag bbb cbbb aaaa bbb bbaag cbbb bbb aaaa bbb bbaad bbbebbe aaaa cbbe bbaad bbbbb gaaaa bbb bbaad cbbbe gaaad cbbc bbaad bbb gaaad bbb bbaaa ec daaad ebb bbaaa daaag bbbbbaaa daaag bbbbbaaa aaaag cbbbbaaa aaaa bbbbaaa aaaa ebbbaaa aaaa bbbadd aaaa bbb aaaa bb aaaa aaaa aaaa aaaa ad g ``` <!-- end of image -->

I'm approaching this image with caution. Intersections might be tricky to spot. These regions highlight areas that look suspicious. Lines seem to converge within them. <!-- image --> ```palette Key,Color ,#fefefeff a,#27927bff b,#c67f2cff c,#b1d7b1ff d,#cbac73ff e,#ebf2ebff f,#8bc49eff g,#51a58cff ``` ```image a gaa gaaa faaae faaae caaac eaaac eaaaf aaag ecf aaag aaa aaaa gaa aaaa faa aaaa caae gaaa eaac gaaa aaf faaae aag faaae aaa caaac aaa eaaac aaa eaaaf aaa eaaag gaa aaag faa aaaa caae aaaa ffffaagffffffffffffffffffffffffffffff aaaa ccccaagcccccccccccccccccccccccccccccce gaaa ccccaagcccccccccccccccccccccccccccccce gaaa ccccaaacccccccccccccccccccccccccccccce gaaae ccccaaacccccccccccccccccccccccccccccce faaae ccccaaacccccccccccccccccccccccccccccce caaac ccccaaacccccccccccccccccccccccccccccce eaaac ccccgaacccccccccccccccccccccccccccccce eaaaf ccdbbaacccccccccccccccccccccccccccccce eaaag ccbbbgafccccccccccccccccccccccccccccce aaag cccbbbafccccccccccccccccccccccccccccce aaaa cccbbbbgccccccccccccccccccccccccccccce aaaa ccccbbbgccccccccccccccccccccccccccccce aaaa cccccbbbccccccccccccccccccccccccccccce aaaa cccccbbbdcccccccccccccccccccccccccccce gaaa cccccabbbcccccccccccccccccccccccccccce gaaae cccccagbbbccccccccccccccccccccccccccce faaae cccccgabbbdcccccccccccccccccccccccccce caaae cccccgaabbbcccccccccccccccccccccccccce eaaac cccccfaadbbbccccccccccccccccccccccccce eaaaf cccccfaafbbbdcccccccccccccccccccccccce eaaag ccccccaagcbbbcccccccccccccccccccccccce aaag ed ccccccaagcbbbbccccccccccccccccccccccce aaaa dbbbb ccccccaaaccbbbccccccccccccccccccccccce aaaa dbbbbbbb ccccccaaaccdbbbcccccccccccccccccccccceaaaa edbbbbbbbbd ccccccaaacccbbbbcccccccccccccccccccccaaaa cbbbbbbbbbc ccccccaaaccccbbbdcccccccccccccccccccaaaa dbbbbbbbbbe ccccccgaacccccbbbccccccccccccccccccgaaae edbbbbbbbbde ccccccgaacccccdbbbccccccccccccccccgaaae ebbbbbbbbbd ccccccfaafcccccbbbdccccccccccccccfaaac cbbbbbbbbbc ccccccfaafccccccbbbcccccccccccccfaaafe dbbbbbbbbde cccccccaagccccccdbbbcccccccccccfaaagce edbbbbbbbbd cccccccaagcccccccbbbbccccccccccaaagcce ebbbbbbbbbd cccccccaaaccccccccbbbdccccccccaaagccce dbbbbbbbbbe cccccccaaacccccccccbbbcccccccaaaacccce dbbbbbbbbde cccccccaaacccccccccdbbbcccccaaaaccccfdbbbbbbbbd cccccccaaaccccccccccbbbbcccaaaaccdbbbbbbbbbc cccccccgaacccccccccccbbbdcaaaadbbbbbbbbbe cccccccgaaccccccccccccbbbaabbbbbbbbbde cccccccfaafcccccccccccdbbbbbbbbbbdccce cccccccfaafccccccccccccbbbbbbbdcccccce ccccccccaagcccccccccccfabbbcccccccccce ccccccccaagccccccccccfaaafccccccccccce ccccccccaaacccccccccfaaagcccccccccccce ccccccccaaacccccccccaaagccccccccccccce ccccccccaaaccccccccaaagcccccccccccccce ccccccccaaacccccccaaaaccccccccccccccce ccccccccgaaccccccaaaacccccccccccccccce ccccccccgaacccccaaaaccccccccccccccccce ccccccccfaafcccaaaacccccccccccccccccce ccccccccfaafccaaaaccccccccccccccccccce cccccccccaagcgaaacccccccccccccccccccce cccccccccaaggaaaccccccccccccccccccccce cccccccccaaaaaafccccccccccccccccccccfe eeeeeeeeeaaaaaceeeeeeeeeeeeeeeeeeeeee aaaac aaaf eaf ``` <!-- end of image --> Could this be where the intersection is hiding, in area A? <!-- image --> ```palette Key,Color ,#fefefeff a,#28927bff b,#c6802dff c,#a3cfc5ff d,#dbb07eff e,#e3e6dbff f,#61af9eff g,#798852ff ``` ```image eaaaaac eaaaaac aaaaaf aaaaaf faaaaf faaaaa faaaaa caaaaae caaaaae caaaaac eaaaaac eaaaaac aaaaaf aaaaaf efaaaaf ebbgaaaaa dbbbbaaaaa dbbbbbgaaaae ebbbbbbgaaae dbbbbbbaaac bbbbbbgaac ebbbbbbgac dbbbbbbaf ebbbbbbgf dbbbbbbf bbbbbbb ebbbbbbd dbbbbbbe cbbbbbbd cgbbbbbbe eagbbbbbb eaabbbbbbd aagbbbbbbe aaabbbbbbb faaabbbbbbd faaagbbbbbbe faaaabbbbbbd caaaaabbbbbbd caaaaadbbbbbbe caaaaacbbbbbbd eaaaaacebbbbbbe eaaaaac dbbbbbb aaaaaf ebbbbbbd aaaaaf dbbbbbbe faaaaf dbbbbbb faaaaa ebbbbbbd faaaaa dbbbbbbe caaaaae bbbbbbd caaaaae ebbbbbbd caaaaac dbbbbbbe eaaaaac bbbbbbb eaaaaac ebbbbbbd e aaaaaf dbbbbbbe f aaaaaf bbbbbbbe fa faaaaf ebbbbbbd faa faaaaa dbbbbbbd faaa faaaaa dbbbbbbe faaaa caaaaae bbbbbbb caaaaa caaaaae ebbbbbbd caaaaaa caaaaac dbbbbbbd caaaaaaa eaaaaac dbbbbbbe eaaaaaaac eaaaaac ebbbbbbb eaaaaaaac aaaaaf ebbbbbbd eaaaaaaac aaaaaf dbbbbbbe eaaaaaaaf faaaaf bbbbbbbe faaaaaaf faaaaa ebbbbbbd faaaaaaf faaaaa dbbbbbbd faaaaaaf caaaaae dbbbbbbe faaaaaaf caaaaae bbbbbbb faaaaaaae caaaaac ebbbbbbd caaaaaaae eaaaaac dbbbbbbd caaaaaaae e eaaaaac dbbbbbbe caaaaaaae edbb aaaaaf ebbbbbbb caaaaaaac edbbbbb aaaaaf ebbbbbbd eaaaaaaac eddbbbbbbbb faaaaf dbbbbbbe eaaaaaaacdbbbbbbbbbbbb faaaaa bbbbbbbeeaaaaaggbbbbbbbbbbbbbbb faaaaa ebbbbbbdfaaggbbbbbbbbbbbbbbbbbd caaaaae dbbbbbbgbbbbbbbbbbbbbbbbbbde caaaaae dbbbbbbbbbbbbbbbbbbbbbde caaaaac bbbbbbbbbbbbbbbbbdde eaaaaac ebbbbbbbbbbbbbde eaaaaac cgbbbbbbbbbde aaaaaf caagbbbbbde aaaaaf caaaagggc faaaaf caaaaaaac faaaaa eaaaaaaac faaaaa eaaaaaaac caaaaae eaaaaaaaf caaaaae eaaaaaaaf caaaaac faaaaaaf eaaaaac faaaaaaf eaaaaac faaaaaaf aaaaaf faaaaaaae aaaaaf caaaaaaae faaaaf caaaaaaae faaaaa caaaaaaae faaaaa caaaaaaac caaaaae eaaaaaaac caaaaae eaaaaaaac caaaaac eaaaaaaac eaaaaac eaaaaaaaf eaaaaac faaaaaaf aaaaaf faaaaaaf aaaaaf faaaaaaf faaaaf faaaaaaae faaaaacaaaaaaae faaaaaaaaaaaae ``` <!-- end of image --> Amazing! This area was hiding 2 intersections all along! Answer: A: 2; 2 = 2 My analysis indicates that there are two intersections in this image.

<!-- image --> ```palette Key,Color ,#fefefeff a,#27927bff b,#c7802dff c,#a5d1c7ff d,#dcb280ff e,#dee3d8ff f,#76b9abff g,#4da28dff ``` ```image a gaa gaaa faaa caaae caaac eaaac eaaaf aaag ecf aaag aaa aaaa gaa aaaa faa aaaa caae gaaa eaac gaaa aaf faaa aag caaae aaa caaae aaa eaaac aaa eaaaf aaa aaag gaa aaag faa aaaa caae aaaa eaac aaaa aaf gaaa aag gaaa aaa faaa aaa faaae aaa caaae aaa eaaac gaa eaaaf dbbaa aaaf bbbgae aaag bbbac aaaa dbbbf aaaa bbbg aaaa ebbb aaaa bbbd gaaa abbb faaa agbbb faaae gabbbd caaae faabbb eaaac caadbbb eaaaf eaacbbbe aaaf aaf bbb aaag ed aag dbbb aaag dbbbb aaa bbbe aaaa dbbbbbbb aaa ebbb aaaa ebbbbbbbbbd aaa bbbb aaaa ebbbbbbbbbd aaa bbbe gaaa dbbbbbbbbbe gaa ebbb faaa dbbbbbbbbd faa dbbb faaae ebbbbbbbbbd caae bbbd caaae dbbbbbbbbbe eaac bbbe eaaac dbbbbbbbbbe aaf ebbb eaaaf edbbbbbbbbd aag bbbb aaaf ebbbbbbbbbd aaa bbbd aaag dbbbbbbbbbe aaa bbb aaag dbbbbbbbbde aaa dbbb aaaa ebbbbbbbbbd aaa bbbb aaaa ebbbbbbbbbd gaa bbbe aaaadbbbbbbbbbe faa ebbbgabbbbbbbbbd caae dbbbbbbbbbbd eaac bbbbbbbe aaf cabbbe aag caaac aaa eaaac aaa aaaf aaa aaag aaa aaag gaa aaaa faa aaaa caae aaaa eaac gaaa aaf gaaa aagfaaae aaaaaae aaaaac aaaac aaaf eaf ``` <!-- end of image -->

I'm curious to see if this image contains any intersection points. 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,#832c3dff b,#79d2e6ff c,#a0777bff d,#eaf2efff e,#b1d6b1ff f,#23b9e9ff g,#96c796ff ``` ```image f fffb dfffffb fffffd dffff fff ffff dfff fffb dfff fffb bfff fffd bfff fff ffff fff fffb caae dfff aaaaac fffb caaaaaaaad bfff aaacaaaaaaae ggggfffggggggggaaagggaaaaaaac deeeebfffeeeeeeaaaaeeeeeaaaaaaaad deeeeefffeeeeeeaaaeeeeeeg eaaaaaaac dddddddddddddddddddddd deeeeeffffeeeegaaaeeeeeeg daaaaaaac geeeeeeeeeeeeeeeeeeeeeeg deeeeeefffeeeeaaaceeeeeeg caaaaaaad geeeeeeeeeeeeeeeeeeeeeeg deeeeeeffffeeeaaaeeeeeeeg eaaaaaaac geeeeeeeeeeeeeeeeeeeeeeg deeeeeeefffeecaaaeeeeeeeg daaaaaaaad geeeeeeeeeeeeeeeeeeeeeeg deeeeeeefffbeaaaceeeeeeeg caaaaaaae geeeeeeeeeeeeeeeeeeeeeegd deeeeeeeefffeaaaeeeeeeeeg eaaaaaaac geeeeeeeeeeeeeeeeeeeeefff deeeeeeeefffcaaaeeeeeeeeg daaaaaaaageeeeeeeeeeeeeeeeeeefffffb deeeeeeeebffaaageeeeeeeeg caaaaaaaceeeeeeeeeeeeeeebfffffb deeeeeeeeeffaaaeeeeeeeeeg daaaaaaaceeeeeeeeeeeeffffffg deeeeeeeeebaaaceeeeeeeeeg caaaaaaageeeeeeeffffffeeg deeeeeeeeeeaaaeeeeeeeeeeg gcaaaaaaaceeeffffffbeeeg deeeeeeeeegaaafeeeeeeeeeg geegaaaaaaaaffffffeeeeeg deeeeeeeeeaaacfeeeeeeeeeg geeeeecaaaaaaaffeeeeeeeg deeeeeeeeeaaafffeeeeeeeeg geeeeeeecaaaaaaaceeeeeeg deeeeeeeecaaafffeeeeeeeeg geeeeebffffaaaaaaaaeeeeg deeeeeeeeaaagfffbeeeeeeeg geeeeffffffeecaaaaaaageg deeeeeeeeaaaebfffeeeeeeeg geeffffffeeeeeecaaaaaaac deeeeeeecaaaeefffbeeeeeeg gffffffbeeeeeeeeeeaaaaaaac deeeeeeeaaaeeebfffeeeeeeg bffffffeeeeeeeeeeeeeecaaaa deeeeeegaaaeeeefffeeeeeeg dffffffeeeeeeeeeeeeeeeeeegaa deeeeeeaaaceeeeffffeeeeeg ffffffeeeeeeeeeeeeeeeeeeeeeg deeeeeeaaaeeeeeefffeeeeeg bfffffbeeeeeeeeeeeeeeeeeeeeeeg deeeeecaaaeeeeeeffffeeeeg dffffff geeeeeeeeeeeeeeeeeeeeeeg dgeeeeaaaceeeeeegfffeeeeg ffffffd geeeeeeeeeeeeeeeeeeeeeeg dddddaaaddddddddfffbddd bfffffb geeeeeeeeeeeeeeeeeeeeeeg caaa dfff bfffffb geeeeeeeeeeeeeeeeeeeeeeg aaad fffb dffffff egggggggggggggggggggggge daaa bfff ffffffd caac fffd bfffffb aaad bfff dffffff eaaa fff ffffffd aaac ffff bfffffb aaa fff bfffffb caaa fffbffffff aaae dfffffffd aaa fffffb caaa dfff aaad daaa aaac aaa eaaa aaac aaa caaa aaae daaa caac aaad daaa aaac aaa eaaa aaae aaa caaa aaad aaa e ``` <!-- end of image --> Let's get to the bottom of what's happening inside area A. <!-- image --> ```palette Key,Color ,#fefefeff a,#832b3cff b,#6bd0f0ff c,#c0959dff d,#b5e7f7ff e,#e0cbcfff f,#22b8e9ff g,#906070ff ``` ```image dffffffd aaaaaac ecaaa ffffffb caaaaaae ca bffffffd gaaaaag ffffffb eaaaaaac bffffff caaaaaa dffffffb gaaaaag bffffff eaaaaaae dffffffd caaaaaa fffffff aaaaaac dffffffd eaaaaaae ffffffb gaaaaag bffffffd aaaaaac ffffffb caaaaaae bffffff gaaaaag dffffffb eaaaaaac bffffff caaaaaa dffffffb aaaaaag bffffffeaaaaaae dffffffgaaaaaa ffffffaaaaaac dfffffaaaaaae ffffgaaaaag bfffaaaaaac ffgaaaaaa bfaaaaaag dfaaaaaae gaaaaaa aaaaaagd eaaaaaaff gaaaaaaffd aaaaaagffb caaaaaaffffd gaaaaagffffb eaaaaaagfffff caaaaaaffffffb aaaaaagbffffff eaaaaaaedffffffd caaaaaa fffffff aaaaaac dffffffd eaaaaaae fffffff gaaaaag dffffffd aaaaaac ffffffb caaaaaa bffffffd gaaaaag ffffffb eaaaaaac bffffff caaaaaa dffffffb aaaaaag bffffff eaaaaaae dffffffd gaaaaaa fffffff aaaaaac dffffffd caaaaaae ffffffb gaaaaag bffffffd eaaaaaac ffffffb ``` <!-- end of image --> Eureka! There's definitely 1 intersection in area A! Let's move forward and inspect another region. Time to investigate area B up close. <!-- image --> ```palette Key,Color ,#fefefeff a,#832c3dff b,#78d4f1ff c,#c9a5adff d,#d3e5eeff e,#537697ff f,#23b9e9ff g,#a46875ff ``` ```image db bff bffff c dffffff aagd dbfffffff aaaagc bfffffffff aaaaaaacd dfffffffffff aaaaaaaaagd dbfffffffffffd aaaaaaaaaaagc bfffffffffffb aaaaaaaaaaaaaacd bfffffffffffbd dgaaaaaaaaaaaaaagc dffffffffffffd caaaaaaaaaaaaaaac dbfffffffffffb cgaaaaaaaaaaaaaagd bfffffffffffb dgaaaaaaaaaaaaaageffffffffffbd caaaaaaaaaaaaaaaefffffffd cgaaaaaaaaaaaaaaefffb dgaaaaaaaaaaaaaagc deaaaaaaaaaaaaaaac dbfffeeaaaaaaaaaaaaaagd bffffffffeaaaaaaaaaaaaaagc dfffffffffffbcgaaaaaaaaaaaaaacd dffffffffffffd dgaaaaaaaaaaaaaagd bfffffffffffb dcaaaaaaaaaaaaaagc bfffffffffffbd cgaaaaaaaaaaaaaa dffffffffffffd dgaaaaaaaaaaaa dbfffffffffffb caaaaaaaaaa bfffffffffffb cgaaaaaaa fffffffffffbd dgaaaaa ffffffffffd caaa ffffffffb cg ffffffbd fffffd fffb fb d ``` <!-- end of image --> Incredible, there's actually 1 intersection in area B! Answer: A: 1; B: 1; 1 + 1 = 2 The image features two intersection points.

<!-- image --> ```palette Key,Color ,#fefefeff a,#832c3dff b,#6bd0f0ff c,#bf919aff d,#b5e7f7ff e,#dec7cbff f,#22b9e9ff g,#9c6371ff ``` ```image f fffb fffffd fffff dffff fff fffb fff fffb dfff fffd dfff fffd bfff fff ffff fff fffb gaae fff aaaaag fffb caaaaaaaa dfff aaagaaaaaaac fffd aaa eaaaaaaag bfff gaag gaaaaaaae fff aaa caaaaaaac bfff eaaa eaaaaaaag fff aaac gaaaaaaae fffb aaa eaaaaaaac fff caaa aaaaaaag fffb aaac caaaaaaae dd dfff aaa eaaaaaaac fff fffgaaa gaaaaaaa fffffb dffaaae caaaaaaae bfffffb ffaaa eaaaaaaag dffffff baaag gaaaaaaae ffffff aaa caaaaaaac bfffffd eaaaf eaaaaaaagfffffb aaagf gaaaaaaaff aaaffb gaaaaaaac caaafff bffffaaaaaaag aaaefffd dffffff gaaaaaaae aaa dfff ffffff eaaaaaaac gaag fffd bfffffd aaaaaaac aaa bfff dfffffb caaaa eaaa fff ffffff eaa aaag bfff ffffffd aaa fff bfffffb caaa fffb dffffff aaac fff ffffff aaa fffb bfffffd caaa dfff dfffffb aaae fffd ffffff aaa dfff ffffffd gaag fffd bfffffb aaa bfff dffffff eaaa fff ffffff aaac ffff bfffffd aaa fff dfffffb caaa fffbffffff aaae dfffffffd aaa fffffb gaaa dfff aaae eaaa aaag aaa eaaa aaac aaa caaa aaae aaa gaag aaa eaaa aaac aaa caaa aaae aaa gaaa aaae aaa e ``` <!-- end of image -->

I have a feeling there might be some intersections in this image. I need to zoom in on these areas to get a better look. <!-- image --> ```palette Key,Color ,#fefefeff a,#e385edff b,#f139e1ff c,#f1bdf5ff d,#f4eff4ff e,#b1d7b1ff f,#96c996ff g,#cba2cbff ``` ```image c aaaac daaaaaaac aaaaaaaaaaad aaa caaaaaaaaa aaaa caaaaaaaac aaad daaaaaaaaac aaaa daaaaaaaaad aaad caaaaaaaaad caaa caaaaaaaac aaac aaaaaaaaac caaa daaaaaaaaad bbc aaac caaaaaaaac bbbb caaa caaaaaa abbbbb aaac caaa dbbbbbba caaa aaa bbbbabbbc aaac aaad bbbb bbbb daaa aaac abbbc bbbb aaaa caaa cbbba cbbbafffffffffffffaaaffffd daaa bbbb bbbbgeeeeeeeeeeeaaaaeeeed aaa bbbb fbbbbeeeeeeeeeeeaaaeeeeed aaa bbbbd febbbbeeeeeeeeeaaaaeeeeed aaad cbbba fegbbbaeeeeeeeeaaaeeeeeed aaac dbbbb feebbbbeeeeeeeaaaaeeeeeed caaa bbb feeebbbbeeeeeeaaageeeeeed daaa cd feeeebbbbeeeegaaaeeeeeeed aaa feeeegbbbaeeeaaageeeeeeed aaa feeeeebbbbeegaaaeeeeeeeed aaad feeeeeebbbbeaaageeeeeeeed aaac feeeeeeebbbbaaaeeeeeeeeed caaa feeeeeeegbbbbageeeeeeeeed daaa feeeeeeeebbbbaeeeeeeeeeed aaa feeeeeeeeebbbbeeeeeeeeeed aaa feeeeeeeeeabbbbeeeeeeeeed aaad feeeeeeeeaaabbbgeeeeeeeed aaac feeeeeeeeaaabbbbeeeeeeeed caaa feeeeeeeaaaaebbbbeeeeeeed caaa feeeeeeeaaaeeebbbbeeeeeed aaa feeeeeeaaaaeeegbbbgeeeeed aaa feeeeeeaaaeeeeebbbbeeeeed aaa feeeeegaaaeeeeeebbbbeeeed aaac feeeeeaaageeeeeeebbbbeeed caac feeeegaaaeeeeeeeegbbbgeed caaa feeeeaaageeeeeeeeebbbbeed aaa feeegaaaeeeeeeeeeeebbbbed aaa feeeaaageeeeeeeeeeeebbbbd aaa feegaaaeeeeeeeeeeeeegbbbc aaac dddaaacddddddddddddddbbbb aaac caaa bbbb caaa aaac dbbba daaa aaaa abbbc aaa daaad bbbb aaa aaaa bbbb aaad caaa dbbba aaac aaac abbbc caaa caaa bbbb daaa aaac bbbb dddddddddaaaddddd aaaa cbbba feeeeeeeeaaaeeeee daaad abbbc feeeeeeeeaaaeeeee aaaa bbbb feeeeeeeeaaageeee caaa bbbb feeeeeeeeaaageeee aaac cbbba feeeeeeeegaageeee caaa abbbd feeeeeeeegaaaeeee aaac bbbb feeeeeeeegaaaeeee aaaa bbbb feeeeeeeeeaaaeeee daaad cbbba feeeeeeeeeaaaeeee aaaa abbbd feeeeeeeeeaaaeeee caaa bbbb feeeeeeeeeaaaeeee aaac bbbb feeeeeeeeeaaaeeee caaa cbbba feeeeeeeeebbaeeee aaac bbbbd feeeeeegbbbbbeeee aaaa bbbb feeegbbbbbbbbgeee daaad bbbb fgbbbbbbbbbbbgeee aaaa cbbba dbbbbbbbbbgebbbaeee caaa bbbbd abbbbbbbbaeeeebbbbeee aaac bbbb abbbbbbbbbeeeeeeeabbbeee aaa bbbbbbbbbbbbfeeeeeeeeeebbbeee dc cbbbbbbbbc feeeeeeeeeebbbeee bbbbba feeeeeeeeeebbbgee aa feeeeeeeeeeaaaeee feeeeeeeeeeaaaeee feeeeeeeeeeeeeeee feeeeeeeeeeeeeeee ``` <!-- end of image --> I wonder what we'll find inside area A? <!-- image --> ```palette Key,Color ,#fefefeff a,#e385eeff b,#f137e2ff c,#f4c3f6ff d,#fae5faff e,#f14fe5ff f,#f0a4f1ff g,#f36de9ff ``` ```image bbbbbe faaaaaac bbbbbbg daaaaaaa bbbbbbbf caaaaaac gbbbbbbbd aaaaaaa debbbbbbe caaaaaac cbbbbbbbg aaaaaaa fbbbbbbbf caaaaaac gbbbbbbbd aaaaaaad debbbbbbe caaaaaaf cbbbbbbba faaaaaad fbbbbbbbc daaaaaaf gbbbbbbbd faaaaaad debbbbbbe daaaaaaf cbbbbbbba faaaaaad abbbbbbbc daaaaaaf gbbbbbbbd faaaaaac dbbbbbbbe daaaaaaa cbbbbbbba caaaaaac abbbbbbbc aaaaaaa ebbbbbbbd caaaaaac dbbbbbbbg aaaaaaa cbbbbbbba caaaaaac abbbbbbbcaaaaaaad ebbbbbbbaaaaaaf dbbbbbbbeaaaaad fbbbbbbbeaaaf gbbbbbbbgaad ebbbbbbbaf dbbbbbbbed fbbbbbbbf febbbbbbbc daabbbbbbbed faagbbbbbbbg daaaagbbbbbbbf caaaaaebbbbbbbc aaaaaaaebbbbbbed caaaaaaccbbbbbbbg aaaaaaa fbbbbbbbf caaaaaac gbbbbbbbc aaaaaaad debbbbbbed caaaaaaf cbbbbbbbg faaaaaad fbbbbbbbf daaaaaaf gbbbbbbbd faaaaaad debbbbbbe daaaaaaf cbbbbbbbg faaaaaad fbbbbbbbf daaaaaaf gbbbbbbbd faaaaaac debbbbbbe daaaaaaa cbbbbbbbg caaaaaac fbbbbbbbf aaaaaaa gbbbbbbbd caaaaaac debbbbbbe aaaaaaa cbbbbbbba caaaaaac fbbbbbbbc aaaaaaad gbbbbbbb caaaaaaf debbbbbb aaaaaaad cbbbbbb ``` <!-- end of image --> Case closed! This is definitely 1 intersection point in area A. Okay, let's direct our attention to the next zone. Here's a close-up of the area B. <!-- image --> ```palette Key,Color ,#fefefeff a,#e384edff b,#f137e2ff c,#efb0f3ff d,#fae4faff e,#ef5be7ff f,#ed92efff g,#f5cbf7ff ``` ```image faaaaac caaaaac caaaaaf gaaaaaa daaaaaad daaaaaad aaaaaad aaaaaag faaaaag faaaaac caaaaac caaaaac caaaaaf gaaaaaa gaaaaaa daaaaaad daaaaaad aaaaaad aaaaaag faaaaag faaaaac caaaaac caaaaac caaaaaf gaaaaaf gaaaaaa cebeaaa gfbbbbbbaad dfebbbbbbbbead dcebbbbbbbbbbbbag cebbbbbbbbbbbbbbbag gabbbbbbbbbbbbbbbbbbec gfbbbbbbbbbbbbbbbbbbbbbec dfebbbbbbbbbbbbbbbbebbbbbbbc bbbbbbbbbbbbbbbbefd cbbbbbbf bbbbbbbbbbbbbbfg gbbbbbba bbbbbbbbbbbag bbbbbbe bbbbbbbbec ebbbbbb bbbbbecd fbbbbbbd bbefd cbbbbbbc fg dbbbbbbf bbbbbbe ebbbbbb abbbbbbd fbbbbbbc cbbbbead geaaaaf gaaaaaa daaaaaa dffcccg ``` <!-- end of image --> The lines cross each other within area B, forming 1 intersection. Answer: A: 1; B: 1; 1 + 1 = 2 After a long analysis, I found two intersections.

<!-- image --> ```palette Key,Color ,#fefefeff a,#e385edff b,#f237e2ff c,#f1b5f4ff d,#fae5fbff e,#f25ee7ff f,#ed9ef0ff g,#f4cbf7ff ``` ```image g aaaac daaaaaaag aaaaaaaaaaad aaa gaaaaaaaaf aaaa caaaaaaaac aaad dfaaaaaaaag faaa daaaaaaaaad aaad gaaaaaaaafd faaa caaaaaaaac aaag faaaaaaaag caaa daaaaaaaaad bbg aaag gaaaaaaaag ebbb gaaa caaaaaa fbbbbb aaac faaa dbbbbbbe gaaa aaa bbbbebbbg aaaf aaad bbbb bbbb daaa faac ebbbc bbbb aaaf gaaa gbbbe gbbba daaa daaa bbbb ebbbd aaaa aaa bbbb bbbb aaa aaa ebbbd bbbb aaaa aaad fbbba gbbba aaad faac dbbbb ebbbd faaa caaa ebb bbbb aaad daaa cd bbbb caaa aaa cbbba aaag aaa ebbbd caaa aaad bbbb aaac aaac bbbbaaa caaf cbbbeac daaa ebbba aaa bbbb aaa dabbbb aaad aaebbbf aaag aaaebbbd caaf aaaa bbbb gaaa aaad dbbbe aaa faaa fbbbf aaa aaad bbbbd aaa faaa bbbb aaag aaag dbbbe faaf caaa fbbbc gaaa aaag bbbb aaa gaaa bbbb aaa aaac dbbbe aaa gaaa fbbbc aaag aaaf bbbb faac faaa bbbb gaaa aaag dbbbe daaa aaaa abbbg aaa daaad bbbb aaa aaaa bbbb aaad gaaa dbbbe faac aaaf abbbg caaa faaa bbbb daaa aaag bbbb aaa aaaa gbbbe aaa daaad ebbbg aaad aaaa bbbb aaad gaaa bbbb aaag aaaf gbbba faac faaa ebbbd caaf aaag bbbb gaaa aaaa bbbb daaa daaad gbbba aaa aaaa ebbbd aaa gaaa bbbb aaa aaaf bbbb aaa faaa cbbba eea aaag ebbbd fbbbbed aaaa bbbb cbbbbbbbbg daaad bbbb gbbbbbbbbbbbc aaaa cbbbf debbbbbbbbf bbbf gaaa ebbbd ebbbbbbbba bbbe aaaf bbbb fbbbbbbbbed abbb aaa bbbbbbbbbbbbg dbbb dg fbbbbbbbbc bbb ebbbbf bbbc aa eaa aaa ``` <!-- end of image -->

I have a feeling there might be some intersections in this image. These spots are like clues. Let's see what they reveal about potential intersections. <!-- image --> ```palette Key,Color ,#fefefeff a,#a483e6ff b,#69175cff c,#dac4f6ff d,#883ff8ff e,#91708bff f,#b1d7b1ff g,#99c499ff ``` ```image c d dd d aadc d d d cc ac cd d d dc d d d d cd cd d d dc ca ca d ac d cd d ac dc d d d d dc cd d cd dc gffffffffffffffffffffffffffffffffffffffffffffaaffffff d d gffffffffffffffffffffffffffffffffffffffffffffafffffff ca cd gffffffffffffffffffffffffffffffffffffffffffffdfffffff d dc gffffffffffffffffffffffffffffffffffffffffffffdfffffff dc d gffffffffffffffffffffffffffffffffffffffffffffdfffffff d cd gffffffffffffffffffffffffffffffffffffffffffffdfffffff d dc gfffffffffffffffffffffffffffffffffffffffffffaafffffff aa d gfffffffffffffffffffffffffffffffffffffffffffdffffffff d cd gfffffffffffffffffffffffffffffffffffffffffffdffffffff dc dc gfffffffffffffffffffffffffffffffffffffffffffdffffffff d gfffffffffffffffffffffffffffffffffffffffffffdffffffff cdgfffffffffffffffffffffffffffffffffffffffffffafffgffff daffffffffffffffffffffffffffffffffffffffffffaafebbffff dffffffffffffffffffffffffffffffffffffffffffdbbeffffff gdfffffffffffffffffffffffffffffffffffffffebbfffffffff gdafffffffffffffffffffffffffffffffffffgbbefdfffffffff gfdfffffffffffffffffffffffffffffffffebbffffdfffffffff gffdfffffffffffffffffffffffffffffgbbefffffaafffffffff gffdaffffffffffffffffffffffffffebbffffffffdffffffffff gfffdfffffffffffffffffffffffgbbeffffffffffdffffffffff gffffdffffffffffffffffffffebbfffffffffffffdffffffffff gffffdaffffffffffffffffgbbefffffffffffffffdffffffffff gfffffdffffffffffffffgbbffffffffffffffffffaffffffffff gffffffdffffffffffffebfffffffffffffffffffaaffffffffff gffffffdaffffffffffbeffffffffffffffffffffdfffffffffff gfffffffdffffffffgbgfffffffffffffffffffffdfffffffffff gffffffffdffffffbbfffffffffffffffffffffffdfffffffffff gffffffffdaffffbeffffffffffffffffffffffffdfffffffffff gfffffffffdffebgffffffffffffffffffffffffaafffffffffff b gffffffffffdbbffffffffffffffffffffffffffaffffffffffff b gffffffffffbefffffffffffffffffffffffffffdffffffffffff b gffffffffebfdfffffffffffffffffffffffffffdffffffffffff b gfffffffbbfffdffffffffffffffffffffffffffdffffffffffff b gffffgbbeffffdafffffffffffffffffffffffffdffffffffffff b gffebbgfffffffdffffffffffffffffffffffffaaffffffffffff b ebbefffffffffffdfffffffffffffffffffffffdfffffffffffff cb bbbffffffffffffffdaffffffffffffffffffffffdfffffffffffff b ebbc gfffffffffffffffdffffffffffffffffffffffdfffffffffffff cb bbe gffffffffffffffffdfffffffffffffffffffffdfffffffffffff b cbbc gffffffffffffffffdaffffffffffffffffffffafffffffffffff cb ebe gfffffffffffffffffdfffffffffffffffffffaafffffffffffff b ebe gffffffffffffffffffdffffffffffffffffffdffffffffffffff cb bbc gffffffffffffffffffaafffffffffffffffffdffffffffffffff b cbb gfffffffffffffffffffdfffffffffffffffffdffffffffffffff cb ebe gfffffffffffffffffffgdffffffffffffffffdffffffffffffff bbe aa ca d ac d d aa d d d d a aa cc d d d d aa d d d d ca aa ac d d d d aa d d d dca adc d ``` <!-- end of image --> My goal is to determine if there's an intersection inside area A. <!-- image --> ```palette Key,Color ,#fefefeff a,#a268fbff b,#69145cff c,#e6d7f2ff d,#8539faff e,#965b8eff f,#c19fbcff g,#c6a3fcff ``` ```image dd cda gdg gdg adc dd da cda gdg gdc adc dd cda cdg gdg adc ad dd cda gdg gdg adc dd da cda cc a gdg cfbbe dg adc cebbbef dd adcfbbbbec gda dbbbbef adg fbbbbec cdd cebbbbe gda fbbbbeadg adg cebbbef adc cdd febbbec ad gda cebbbef da adg febbbec cda cddc cebbbef gdg gda febbbec gdg adg cebbbbf adc cddc febbbec dd gda cebbbbf da adg febbbec cda cddc cebbbbf gdg gda febbbec adc adg cebbbbfc ad cddc febbbec dd gda cbbbbfc cda adg fbbef gdg cddc ebbf gdg gda cbbbc adc adg fbbe dd cddc cebbf da gda cbbbc cda adg fbbe gdg cddc cebbf gdc gda fbbec adc adg ebbe dd cddc cebbf cda gda fbbec cdg adg ebbf gdg cddcebbf adc gdbbec ad ebbe dd cbbbddc cda fbbe gda gdg ebbf adg gdg cbbbc cddc adc cebbe gda dd cfbbbbf adg da febbbef cddc cda cebbbbfc gda gdg cfbbbbec adg adc febbbef cddc adc bbbbec gda dd bef adg cda c cddc cdg gda gdg adg adc cddc ad gda da adg cda cddc gdg gda gdg adg adc cddc dd gda da adg cda cddc gdg gda adc adg ad cddc dd ``` <!-- end of image --> There is 2 intersections point visible in this close-up of area A. Answer: A: 2; 2 = 2 I've identified a total of two intersection points.

<!-- image --> ```palette Key,Color ,#fefefeff a,#a66efbff b,#69145cff c,#e6d7f5ff d,#873bfaff e,#93578bff f,#be9ab9ff g,#c8a6fcff ``` ```image c d dd d gadc a d d gg ag gd a d dc d dc d d cd gd d d dc ca ga d gg d cd d ag dc d d d d dc cd d cd dc gg d d ac ga cd d d dc d ag d d d cd ca d dg gg ga d a d cd d dc dg d d d cd ca c dg ac ebe d dbbf cd ebb ag cbbf d d ebe d cd cbbf gg ag ebe ac d cbbf d cd ebb d ag cbbf d d cbbc ca cd eb gg ag be d d cbc d cd eb d ag be d d fbc ca bc cdeb ac cb be d b fb d d cb bb cd d b cbbf ag a cb ebbc d gg b fbbf cd ac cb ebe ag d b fbbc d d cb cbbf cd d b fbbc ag ca cb fbe d gg b ebf cd d cb cbbf ag d b fbbc d d cb fbe cd d bbf ag gg d ac cd d ag d d d d ca ag gg d a d d ag d d d d ca aa ac d d d d aa d d d dgg adc d ``` <!-- end of image -->

I'm curious to see if this image contains any intersection points. These spots mark what I'd call 'danger zones' - areas where intersections are more likely. <!-- image --> ```palette Key,Color ,#fefefeff a,#e4afa9ff b,#66b678ff c,#f1f3eeff d,#94c996ff e,#37a353ff f,#edcac6ff g,#b1d7b1ff ``` ```image f aa aaa a aa a aa a aa a aa a aa a aa a aa a aa a aa ca aa ca aa ca aa ca aa ca aa ca aa fa aa fa aa fa aa fa aa fa aa fa aa fa aa fa fa aa aa af aa faa af aa afa af aa ca a af fa aa a af fa a a af fa fa a af fa ac a ccccafccccccccccc fac ca ac ggggagggggggggggd fac af ac ggggagggggggggggd fac a af ggggagggggggggggd fac aa af ggggagggggggggggd fac ac af ggggagggggggggggd faf fa fa ggggagggggggggggd cddaaaaagdddddddddddddddddddddddagdddddaadddddd ggggagggggggggggd cggggggaaaaaggggggggggggggggggggaggggggaagggggg ggggagggggggggggd cggggggggggaaaaagggggggggggggggaagggggggagggggg ggggagggggggggggd cggggggggggggggaaaaagggggggggggaggggggggagggggg ggggagggggggggggd cggggggggggggggggggaaaaaggggggaaggggggggagggggg ggggagggggggggggd cggggggggggggggggggggggaaaaaggagggggggggagggggg gggbabbbddddggggd cggggggggggggggggggggggggggaaaagggggggggagggggg gggeaeeeeeeeeeeeeeeeeeeeeeeebbbddgggccc cgggggggggggggggggggggggggggggggggggggggagggggg ggggagggggggggggd ccgggdddbbeeeeeeeeeeeeeeeeeeebgggggggggggggggggggggggggggggggagggggg ggggagggggggggggd cggggdbeeeeeebdgggggggggggggggggggggggggagggggg ggggagggggggggggd cggggggggggdbeeeeeebdgggggggggggggggggggagggggg ggggagggggggggggd cggggggggggggggggbeeeeeebdggggggggggggggagdgggg ggggagggggggggggd cgggggggggggggggggggggdbeeeeeebbbeeeeeeeabegggg ggggagggggggggggd cgggggggggggggggggggggggggggdbeeebbbddggaaggggg ggggagggggggggggd cgggggggggggggggggggggggggggggggggggggggaaggggg ggggagggggggggggd cgggggggggggggggggggggggggggggggggggggggaaggggg ggggagggggggggggd cgggggggggggggggggggggggggggggggggggggggaaggggg ggggagggggggggggd cgggggggggggggggggggggggggggggggggggggggaaggggg ggggagggggggggggd cggggggggggggggggggggggggggggggggggggggggaggggg dddgadddddddddddg cggggggggggggggggggggggggggggggggggggggggaggggg fa cggggggggggggggggggggggggggggggggggggggggaggggg fa cggggggggggggggggggggggggggggggggggggggggaggggg fa cggggggggggggggggggggggggggggggggggggggggaggggg fa cggggggggggggggggggggggggggggggggggggggggaggggg fa cdgggggggggggggggggggggggggggggggggggggggaggggg fa ccccccccccccccccccccccccccccccccccccccccaccccc aa ac af ac af af af af af af af fa af fa af fa af ca ac ca ac ca ac a ac a a a ``` <!-- end of image --> My goal is to determine if there's an intersection inside area A. <!-- image --> ```palette Key,Color ,#fefefeff a,#e3ada7ff b,#5bb473ff c,#f3e6e3ff d,#8cca9cff e,#35a352ff f,#eecbc8ff g,#b8dec2ff ``` ```image caac caac caac caac caac caac caac caac caac caac faac faa faa faa faa faa faa faa faa faa faa faa faa gbaaadddddggggggcccc geaaaeeeeeeeeeeeeeeeeeeebb gbaaaeeeeeeeeeeeeeeeeeeeee aaf ccccggggggddddddbbb aaf aaf aaf aaf aaf aaf aaf aaf aaf aaf caaf caac caac caac caac caac caac caac caac caac caac caac ``` <!-- end of image --> There is 1 intersection point visible in this close-up of area A. Hmm, interesting. Let's check out another area. I'm now examining the contents of area B in detail. <!-- image --> ```palette Key,Color ,#fefefeff a,#e5aea9ff b,#64b679ff c,#f1eae6ff d,#8eca9dff e,#37a353ff f,#eecbc8ff g,#badfc4ff ``` ```image faaaaafcc aaa faa faaaaaaaafcc caaf faa cfaaaaaaaaafcc faa faa cfaaaaaaaaafcc caaf faa cfaaaaaaaaafcc faac faac cfaaaaaaaaaffc aaa caac cffaaaaaaaaffc faac caac cffaaaaaaaaffc aaa caac cffaaaaaaaaffc caaf caac cffaaaaaaaaffc faac caaf cffaaaaaaaaffc aaf aaf cffaaaaaaaaffc faac aaf cffaaaaaaaaaaa aaf cffaaaaaaf aaf cffaa aaa faa ebbbbbdddddgc faa eeeeeeeeeeeeeebdggc faa bbbbeeeeeeeeeeeeeeeebdgc faa ccgdbeeeeeeeeeeebddgc faa cggdbeeeeeeeeeeebdgg faac cgdbbeeeeeeeeeebbdgc caac cgdbeeeeeeeeeeebdggc caac cgddbeeeeeeeeeeebdgc caacccc cgdbeeeeeeeeeeebddgc ccgggdddbbbaabeee cggdbeeeeeeeeeeebdddbbbeeeeeeeeeeeeeeaabeee cgdbbeeeeeeeeeeeeeeeeeeeeeeeeebaadddg cgdbeeeeebbbbdddgggcc aaf cc aaf aaf aaa faa faa faa faa faa faac caac caac caac caac caaf aaf aaf aaf aaf aaa faa faa ``` <!-- end of image --> There is 1 intersection point visible in this close-up of area B. Answer: A: 1; B: 1; 1 + 1 = 2 The final answer is: two intersections found.

<!-- image --> ```palette Key,Color ,#fefefeff a,#e5aea9ff b,#5bb473ff c,#f2e2dfff d,#87c596ff e,#35a352ff f,#ebc3bfff g,#b5ddc0ff ``` ```image c aa aaa a aa a aa a aa a aa a aa a aa a aa a aa a aa a aa ca aa ca aa ca aa ca aa ca aa ca aa ca aa fa aa fa aa fa aa fa aa fa fa fa ff fa aa ff fa caa af fa afa af fa a a af fa aa a af fa a a af fa fa a ac fa ac a ac fa ca ac ac fa af ac ac fa a ac ac fa fa af ac fa ac af ac fac ca ff a faaaac ac fa a cfaaaac ca fa a cfaaaac af ca a cfaaaac a ca a cfaaaac fa a a cfaaaac ac a baddggggc cfaaa a baeeeeeeeeeeeeeeeeeeeeeeebbdddgggcc a a ccgggdddbbbeeeeeeeeeeeeeeeeebg a a cdbeeeeedg a a gdeeeeebdc ac a cgbeeeeebg acc a gdeeeeeeddbeeeeeeeade a gbeebbdggc af ca af ca fa ca fa ca ca ca ca ca ca ca a fa a fa a fa a fa a fa a ff ac af ac af ac af af af af af fa ac fa ac ca ac ca ac ca ac a ac a ac a a a ``` <!-- end of image -->

Time to put on my detective hat and find those intersection points! Could these regions be concealing intersection points? Let's find out. <!-- image --> ```palette Key,Color ,#fefefeff a,#16b528ff b,#c92eb3ff c,#b0d6b1ff d,#efefeeff e,#50be5bff f,#d587c9ff g,#93cb94ff ``` ```image ddddddddddddddddddddd ccccccccccccccccccccgd cccccccccccfbbbbfccccd cccccccccccbbbbbbbbbcd caa cccccccccccbbbbbbbbbbbbf aaae cccccccccccbbbcfbbbbbbbbbbbd aaaad ccccccccccbbbbcccccbbbbbbbbbbbf aaaaa ccccccccccbbbccccccccdfbbbbbbbbbbfd daaaaae ccccccccccbbbccccccccd dbbbbbbbbbbbf caaaaaad cccccccccfbbbccccccccd fbbbbbbbbbbfd eaaeaaaa cccccccccbbbfccccccccd dbbbbbbbbbbbf aaagdaaae ccgacccccbbbcccccccccd fbbbbbbbbbbfd aaad gaaad ccaaaagccbbbcccccccccd dbbbbbbbbbbbf aaa aaaa ccaaaaaabbbbcccccccccd dfbbbbbbbbbb aaa aaae ccgaaaaabbbccccccccccd fbbbbbbbf daaa gaaac cccccaaabbbaeccccccccd dfbbbb gaaa aaaa cccccccgbbbaaaaccccccd bbb eaae aaae cccccccbbbeaaaaaaccccd bbbf aaac gaaac cccccccbbbceaaaaaaagcd fbbb aaad aaaa cccccccbbbcccgaaaaaaac bbb aaa aaaa ccccccbbbbcccccgaaaaaaag cggggbbbfggggggaaagggggg caaac ccccccbbbcccccccccaaaaaaag gccccfbbbcccccgaaaccccccd aaaa ccccccbbbcccccccccccaaaaaaae gcccccbbbccccceaaaccccccd aaaa cccccfbbbccccccccccccdeaaaaaaad gcccccbbbbccccaaaeccccccd caaac cccccbbbfccccccccccccd gaaaaaaad gcccccfbbbccccaaagccccccd aaaa cccccbbbcccccccccccccd caaaaaaac gccccccbbbccccaaacccccccd aaaa cccccbbbcccccccccccccd daaaaaaac gccccccbbbbcccaaacccccccd caaag ccccbbbbcccccccccccccd daaaaaaag gccccccfbbbcccaaacccccccd aaaa ccccbbbccccccccccccccd eaaaaaae gcccccccbbbccaaaacccccccd aaae ccccbbbccccccccccccccd eaaaaaae gcccccccbbbbcaaagcccccccd cac cccfbbbcccccccccccccgd gaaaaaaad gccccccccbbbeaaaccccccccd dddbbbfdddddddddddddd caaaaaaadgccccccccbbbeaaeccccccccd bbb caaaaaaagcccccccbbbbaacccccccccd dbbb daaaaaaaeccccccbbbaecccccccccd bbbb daaaaaaaeccccbbbeccccccccccd bbbd aaaaaaaeccbbbbccccccccccd bbb gceaaaaaaaabbbccccccccccd f gccceaaaaaabbbfcccccccccd gcccccgaaaabbbbcccccccccd gcccccccgaaabbbcccccccccd gcccccccccccbbbfccccccccd gcccccccccccfbbbccccccccd gccccccccccccbbbccccccccd gccccccccccccbbbfcccccccd gccccccccccccfbbbcccccccd gcccccccccccccbbbcccccccd gcccccccccccccbbbfccccccd gcccccccccccccfbbbccccccd gccccccccccccccbbbccccccd d gccccccccccccccbbbbcccccd bbbf cgggggggggggggggbbbggggg bbb bbbd bbb bbbb fbbb dbbb bbbf bbbd bbbd bbbb bbb dbbb dbbb bbbd fbbb bbbb bbbf dbbb bbbd bbbf bbb fbbb dbbb bbb fbbb bbbf bbbf fbbb bbb bbb bbb bbbf dbbb fbbb fbbf bbb bbbf bbbf bbb fbbb bbb bbb fbbb bbbf bbbf fbbb bbbd bbbdbbb bbbbbbb dbbbbbb bbbbbf bbbbbd dbbbb bbbb bbbb bbd ``` <!-- end of image --> I wonder what we'll find inside area A? <!-- image --> ```palette Key,Color ,#fefefeff a,#17b529ff b,#ca2db3ff c,#b9e8bfff d,#ecb8e5ff e,#6dce78ff f,#db72cbff g,#7a6c76ff ``` ```image ddd fbbbbfd dbbbbbbbbbfd fbbbbbbbbbbbbfd bbbbbbbbbbbbbbbbbfd dbbbbbbbbbbbbbbbbbbb fbbbbbbbbbbbbbbbbbbb bbbbbbbbbbbbbbbbbbbb dbbbbbbd ddfbbbbbbbbb fbbbbbb dfbbbbbb fbbbbbb dffbb bbbbbbf d dbbbbbbd fbbbbbb bbbbbbf dbbbbbbd fbbbbbb fbbbbbb bbbbbbf c dbbbbbbd caae fbbbbbb eaaaaec bbbbbbf aaaaaaaec dbbbbbbd eaaaaaaaaaec fbbbbbb aaaaaaaaaaaaabbbbbbb eaaaaaaaaaaaabbbbbbf eaaaaaaaaagbbbbbbd eaaaaaaagbbbbbbe caaaaabbbbbbgaaec caaabbbbbbgaaaaec cgbbbbbbaaaaaaaac fbbbbbbaaaaaaaaaac bbbbbbgaaaaaaaaaaaae dbbbbbbeaaaaaaaaaaaaaae fbbbbbb caaaaaaaaaaaaaaec bbbbbbf caaaaaaaaaaaaaaec dbbbbbbd ceaaaaaaaaaaaaa fbbbbbb ceaaaaaaaaaaa fbbbbbb ceaaaaaaaaa bbbbbbf eaaaaaaa dbbbbbbd eaaaaa fbbbbbb caaa bbbbbbf ce dbbbbbbd fbbbbbb fbbbbbf bbbbbbf dbbbbbbd fbbbbbb bbbbbbf dbbbbbbd fbbbbbb fbbbbbf bbbbbbf dbbbbbbd fbbbbbb bbbbbbf dbbbbbbd ``` <!-- end of image --> 1 intersection present within area A. Now, let's turn our attention to the next spot. I'm eager to see what's happening in this magnified view of area B. <!-- image --> ```palette Key,Color ,#fefefeff a,#15b527ff b,#c92db2ff c,#c6eccaff d,#eaafe1ff e,#4cba58ff f,#d969c8ff g,#8ad993ff ``` ```image bbbbbbf aaaaaag fbbbbbb aaaaaac dbbbbbbd caaaaaac bbbbbbf gaaaaaa fbbbbbb gaaaaaa dbbbbbbd eaaaaae bbbbbbf eaaaaag fbbbbbb aaaaaag dbbbbbbd caaaaaac bbbbbbf caaaaaac fbbbbbb gaaaaaa dbbbbbbd gaaaaae bbbbbbf eaaaaae fbbbbbb aaaaaag dbbbbbbd aaaaaag bbbbbbf gaaaaaac fbbbbbb eaaaaaa dbbbbbbd caaaaaae bbbbbbb eaaaaaac fbbbbbbdcaaaaaae dbbbbbbfgaaaaaag bbbbbbbaaaaaaa dbbbbbbeaaaaag c bbbbbbbaaaaa aec fbbbbbbaaaag aaaeg dbbbbbbeaaac aaaaaag bbbbbbbaae aaaaaaaagc fbbbbbbaac aaaaaaaaaaec dbbbbbbee aaaaaaaaaaaaec bbbbbbbg eaaaaaaaaaaaaaec bbbbbbb ceaaaaaaaaaaaaaeg gebbbbbbd cgaaaaaaaaaaaaaaaabbbbbbf gaaaaaaaaaaaaaabbbbbbb gaaaaaaaaaaaaebbbbbbd geaaaaaaaaaabbbbbbf ceaaaaaaaabbbbbbb ceaaaaaaebbbbbbd ceaaaaabbbbbbf cgeecfbbbbbb dbbbbbbd bbbbbbf fbbbbbb dbbbbbbd bbbbbbb dbbbbbbd dbbbbbbf fbbbbbb dbbbbbbd bbbbbbf fbbbbbb dbbbbbbd bbbbbbf fbbbbbb dbbbbbbd bbbbbbf fbbbbbb dbbbbbbd bbbbbbf fbbbbbb ``` <!-- end of image --> 1 intersection present within area B. Answer: A: 1; B: 1; 1 + 1 = 2 There are precisely two intersections present in the image.

<!-- image --> ```palette Key,Color ,#fefefeff a,#16b527ff b,#ca2eb3ff c,#c6eccaff d,#efc1e8ff e,#4abe57ff f,#df82d1ff g,#8cd694ff ``` ```image dd dbbbbf bbbbbbbbbd caa bbbbbbbbbbbbf aaae dbbb fbbbbbbbbbbbd aaaa bbbb dbbbbbbbbbbbf aaaaa bbbd fbbbbbbbbbbfd aaaaae bbb dbbbbbbbbbbbf gaaaaaac fbbb fbbbbbbbbbbfd eaaeaaaa bbbf dbbbbbbbbbbbd aaag aaae ca bbb fbbbbbbbbbbf aaac gaaac aaaac dbbb dbbbbbbbbbbbd aaa aaaa aaaaaabbbb fbbbbbbbbbb aaa aaae caaaaabbbd dbbbbbbbf caaa gaaac eaabbbae fbbbb gaaa aaaa gbbbaaae bbb eaae aaae bbbeaaaaaa bbbf aaag gaaac bbb gaaaaaaac fbbb aaa aaaa dbbb caaaaaaac bbb aaa aaaa bbbb caaaaaaag bbbf aaa gaaac bbbd aaaaaaag fbbb caaa aaaa bbb eaaaaaae bbb gaaa aaaa fbbb eaaaaaae bbbf eaag caaag bbbf gaaaaaaac dbbb aaac aaaa bbb caaaaaaac bbb aaa aaaa dbbb caaaaaaag bbbf aaa caaag bbbb aaaaaaag dbbb aaa eaaa bbbd eaaaaaae bbbd eaaa aaae bbb eaaaaaae bbbb aaac cac fbbb gaaaaaaa dbbbgaaa bbbf gaaaaaaac bbbeaag bbb caaaaaaac bbbbaa dbbb caaaaaaag bbbae bbbb aaaaaaae bbbe bbbd eaaaaaae bbbb bbb gaaaaaaaabbb d gaaaaaabbbd caaaabbbb caaabbb bbbf fbbb bbb bbbf fbbb bbb bbbf dbbb bbb bbbf bbbd dbbb bbb bbb bbb bbbb dbbb dbbb bbbf bbbd bbbd bbbb bbb dbbb bbb bbbd fbbb bbbb bbbf bbb bbbd bbbd bbb fbbb dbbb bbb fbbb bbbf bbbf fbbb bbb bbb bbb bbbf dbbb fbbb fbbf bbb bbbd bbbf bbb fbbb bbb bbb fbbb bbbf bbbf dbbb bbbd bbb bbb bbbbbbb dbbbbbb bbbbbf bbbbb dbbbb bbbb bbbb bb ``` <!-- end of image -->

I'm analyzing this image to identify any points where lines intersect. 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,#0f7074ff b,#f9e25bff c,#539a92ff d,#c7d687ff e,#b1d7b1ff f,#95c897ff g,#fcf0acff ``` ```image c aa fa ac ca fffbdacfffff eeebdaaeeeee eeebdfafeeee eeebbeaaeeee eeebbefaeeee eeebbeeaaeee eeebbeecaeee eeebbeeeacee eeedbeeecaee eeedbeeeeace eeedbeeeeaae eeedbeeeefaf eeeebeeeeeaa eeeebeeeeefa eeeebeeeeeeac eeeebdeeeeeca eeeebdeeeeeeac eeeebdeeeeeeca eeeebdeeeeee ae ffffbbffffff aa gb a bg aa efffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffe bb ea feeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeef b ac feeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeef bb ca feeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeef gb ac feeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeafeef bg ca feeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeaaeeef bb ae feeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeaaeeeef b aa feeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeaaeeeeef bb a feeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeaaeeeeeef gb aa feeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeaaeeeeeeef bg ea feeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeaaeeeeeeeef bb ac feeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeaaeeeeeeeeef b ca feeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeaaeeeeeeeeeef bb ac feeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeaaeeeeeeeeeeef gb ca feeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeaaeeeeeeeeeeeef bg ae feeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeaaeeeeeeeeeeeeef bb aa feeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeaaeeeeeeeeeeeeeef gb a feeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeaaeeeeeeeeeeeeeeef bg aafeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeaaeeeeeeeeeeeeeeeef gb eafeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeaaeeeeeeeeeeeeeeeeef bg aaeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeaaeeeeeeeeeeeeeeeeeef bb caeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeaaeeeeeeeeeeeeeeeeeeef gb aceeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeaaeeeeeeeeeeeeeeeeeeeef bg aaeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeaaeeeeeeeeeeeeeeeeeeeeef bb fafeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeaaeeeeeeeeeeeeeeeeeeeeeef b faaeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeefaaeeeeeeeeeeeeeeeeeeeeeeef bb ffafeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeefaaeeeeeeeeeeeeeeeeeeeeeeeef gb feaaeeeeeeeeeeeeeeeeeeeeeeeeeeeeeefaaeeeeeeeeeeeeeeeeeeeeeeeeef bg fecaeeeeeeeeeeeeeeeeeeeeeeeeeeeeefaaeeeeeeeeeeeeeeeeeeeeeeeeeef bb feeaceeeeeeeeeeeeeeeeeeeeeeeeeeefaaeeeeeeeeeeeeeeeeeeeeeeeeeeef b feecaeeeeeeeeeeeeeeeeeeeeeeeeeefaadeeeeeeeeeeeeeeeeeeeeeeeeeeef bb feeeaceeeeeeeeeeeeeeeeeeeeeeeefaadeeeeeeeeeeeeeeeeeeeeeeeeeeeef gb feeeaaeeeeeeeeeeeeeeeeeeeeeeefaadeeeeeeeeeeeeeeeeeeeeeeeeeeeeef bg feeeeafeeeeeeeeeeeeeeeeeeeeefaadeeeeeeeeeeeeeeeeeeeeeeeeeeeeeef bb feeeeaaeeeeeeeeeeeeeeeeeeeefaadeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeef b feeeefaeeeeeeeeeeeeeeeeeeefaadeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeef bb feeeeeaaeeeeeeeeeeeeeeeeefaadeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeef gb feeeeecaeeeeeeeeeeeeeeeefaadeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeef bg feeeeeeaceeeeeeeeeeeeeefaadeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeef bb feeeeeecaeeeeeeeeeeeeedaaeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeef gb feeeeeeeaceeeeeeeeeeedaaeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeef bb feeeeeeeaaeeeeeeeeebdaaeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeef gb feeeeeeeeafeeeeeeebdaaeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeef bgfeeeeeeeeaaeeeeebbdaaeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeef bbfeeeeeeeefaeeeebbfaaeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeef gbfeeeeeeeeeaaebbbfaaeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeef bdeeeeeeeeecabbdcaaeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeef bbeeeeeeeeebacecaaeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeef bdeeeeeedbbcacaaeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeef bbeeeeebbbeeaaaeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeef dbeeedbbdeeeaceeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeef fbdebbbeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeef fbbbbdeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeef febbeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeef feeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeef feeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeef feeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeef ``` <!-- end of image --> I'm now examining the contents of area A in detail. <!-- image --> ```palette Key,Color ,#fefefeff a,#0c6f75ff b,#fbe259ff c,#6fa9acff d,#fdf4c3ff e,#b1d0d2ff f,#39898eff g,#fbeb91ff ``` ```image deaaa gbbdfaae gbbdeaaf gbbd aaae dbbg caaf dbbg aaae dbbg caac dbbg eaaa dbbg faac bbb eaaa bbb faae bbb eaaf bbb aaae bbb caaf bbb aaae gbbd caac gbbd eaaa gbbd faac gbbd eaaa gbbd faae dbbg eaaf dbbg aaae dbbg caaf dbbg aaae dbbg caac bbb eaaa bbb faa bbb eaa bbb fa bbb ea bbbd a gbbd c gbbd gbbd gbbd gbbd dbbg dbbg dbbg ``` <!-- end of image --> There is no intersection present within area A. Alright, let's examine the next area. I'm determined to find out if an intersection exists in area B. <!-- image --> ```palette Key,Color ,#fefefeff a,#0e7075ff b,#fae35eff c,#509489ff d,#dce9eaff e,#9dc3c2ff f,#afbe68ff g,#fcf4c6ff ``` ```image ed caad caaac caaac caaac caaac aaac caac caac caac caaa caaac caaac caaac caaac aaac caac caac caac caaa caaaf caaaf caaaf aaaf caaf caaf caaf e caaa a caaaf ae caaaf ac caaaf aac caaaf aaad daaaf caae dcaaf eaaa dcaaf caa dcaaf eaa dcaaa aae dcaaaf eac dcaaaf daad daaaaf daad daaafg aae daaafg aaa daaafg caae daaafg eaaa daaaag aaae daaaaf eaac daaaafg daaad daaaafg daaad aaaafg caae daaafg eaaa daaafg aaae daaafg eaac daaafg aaae daaaag eaac daaaaf daaa daaaafg caa daaaafg cae aaaafg eaa daaafg aae daaafg eac daaafg aae daaafg aac eaaaag aaad eaaaaf caac faaaag daaad faaaad eaaa gbfaaad aaae gbbfaaad eaac gbbfaaad aaae gbbbfaaad eaac gbbbfaaaa daaad gbbbfaaacd caac gbbbfaaacd daaad gbbbbeaaacd b eaaa gbbbbbgaaacd bg aaagbbbbb eaacd bb eaabbbbg eaacd bb daafbb eaacd bbg gbcacg eaaad bbb gbbbaad eaaac bbbg gbbbbbcaceaaacd gbbg gbbbbb daaaaac gbbb bbbbbg aaaac gbb gbbbbg cac bbg gbbbb d bbg gbbbbb gbb gbbbbb bbbbbbbg gbbbbb bbbg bb ``` <!-- end of image --> Amazing! This area was hiding 2 intersections all along! Answer: A: 0; B: 2; 0 + 2 = 2 The image features two intersection points.

<!-- image --> ```palette Key,Color ,#fefefeff a,#0d6f74ff b,#f8e15cff c,#6fa9adff d,#eef1e1ff e,#a9cbcbff f,#3a898cff g,#fcefa6ff ``` ```image f af ca ac fa bgae bgaa bgdad bg aa bb ea bb af bb ca bb ac gb fa gb ae gb aa db dad db aa b ea b af bd ca bg ac bg fa bg ae bb aa gb dad bg aa bb ea bd af bb ca gb ac ad bg fa aa bb ae aa db aa aa bb dad aa gb aa aa bg ea aa bb af aa db ca aa bb ac aa gb fa aa bg ae aa bb aa aa db dad aa bg aa aa gb ea aa bd af daa bb ca daa gb ac daad bg fa daad bb ae daad bd aa daad bb dad daad gb aa daad bg ea daad bb af daad bd ca daad bb ac daad gb fa daad bg ae daad bb aa daad db dad daad bb aa eaad gb ea eaad bg af eaad bb ca baa db ac dbaa bg fa bbaf gb ae dbbaf bd aa bbbaf bb ead dbbeaf gb aa bbbeaf bg eabbgeaf bb baf eaf bd dbbfaeaf bb bbb aaf gb dbbg ff bg bbb bbbbg bb ``` <!-- end of image -->

I'm examining this image closely. My goal: find any and all intersections. The image has some tight areas where segments are too close. I should investigate those closely. <!-- image --> ```palette Key,Color ,#fefefeff a,#cf6b19ff b,#d20b62ff c,#efbdbeff d,#d19f71ff e,#d7548bff f,#b1d7b1ff g,#98c895ff ``` ```image c ebb bbbb bbbb cbbbbe bbbbbb bbbbbbe bbbcbbb c ebbb bbbe cebbbbb bbbc ebbb cebbbbbbbbbb bbb bbbc cebbbbbbbbbbbbbbbb cbbb ebbb cebbbbbbbbbbbbbbec cbbb aaa ebbb bbbc cebbbbbbbbbbbbbec bbbe aaa bbbc ebbb ebbbbbbbbbbbbec cbbb aaa bbb bbbc cbbbbbbbbbbbec bbbc aaa cbbb bbbb cebbbbbbbbbbbc ebbb aaa ebbe bbb ebbbbbbbbbbbc bbbc aaa bbbc bbbbbbbbbbbbe bbbb aaa bbb bbbbbbbec bbb aaa cbbb bbbbc bbbb aaa bbbe cbbb aaa bbb bbbe aaa bbb cbbb aaa ebbb fgggbbbeggggggaaaggg bbbe gfffebbbffffffaaafff bbb gffffbbbdfffffaaafff bbb gffffbbbbfffffaaafff ebbb gfffffbbbfffffaaafff bbbc gfffffbbbbffffaaafff ggggggggggbbbggggggf gffffffbbbffffaaafff fffffffffgbbbffffffg gffffffbbbefffaaafff fffffffffebbbffffffg gffffffdbbbffgaaafff fffffffffbbbdffffffg gfffffffbbbefgaaafff fffffffffbbbfffffffg gfffffffebbbfgaaafff ffffffffdbbbfffffffg gffffffffbbbdgaaafff ffffffffbbbefffffffg caaa gffffffffebbbdaaafff ffffffffbbbgfffffffg caaaaaaac gfffffffffbbbdaaafff ffffffffbbbffffffffg caaaaaaaaaaac gfffffffffbbbbaaafff fffffffebbbffffffffg caaaaaaaaaaaaaaac gffffffffffbbbaaafff fffffffbbbeffffffdaaaaaaaaaaaad aaac gffffffffffbbbaaafff fffffffbbbfffdaaaaaaaaaaaad aaac gffffffffffdbbaaafff fffffffbbbaaaaaaaaaaaad aaac gfffffffffffbaaaafff fffffdaaaaaaaaaaaadg aaad gfffffffffffeaaaafff ffaaaaaaaaaaaadffffg aaad gffffffffffffaaaafff ffaaaaaaaadffffffffg aaad gffffffffffffaaaafff ffaaaaabbffffffffffg daad gffffffffffffdaaafff ffgffebbbffffffffffg daad gffffffffffffdaaadff fffffbbbdffffffffffg daad gffffffffffffaaadfff fffffbbbfffffffffffg daad gffffffffffffaaadfff ffffdbbbfffffffffffg daad gffffffffffffaaadfff ffffebbbfffffffffffg daad gffffffffffffaaadfff ffffbbbdfffffffffffg daaa gffffffffffffaaadfff ffffbbbffffffffffffg daaa gffffffffffffaaadfff fffdbbbffffffffffffg daaa gffffffffffffaaadfff fffbbbeffffffffffffg caaa gffffffffffffaaadfff fffbbbfffffffffffffg caaa gffffffffffffaaadfff fffbbbfffffffffffffg caaa gffffffffffffaaadfff ffebbbfffffffffffffg caaa gffffffffffffaaagfff bbbe caaa fggggggggggggaaagggg bbb caaa aaac ebb caaa aaa caaa aaa caaa aaa aaa aaa aaa aaa aaa aaa aaa aaa aaa aaa aaa aaa aaa aaa aaa aaa aaa aaa aaa aaa aaa aaa aaa aaa aaa ccddaaaa aaa ccddaaaaaaaaaaaaaaaa aaa ccddaaaaaaaaaaaaaaaaaaaaaaaaaaaa aaa ccddaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaddc aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaddcc aaaaaaaaaaaaaaaaaaaddcc daaaaaaddcc ``` <!-- end of image --> I'm analyzing this close-up of area A with precision. <!-- image --> ```palette Key,Color ,#fefefeff a,#cf6b1aff b,#d30b62ff c,#eb96bbff d,#de9b64ff e,#df518eff f,#eac19fff g,#f6d8dcff ``` ```image ebbbbbb bbbbbbe gbbbbbbc cbbbbbbg ebbbbbe bbbbbbe gbbbbbbc cbbbbbb ebbbbbe bbbbbbc cbbbbbbg ebbbbbb bbbbbbe gbbbbbbc cbbbbbbg ebbbbbb bbbbbbe gbbbbbbc cbbbbbbg ebbbbbb g bbbbbbe gfdaa gbbbbbbc gfdaaaaaa cbbbbbbg gfdaaaaaaaaaa ebbbbbe gfdaaaaaaaaaaaaaa bbbbbbaaaaaaaaaaaaaaaaaaa cbbaaaaaaaaaaaaaaaaaaaaaaa gfdaaaaaaaaaaaaaaaaaaaaaaaadf gfdaaaaaaaaaaaaaaaaaaaaaaaadfg daaaaaaaaaaaaaaaaaaaaaaaadfg daaaaaaaaaaaaaaaaaaaadfg faaaaaaaaaaaaaaaadfg gaaaaaaaaaaaaaeg aaaaaaaaabbbbc daaadfcbbbbbbg gfg ebbbbbb bbbbbbe gbbbbbbc cbbbbbbg ebbbbbb bbbbbbe gbbbbbbc cbbbbbb ebbbbbe bbbbbbc cbbbbbbg ebbbbbb ebbbbbe gbbbbbbc cbbbbbbg ebbbbbb bbbbbbe gbbbbbbc cbbbbbbg ebbbbbb bbbbbbe gbbbbbbc ``` <!-- end of image --> Yes! I knew it! There's 1 intersection right here in area A! Now, let's dive into another area. I'm determined to find out if an intersection exists in area B. <!-- image --> ```palette Key,Color ,#fefefeff a,#cf6b18ff b,#d30b63ff c,#e9afa0ff d,#d88646ff e,#e15e96ff f,#d04139ff g,#f3d4cfff ``` ```image bbbbbbb daaaaac cbbbbbbc daaaaac bbbbbbb daaaaac ebbbbbbc aaaaaac gbbbbbbb aaaaaac ebbbbbbg aaaaaac gbbbbbbe aaaaaac ebbbbbbg aaaaaac cbbbbbbe aaaaaac bbbbbbb aaaaaac cbbbbbbe aaaaaag bbbbbbb aaaaaag ebbbbbbc aaaaaag gbbbbbbb aaaaaag ebbbbbbg aaaaaag gbbbbbbe gaaaaaag ebbbbbbg gaaaaaag cbbbbbbe gaaaaaag bbbbbbb gaaaaaag cbbbbbbe gaaaaaag bbbbbbb gaaaaaag ebbbbbbc gaaaaaag gbbbbbbb gaaaaaag ebbbbbbg gaaaaaa gbbbbbbe gaaaaaa ebbbbbbggaaaaaa gbbbbbbegaaaaaa bbbbbbbcaaaaaa cbbbbbbeaaaaaa bbbbbbfaaaaaa ebbbbbfaaaaaa bbbbbfaaaaaa ebbbbfaaaaaa gbbbbfaaaaaa ebbbfaaaaaa gbbbfaaaaad bbbfaaaaad cbbfaaaaad bbfaaaaad ebfaaaaad bfaaaaad efaaaaad gfaaaaaa faaaaafg daaaaafe daaaaafbg daaaaafbe daaaaafbc daaaaad daaaaad daaaaac daaaaac daaaaac daaaaac daaaaac daaaaac daaaaac daaaaac aaaaaac aaaaaac aaaaaac aaaaaac aaaaaac aaaaaac aaaaaac aaaaaac aaaaaag aaaaaag aaaaaag aaaaaag gaaaaaag ``` <!-- end of image --> As I suspected, there's 1 intersection within area B. Answer: A: 1; B: 1; 1 + 1 = 2 I can confirm there's two intersections in there.

<!-- image --> ```palette Key,Color ,#fefefeff a,#cf6b19ff b,#d30b62ff c,#ea91b8ff d,#dd9960ff e,#de4a8bff f,#e9be9aff g,#f5d6d7ff ``` ```image c ebb bbbb bbbb cbbbbe bbbbbb bbbbbbe bbbcbbb g ebbb bbbc cebbbbb bbbc cbbb cebbbbbbbbbb bbb bbbc cebbbbbbbbbbbbbbbe gbbb ebbb cebbbbbbbbbbbbbbeg gbbb aaa ebbb bbbg gebbbbbbbbbbbbbeg bbbe aaa bbbc ebbb cbbbbbbbbbbbbeg cbbb aaa bbb bbbg cbbbbbbbbbbbeg bbbc aaa gbbb bbbb gebbbbbbbbbbbc ebbb aaa ebbe bbbgebbbbbbbbbbbc bbbg aaa bbbg bbbbbbbbbbbbeg ebbb aaa bbb gbbbbbbbeg bbb aaa cbbb bbbbc bbbb aaa bbbe gbbb aaa bbbg bbbe aaa bbb cbbb aaa cbbb bbbc aaa bbbc ebbb aaa bbb bbbg aaa gbbb ebbb aaa ebbb bbb aaa bbbc bbbb aaa bbb gbbb aaa gbbb bbbe gaaa ebbe cbbb gaaa bbbg bbbc gaaa bbb cbbb gaaa cbbb bbbcgaaa bbbe faaa ebbbfaaa bbbg faaaaaaag bbbfaaa bbb faaaaaaaaaaaf bbbbaaa cbbb faaaaaaaaaaaaaaaf gbbbaaa bbbe faaaaaaaaaaaadg aaaf bbbaaa bbb faaaaaaaaaaaadg aaaf gbbaaa bbbaaaaaaaaaaaadg aaaf baaaa faaaaaaaaaaaadg aaaf caaad aaaaaaaaaaaadg aaaf aaaa aaaaaaaadg daad aaaa aaaaabb daad daaag gg ebbb daad daaac bbbc daad daad bbb daad daad gbbb daad daad ebbe daad aaaf bbbg daad aaaf bbb faaa aaaf cbbb faaa aaaf bbbe faaa aaaf bbbg faaa aaaf bbb faaa aaag cbbb faaa aaag bbbc faaa aaag bbb gaaa aaag ebb gaaa aaag gaaa aaag gaaa aaa gaaa aaa gaaa aaa aaa aaa aaa aaa aaa aaa aaa aaa aaa aaa aaa aaa aaa aaa aaa aaa aaa aaa aaa aaa aaa gfddaaaa aaa gffdaaaaaaaaaaaaaaaa aaa gffdaaaaaaaaaaaaaaaaaaaaaaaaaaaa aaa gffdaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaddffg aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaadffg aaaaaaaaaaaaaaaaaaadffg daaaaaadffg ``` <!-- end of image -->

Hmm, I'm not sure what to expect from this image. Let's see if any lines cross. These spots mark what I'd call 'danger zones' - areas where intersections are more likely. <!-- image --> ```palette Key,Color ,#fefefeff a,#d9c181ff b,#bb977dff c,#e1d0b0ff d,#a2cfa2ff e,#f0f4edff f,#b2d7b1ff g,#c0bb98ff ``` ```image eaaae caaaaae aaaaaaaae aaacaaaaaa eeecgeeeeeeaaaeecaaaaaa ddbbbdddddaaagddddgaaaaaa ffbbbgffffaaafffffffgaaaaaa fffbbbffffaaafffffffd caaaaaa fffbbbgfffaaafffffffd caaaaaa fffgbbbffaaagfffffffd caaaaaa ffffbbbffaaaffffffffd caaaaaa ffffgbbbfaaaffffffffd caaaaaa fffffbbbfaaaffffffffd caaaaaa fffffbbbbaagffffffffd caaaaaa ffffffbbbaafffffffffd caaaaaa ffffffbbbaafffffffffd caaaaaa ffffffdbbbafffffffffd caaaaaa fffffffbbbgfffffffffd caaaaaa fffffffbbbbfffffffffd caaaaaa fffffffabbbfffffffffd caaaaaa fffffffabbbgffffffffd caaaaaa bbb ffffffgaabbbffffffffd caaaaaa bbb ffffffaaabbbgfffffffd caaaaac bbb ffffffaaafbbbfffffffd caaaaac bbb ffffffaaafbbbfffffffd aaaaaac bbb fffffgaagfgbbbffffffd aaaaaac eeeeeeeeeeeeeebbgeee fffffaaafffbbbffffffd aaaaaacdddddddddddddgbbgddd fffffaaafffgbbbfffffd aaaaaaafffffffffffgbbgfff fffffaaaffffbbbfffffd aaaaaaafffffffffbbbffff ffffgaagffffbbbgffffd aaaaaaafffffffbbbffff ffffaaaffffffbbbffffd edaaaaaaafffffbbbffff ddddaaaddddddbbbddddd edffaaaaaaafffbbbffff aaa cbbb edffffaaaaaaafbbbffff caac bbb edffffffaaaaaabbbffff aaae cbbb edffffffffaaaabbgffff aaa bbb edffffffffffabbbgffff aaa bbbc edfffffffffffbbbfffff caac bbb edfffffffffffbbbfffff aaae bbbc edfffffffffffbbbfffff aaa ebbb edfffffffffffbbbfffff ca bbbe edfffffffffffbbbfffff cbbb edfffffffffffbbbfffff bbb edffffffffffgbbbfffff gbbg edffffffffffgbbafffff bbb edffffffffffbbbafffff bbbc edffffffffffbbbafffff ebbb edffffffffffbbbafffff bbbe edffffffffffbbbagffff cbbb edffffffffffbbbagffff bbb edffffffffffbbbagffff gbbg edfffffffffdbbbaaffff bbb edfffffffffgbbbaaffff bbbc edfffffffffbbbaaaffff ebbb edfffffffffbbbaaaffff bbbe edfffffffffbbbaaaffff cbbb edfffffffffbbbaaaffff bbb edfffffffffbbbaaaffff cbbg edfffffffffbbbaaaffff bbb edfffffffffbbbaaaffff bbbc edffffffffgbbgaaaffff ebbb edffffffffgbbgaaaffff bbbe edffffffffbbbfaaaffff ebbb edffffffffbbbfaaaffff bbbe edffffffffbbbfaaaffff cbbb edffffffffbbbfaaaffff bbb edffffffffbbbfgaaffff gbbg edffffffffbbbfgaagfff bbb edfffffffgbbgfgaagfff bbbc edfffffffgbbgffaagfff ebbb edfffffffbbbfffaaafff bbbe edfffffffbbbfffaaafff cbbb edfffffffbbbfffaaafff bbb edfffffffbbbfffaaafff gbbg edfffffffbbbfffaaafff bbb edfffffffbbbfffaaafff bbbc edffffffdbbbfffaaafff ebbb edffffffgbbgfffaaafff bbbceeeeeeeeeee edffffffbbbdfffaaafff cbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbffffaaafff bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbffffaaafff cccgggggggggbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbffffffffff edfffffffffffffffffff edddddddddddddddddddd ``` <!-- end of image --> Eureka! Let's inspect this close up of area A <!-- image --> ```palette Key,Color ,#fefefeff a,#d9c080ff b,#bb977dff c,#e3d2b8ff d,#ccb19dff e,#ede4d4ff f,#e1cd99ff g,#f7f3edff ``` ```image gcbd eaaaaaf gcaaaaaaa edbbbbe caaaaac gcaaaaa dbbbbbd faaaaae gcaaa ebbbbbbg aaaaaag gca bbbbbbc gaaaaaf g cbbbbbb caaaaac gbbbbbbc faaaaae dbbbbbd aaaaaag gbbbbbbe gaaaaaf dbbbbbd eaaaaac ebbbbbbg faaaaae bbbbbbc aaaaaag cbbbbbbg gaaaaaa gbbbbbbc eaaaaac cbbbbbb faaaaae gbbbbbbe aaaaaag dbbbbbdgaaaaaa ebbbbbbcaaaaac dbbbbbdaaaaae cbbbbbbaaaaag bbbbbbbaaaa cbbbbbbaaaf gbbbbbbaaae dbbbbbbaag ebbbbbbaa dbbbbbbf ebbbbbbc bbbbbbd gbbbbbbb eabbbbbbc cabbbbbbd faabbbbbbe gaaabbbbbbd eaaaabbbbbbg caaaabbbbbbc faaaaabbbbbbg gaaaaaabbbbbbc eaaaaafcbbbbbb caaaaacgbbbbbbe faaaaae dbbbbbd gaaaaaa ebbbbbbg eaaaaaf dbbbbbd caaaaac cbbbbbbg faaaaae bbbbbbc aaaaaa cbbbbbb eaaaaaf gbbbbbbe caaaaac dbbbbbd faaaaae ebbbbbbe aaaaaag dbbbbbd eaaaaaf ebbbbbbg caaaaac bbbbbbc faaaaae cbbbbbb aaaaaag gbbbbbbe gaaaaaf dbbbbbd ``` <!-- end of image --> There is 1 intersection point visible in this close-up of area A. Now, let's turn our attention to the next spot. Let's see what secrets area B holds. <!-- image --> ```palette Key,Color ,#fefefeff a,#d9c080ff b,#bb977dff c,#eadecbff d,#d9c5b7ff e,#f4eee4ff f,#e3d0a2ff g,#cbb09aff ``` ```image ebbbbbg cbbbbbd fe dbbbbbd aafe dbbbbbc aaaafe gbbbbbc aaaaaafe gbbbbbe aaaaaaaafe bbbbbb aaaaaaaaaafe bbbbbb aaaaaaaaaaaafe ebbbbbg caaaaaaaaaaaafe cbbbbbg caaaaaaaaaaaafe cbbbbbd caaaaaaaaaaaafe dbbbbbc caaaaaaaaaaaafe gbbbbbc caaaaaaaaaaaafe gbbbbbe caaaaaaaaaaaaf bbbbbb caaaaaaaaaaafbbbbbb caaaaaaaaaabbbbbg caaaaaaaabbbbbg caaaaaabbbbbd caaabbbbbbd cabbbbbbc bbbbbbe bbbbbbe bbbbbb bbbbbb bbbbbg bbbbbg bbbbbg bbbbbf bbbbbf bbbbbf bbbbbf ebbbbbf cbbbbbf cbbbbba dbbbbaa gbbbbaa gbbbbaa bbbbbaae bbbbbaae ebbbbbaae ebbbbbaae cbbbbbaae dbbbbaaac dbbbbaaac gbbbbaaac gbbbbaaac bbbbbaaaf ebbbbbaaaf ebbbbbaaaf cbbbbbaaaf dbbbbbaaaf dbbbbaaaaa gbbbbaaaaa gbbbbaaaaa bbbbbaaaaa bbbbbaaaaa ebbbbbaaaaae cbbbbgaaaaae cbbbbgaaaaae dbbbbgaaaaae gbbbbfaaaaac gbbbbfaaaaac bbbbbcaaaaac bbbbbcaaaaac ebbbbgcaaaaac cbbbbgeaaaaaf cbbbbdeaaaaaf dbbbbdeaaaaaf dbbbbceaaaaaf gbbbbe aaaaaf gbbbbe aaaaaa bbbbb aaaaaa ebbbbb aaaaaa ebbbbb aaaaaa cbbbbb faaaaa dbbbbb faaaaae dbbbbb faaaaae gbbbbb faaaaae gbbbbb faaaaae bbbbbb caaaaac bbbbbb caaaaac ebbbbbg caaaaac cbbbbbg caaaaac dbbbbbc eaaaaaf gbbbbbc eaaaaaf gbbbbbe eaaaaaf bbbbbb eaaaaaf bbbbbb aaaaaf ebbbbbg aaaaaa cbbbbbg aaaaaa cbbbbbd aaaaaa dbbbbbd aaaaaa dbbbbbc faaaaae gbbbbbe faaaaae bbbbbbe faaaaae bbbbbb faaaaae ebbbbbg faaaaac ebbbbbg caaaaac cbbbbbd caaaaac dbbbbbd caaaaac dbbbbbc caaaaac gbbbbbe caaaaaf ddddddddddddddddbbbbbbe eaaaaaf bbbbbbbbbbbbbbbbbbbbbb eaaaaaf bbbbbbbbbbbbbbbbbbbbbb eaaaaaf bbbbbbbbbbbbbbbbbbbbbg eaafffc bbbbbbbbbbbbbbbbbbbbbd bbbbbbbbbbbbbbbbbbbbg cccccccccccccccddddc ``` <!-- end of image --> I can confirm that 1 intersection exists in area B. Answer: A: 1; B: 1; 1 + 1 = 2 I can confirm there's two intersections in there.

<!-- image --> ```palette Key,Color ,#fefefeff a,#dac180ff b,#bb977dff c,#e6d8bfff d,#d3bcacff e,#f1eae1ff f,#e1ce9bff g,#c6a88fff ``` ```image eaaa faaaaa aaaaaaaa aaacaaaaaa dg eaaf caaaaaa bbb faae caaaaaa gbbd aaa caaaaaa bbb aaa caaaaaa bbbe eaaa caaaaaa ebbb faac caaaaaa bbb aaa faaaaaa dbbg aaa faaaaaa bbbeaaa faaaaaa gbbgaac faaaaaa bbbaa faaaaaf bbbaa faaaaaf ebbba faaaaaf bbbc faaaaaf gbbb faaaaaf abbb faaaaaf abbbd faaaaaf bbb caabbb faaaaaf bbb aaabbbc faaaaaf bbb aaaebbb faaaaaf bbb aaa bbbe faaaaaf bbb caac cbbb faaaaaf ebbg aaa bbb faaaaaf cbbd aaa dbbg faaaaaf dbbe aaa bbb faaaaaf bbb caac bbbd faaaaaf bbb aaa bbb faaaaaf bbb aaa bbbe faaaaaf bbb aaa cbbb aaaaaaf bbb caac bbb aaaaaabbg aaae dbbg aaagbbd aaa bbb agbbc aaa gbbd bbbe caaf bbb bbb aaae bbbc bbb aaa ebbb bbb ca bbb bbb dbbg bbb bbb ebbb gbbd dbbg bbb gbba bbbc bbbae ebbb bbbae bbbe bbbae cbbb bbbac bbb bbbac dbbg ebbbaf bbb cbbgaf bbbc dbbaaa ebbb bbbaaa bbbe bbbaaa cbbb bbbaaa bbb bbbaaa dbbg bbbaaa bbb ebbgaaa gbbd cbbdaaa bbb dbbcaaa bbbe gbb aaa ebbb bbb aaa bbb bbb faa dbbg bbb faae bbb bbb caae gbbd bbg caac bbb ebbd caac bbbc dbbc eaac ebbb gbbe eaaf bbbe bbb aaf cbbb bbb aaa bbb bbb aaa gbbd bbb aaa bbb bbb aaa bbbc ebbd aaa ebbb cbbc aaa bbbceeeeeeeee dbbe aaa cbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb aaa bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb aff dddddddggggggggbbbbbbbbbbbbbbbbbbbbbbbbbbg ``` <!-- end of image -->

Let's examine this image for potential line intersections. 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,#43a852ff b,#a1ec3aff c,#0d9026ff d,#b1d7b0ff e,#7cc286ff f,#edf6eaff g,#b2e877ff ``` ```image fdddddddddddddddddddddddddddddd fdddddddddddddddddddddddddddddd fdddddddddddddddddddddddddcdddd fddddddddddddddddddddddddcccddd fdddddddddddddddddddddgbccccddd fdddddddddddddddddddgbbccccdddd fddddddddddddddddddbbbccccddddd fddddddddddddddddbbbbccccdddddd fddddddddddddddbbbbbccccbdddddd fddddddddddddgbbbbbccccbbdddddd fddddddddddgbbbbbgacccebbdddddd fdddddddddbbbbbgdacccegbbgddddd fdddddddbbbbbbddaccceddbbgddddd fdddddbbbbbbdddacccedddbbbddddd aaa fdddgbbbbbddddaccceddddbbbddddd ccc fdgbbbbbgddddacccedddddbbbddddd ccc dbbbbbgdddddaccceddddddbbbddddd acc fbbbbbbddddddacccedddddddbbbddddd acc bbbbbbdddddddaccceddddddddbbbddddd acc gbbbbbddddddddacccedddddddddbbbddddd acc gbbbbbffdddddddaccceddddddddddgbbddddd acc dbbbbbg fddddddacccedddddddddddgbbddddd eccf fbbbbbg fffffeccceffffffffffffdbbdffff eccf bbbbbb eccce fbbg eccf bbbbbbf eccce bbg eccf gbbbbbf eccce bbb eccd dbbbbbd eccce bbb dccd f fbbbbbg eccce bbb dccd bbg fbbbbbg dccce bbb dccd bbb bbbbbb dccce bbb dccd fbbb gbbbbbf dccce bbb dcce gbbb gbbbbbf dccce gbb fcce bbbb dbbbbbg dccca gbbf fcce bbbbf fbbbbbg dccca dbbf fcce bbbbg bbbbbb dccca fbbd fcce fbbbbg bbbbbbf dccca bbg fffccaffffdbbbbbf gbbbbbf dccca bbg dddccaddddbbbbbbdfdbbbbbd dccca bbb dddccaddddbbbbbbgbbbbbg dccca bbb dddcccddddbbbbbbbbbbg fccca bbb dddcccddddbbbgbbbbb fccca bbb dddcccdddgbbggbbbf fccca bbb dddcccdddgbbddggdf fccca dddcccdddbbbdddddf fccca dddcccdddbbbdddddf fccca dddcccdddbbbdddddf fcccc dddcccdddbbgdddddf fcccc dddcccddgbbgdddddf fcccc dddcccddbbbddddddf fcccc dddcccddbbbddddddf fcccc dddcccddbbbddddddf fcccc dddcccddbbbddddddf fcccc dddcccdgbbgddddddf fcccc dddcccdgbbdddddddf cccc dddcccdbbbdddddddf cccc dddcccdbbbdddddddf cccc dddcccdbbbdddddddf cccc dddcccdbbgdddddddf cccc dddcccgbbgdddddddf cccc dddcccbbbddddddddf cccc dddcccbbbddddddddf cccc dddcccbbbddddddddf cccc dddaccbbbddddddddf cccc dddaccbbgddddddddf cccc dddaccbbdddddddddf cccc dddaccbbdddddddddf cccc dddaccbbdddddddddf cccc dddaccbbdddddddddfcccc dddaccbgdddddddddcccc dddeccbdddddddddcccc dddeccbddddddddcccc dddeccbdddddddcccc dddeccaddddddccccf dddeccadddddccccdf dddeccaddddccccddf dddbccadddccccdddf dddbccaddccccddddf dddbccadccccdddddf dddbccaccccddddddf ddgbccccccdddddddf ddgbcccccddddddddf ddbbccccdddddddddf ddbbcccddddddddddf ddddccdddddddddddf dddddddddddddddddf dddddddddddddddddf ``` <!-- end of image --> Let's take a closer look at area A. <!-- image --> ```palette Key,Color ,#fefefeff a,#3ea74fff b,#a1ec3aff c,#0c9026ff d,#aed9b6ff e,#74bf80ff f,#dff4ceff g,#c1f27fff ``` ```image ccccca gbbbbbbbbbbf ccccca gbbbbbbbbbbf ccccca bbbbbbbbbbbf ccccca fbbbbbgbbbbbg acccca fbbbbbgbbbbbb acccca gbbbbbfbbbbbb acccca gbbbbb bbbbbb acccca bbbbbb gbbbbb accccc bbbbbg gbbbbb accccc fbbbbbg fbbbbb accccc gbbbbbf gbbbg accccc gbbbbbf fgf accccc bbbbbb eccccc bbbbbg eccccc fbbbbbg eccccc fbbbbbf ecccccf gbbbbbf ecccccf gbbbbb ecccccf bbbbbb ecccccf bbbbbg ecccccf fbbbbbg ecccccf gbbbbbf ecccccf gbbbbb dcccccd bbbbbb dcccccd bbbbbg dcccccd fbbbbbg dcccccd fbbbbbf dcccccd gbbbbbf dcccccd gbbbbb dcccccd bbbbbb dcccccd fbbbbbg dcccccd fbbbbbg fccccce gbbbbbf fccccce gbbbbb fccccce bbbbbb fccccce bbbbbg fccccce fbbbbbg fccccce fbbbbbf fccccce gbbbbbf ccccce gbbbbb ccccce bbbbbg cccccefbbbbbg cccccafbbbbbf cccccagbbbbbf cccccagbbbbb cccccabbbbbb cccccabbbbbg accccabbbbbg accccabbbbbf acccccbbbbbf acccccbbbbb acccccbbbbg acccccbbbbg acccccbbbbf acccccbbbbf acccccbbbb ecccccbbbb ecccccbbbg ecccccbbbg ecccccbbbf ecccccbbb ecccccbbb ecccccbbg ecccccbbg ecccccbbf ecccccbbf d dcccccbb dc dcccccbb dcc dcccccbg dccc dcccccbg dcccc dcccccbf dccccc dccccca dcccccc dccccca dccccccc dccccce dccccccca dccccce dccccccca gccccce dccccccca gccccce dccccccca bccccce fccccccca bccccce fccccccca fbccccce fccccccca fbccccce fccccccca gbccccce fccccccca gbccccce fccccccca bbcccccefccccccca bbcccccaccccccca fbbccccccccccccaf fbbcccccccccccaf gbbccccccccccaf gbbcccccccccaf bbbccccccccaf fbbbcccccccaf fbbbccccccaf ffaccccaf faccaf dd ``` <!-- end of image --> Case closed! This is definitely 1 intersection point in area A. Onward to the next region of interest. I wonder what we'll find inside area B? <!-- image --> ```palette Key,Color ,#fefefeff a,#45aa59ff b,#a1ec39ff c,#0e9127ff d,#a9d7b2ff e,#b7f069ff f,#e4f5d6ff g,#d0f59dff ``` ```image f fcd fcccd fcccccd f fcccccccd gbbbcccccccaf gbbbbcccccccaf febbbbcccccccaf febbbbbcccccccaf febbbbbbcccccccaf gbbbbbbbccccccccf gbbbbbbbbccccccccf febbbbbbbbccccccccb febbbbbbbbbccccccccbb febbbbbbbbbbccccccccbbb gbbbbbbbbbbbacccccccbbbb gbbbbbbbbbbbgacccccccbbbbbf gbbbbbbbbbbbgfacccccccebbbbbf febbbbbbbbbbg facccccccfgbbbbbf febbbbbbbbbbef acccccccf fbbbbbg febbbbbbbbbbef acccccccf fbbbbbg gbbbbbbbbbbbg acccccccf fbbbbbg gbbbbbbbbbbbg acccccccf bbbbbe febbbbbbbbbbg acccccccf bbbbbe febbbbbbbbbbef acccccccd ebbbbe febbbbbbbbbbef acccccccd ebbbbb gbbbbbbbbbbef acccccccd ebbbbb gbbbbbbbbbbbg acccccccd gbbbbbf gbbbbbbbbbbbg acccccccd gbbbbbf febbbbbbbbbbg acccccccd gbbbbbf bbbbbbbbbbef acccccccd fbbbbbg bbbbbbbbef acccccccd fbbbbbg bbbbbbbg acccccccd fbbbbbg bbbbbg acccccccd bbbbbe bbbg acccccccd bbbbbe bef acccccccd bbbbbe f acccccccd ebbbbb acccccccd ebbbbb acccccccd gbbbbb ``` <!-- end of image --> I can confirm that 1 intersection exists in area B. Answer: A: 1; B: 1; 1 + 1 = 2 The final answer is: two intersections found.

<!-- image --> ```palette Key,Color ,#fefefeff a,#41a853ff b,#a2ec3aff c,#0c9026ff d,#a9d7b2ff e,#75c081ff f,#dff4d0ff g,#c4f285ff ``` ```image c ccc gbccccf fbbccccf bbbccccf bbbbccccf gbbbbccccb gbbbbbacccbb fbbbbbgacccgbbf fbbbbbg acccffbbf bbbbbb acccf bbg bbbbbb acccf bbg aaa gbbbbbf acccf bbb ccc gbbbbbf acccd bbb ccc fbbbbbg acccd bbb acc bbbbbb acccd bbb acc bbbbbb acccd bbb acc gbbbbbf ecccd bbb acc gbbbbbf ecccd gbb acc fbbbbbg ecccd gbbf ecc fbbbbbg ecccd fbbf eccf bbbbbb ecccd fbbg eccf bbbbbb eccce bbg eccf gbbbbbf eccce bbb eccf gbbbbbf eccce bbb dccd f fbbbbbg dccce bbb dccd bbb bbbbbb dccce bbb dccd bbb bbbbbb dccce bbb dccd fbbb gbbbbbf dccce bbb fcce gbbb gbbbbbf dccce gbb fcce bbbb fbbbbbg dccce gbbf fcce bbbbf fbbbbbg dccca fbbf fcce bbbbg bbbbbb dccca fbbg cce bbbbg bbbbbb dccca bbg cca gbbbbb gbbbbbf dccca bbb cca bbbbbb gbbbbbg fccca bbb cca bbbbbbfbbbbbg fccca bbb cca bbbbbbbbbbb fccca bbb cca bbbgbbbbb fccca bbb ccc fbbgfbbbf fccca bbb ccc gbbf ff fccca ccc bbb fccca ccc bbb fccca ccc bbb fccca ccc bbg fcccc ccc gbbf fcccc ccc bbb cccc ccc bbb cccc ccc bbb cccc ccc bbb cccc ccc fbbg cccc ccc gbb cccc ccc bbb cccc ccc bbb cccc ccc bbb cccc cccfbbg cccc cccgbbf cccc cccbbb cccc accbbb cccc accbbb cccc accbbg cccc accbbf cccc accbb cccc eccbb cccc eccbb cccc eccbb cccc eccbg cccc eccbf cccc dccb cccc dccb cccc dcca cccc dcce cccc gcce cccc bcce cccc bcce cccc bcce cccc bccecccc fbccccccf gbcccccf bbccccf bbcccf acf ``` <!-- 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,#18a8f5ff b,#31748eff c,#67c3e4ff d,#679da4ff e,#b1d7b1ff f,#94c89bff g,#e9f3f1ff ``` ```image g g fbg a beb ag gb db ag bf bd ag b bg ag db gb ac bg db ac gb bd cc be be cc b gbg cc db eb cc bg db cc gb bf ca be bg ga b gb ga dd db ga bg bd ga gb bg ga be gb a b db a dd bd a b be a eb gbg a be eb a b db ffffaffffffbbffff bf eeeeaeeeeeebeeeeeg bg ggggggggggggggggggggggggggggggggggggggggg eeeeaeeeeefbeeeeeg gbfeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeefg eeeeaeeeeebfeeeeeg dbeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeg eeeeaeeeeebeeeeeeg bdeeeeeeeeeeeeeeeeeeeeeecaeeeeeeeeeeeeeeeeg eeeeaeeeebdeeeeeeg fbfeeeeeeeeeeeeeeeeeeeecaaceeeeeeeeeeeeeeeg eeeeaeeeebeeeeeeeg ffbeeeeeeeeeeeeeeeeeeecaefaeeeeeeeeeeeeeeeg eeeeaeeedbeeeeeeeg fedbeeeeeeeeeeeeeeeeecaeeeaeeeeeeeeeeeeeeeg eeeeafeebfeeeeeeeg feebbeeeeeeeeeeeeeeecaeeeeaceeeeeeeeeeeeeeg eeeeaceebeeeeeeeeg feeebdeeeeeeeeeeeeefaeeeeeeaeeeeeeeeeeeeeeg eeeeacebdeeeeeeeeg feeeebeeeeeeeeeeeeeaeeeeeeeaeeeeeeeeeeeeeeg eeeeacebeeeeeeeeeg feeeedbeeeeeeeeeeeafeeeeeeeaceeeeeeeeeeeeeg eeeeacdbeeeeeeeeeg feeeeebbeeeeeeeeeaceeeeeeeeeaeeeeeeeeeeeeeg eeeeacbfeeeeeeeeeg feeeeeebdeeeeeeeaceeeeeeeeeeaeeeeeeeeeeeeeg eeeeccbeeeeeeeeeeg feeeeeeebfeeeeeaceeeeeeeeeeecceeeeeeeeeeeeg eeeecadeeeeeeeeeeg feeeeeeefbeeeeaceeeeeeeeeeeeeaeeeeeeeeeeeeg eeeecaeeeeeeeeeeeg feeeeeeeedbeeaceeeeeeeeeeeeeeaeeeeeeeeeeeeg eeeedaeeeeeeeeeeeg feeeeeeeeebdaaeeeeeeeeeeeeeeecaeeeeeeeeeeeg eeeebaeeeeeeeeeeeg feeeeeeeeeeaaeeeeeeeeeeeeeeeeeaeeeeeeeeeeeg eeeebaeeeeeeeeeeeg feeeeeeeeeaabeeeeeeeeeeeeeeeeeaeeeeeeeeeeeg eeebdaeeeeeeeeeeeg feeeeeeeeaaedbeeeeeeeeeeeeeeeecaeeeeeeeeeeg eeedeaeeeeeeeeeeeg feeeeeeeaaeeebbeeeeeeeeeeeeeeeeaeeeeeeeeeeg eeeeeaeeeeeeeeeeeg feeeeeeaaeeeeebdeeeeeeeeeeeeeeeafeeeeeeeeeg eeeeeaeeeeeeeeeeeg feeeeecaeeeeeeebeeeeeeeeeeeeeeecaeeeeeeeeeg eeeeeaeeeeeeeeeeeg feeeecaeeeeeeeedbeeeeeeeeeeeeeeeaeeeeeeeeeg eeeeeaeeeeeeeeeeeg feeecaeeeeeeeeeebbeeeeeeeeeeeeeeaceeeeeeeeg eeeeeaeeeeeeeeeeeg feecaeeeeeeeeeeeebdeeeeeeeeeeeeecaeeeeeeeeg eeeeeaeeeeeeeeeeeg fecaeeeeeeeeeeeeeebfeeeeeeeeeeeeeaeeeeeeeeg eeeeeaeeeeeeeeeeeg ffaeeeeeeeeeeeeeeefbeeeeeeeeeeeeeaceeeeeeeg eeeeeaeeeeeeeeeeeg faeeeeeeeeeeeeeeeeedbeeeeeeeeeeeecaeeeeeeeg eeeeeaeeeeeeeeeeeg gafeeeeeeeeeeeeeeeeeebdeeeeeeeeeeeeaeeeeeeeg eeeeeaeeeeeeeeeeeg adeeeeeeeeeeeeeeeeeeeebfeeeeeeeeeeeaceeeeeeg eeeeeaeeeeeeeeeeeg acfeeeeeeeeeeeeeeeeeeeefbeeeeeeeeeeefaeeeeeeg eeeeeaaeeeeeeeeeeg ac feeeeeeeeeeeeeeeeeeeeedbeeeeeeeeeeeaeeeeeeg ffffffaacffffffff ac feeeeeeeeeeeeeeeeeeeeeebbeeeeeeeeeeaceeeeeg gaa ac feeeeeeeeeeeeeeeeeeeeeeebdeeeeeeeeeeaeeeeeg cac ac feeeeeeeeeeeeeeeeeeeeeeeebeeeeeeeeeeaeeeeeg aa aa feeeeeeeeeeeeeeeeeeeeeeeedbeeeeeeeeeaceeeeg cac aa feeeeeeeeeeeeeeeeeeeeeeeeebbeeeeeeeeeaeeeeg aag aa feeeeeeeeeeeeeeeeeeeeeeeeeebdeeeeeeeeaeeeeg gac aa feeeeeeeeeeeeeeeeeeeeeeeeeeebfeeeeeeeaceeeg aag ca feeeeeeeeeeeeeeeeeeeeeeeeeeefbeeeeeeeeaeeeg gaa ca feeeeeeeeeeeeeeeeeeeeeeeeeeeedbeeeeeeeaeeeg aag ca feeeeeeeeeeeeeeeeeeeeeeeeeeeeebdeeeeeeeeeeg gaa ca feeeeeeeeeeeeeeeeeeeeeeeeeeeeeebfeeeeeeeeeg cag ca feeeeeeeeeeeeeeeeeeeeeeeeeeeeeefbeeeeeeeeeg gaa gag feeeeeeeeeeeeeeeeeeeeeeeeeeeeeeedbeeeeeeeeg caag feeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeebbeeeeeeeg g feeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeebdeeeeeeg feeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeebeeeeeeg feeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeefbeeeeeg feeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeebbeeeeg feeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeebdeeeg efffffffffffffffffffffffffffffffffffffbfff ``` <!-- end of image --> I'm now examining the contents of area A in detail. <!-- image --> ```palette Key,Color ,#fefefeff a,#15a7f6ff b,#307590ff c,#8ad3faff d,#6d9db0ff e,#abc6d0ff f,#50bdf7ff g,#cee8f5ff ``` ```image faf ebbg caf dbd caf gbbe caf dbb caf bbe caf ebbg caf dbd caa gbbe caa dbb gaa bbe gaa ebb gaa dbd gaa gbbg gaa dbb gaag bbe gaag ebb aag dbd aag gbbg aag dbb aag bbe aag ebb aac dbd aac gbbg aac dbd fac bbe fac ebb fac bbd facgbbg facdbd fafbbe fafbb caabd caabg caad caae faa baa ebaa dbaa gbbaa ebbaa bbdaa ebbgaa gddgaa gaag gaag aag aag aag aag aag aac aac fac fac fac fac fac fac faf caf caf caf caf caf caf caa gaaac caaafg ``` <!-- end of image --> Amazing! This area was hiding 1 intersection all along! Now, let's turn our attention to the next spot. Let's put area B under the microscope. <!-- image --> ```palette Key,Color ,#fefefeff a,#17a8f7ff b,#31748eff c,#97d8fbff d,#6698abff e,#a3c0ccff f,#57c0f9ff g,#d4e9f3ff ``` ```image d be bbg bbb fac gbbd faaf ebbe faaaag dbbg faafaac dbbg caaf faf gbbd caaf gaag ebbe caaf aac ebbe caaf caa dbbg caaf gaag gbbd gaaf aac gbbd gaaa caa ebbe gaaag gaag dbbg gaaag faf bbb gaaag caa gbbd gaaag gaag ebbe aaag faf dbbg faag caa dbbg faac gaac gbbd faac faf ebbe faac caa ebbe faac aac dbbg faac faf gbbd faac caa gbbd caaf aac ebbe caaf faf dbbg caaf caag bbb caaf aac gbbdcaaf faf ebbaaf gaag daaa aac gaaabg faf gaaabbd gaag gaaagebbe aac gaaag ebbe caa aaag dbbg gaag faag gbbd aac faac gbbd caa faac ebbe gaag faac dbbg faf faac bbb caa faac gbbd gaag faac ebbe faf caaf dbbg caa caaf dbbg gaag caaf gbbd faf caaf ebbe caa caaf ebbe aac gaaf dbbg faf gaaa gbbd caa gaaag gbbd aac gaaag ebbe faf gaaag dbbg caa gaaag bbb aac aaag gbbd faf aag ebbe caag ac dbbg aac c dbbg faf gbbd gaag ebbe aac ebbe faf dbbg gaag gbbd aac gbbd caa ebbe gaag dbbg aac bbb caa gbbd gaag ebbe faf dbbg caa dbbg gaag gbbd faf ebbd caa ebbe gaac dbbg faf gbbd caa gbbd aac ebbe faf dbbg caa bbb c gbbd ebbe dbbg dbbg gbbd ebbd ebbe dbbg gbbd gbbd ebbe dbbg bbbg gbbd ebbe dbbg dbbg gbbd gbbd ebbe ``` <!-- end of image --> Area B contains 1 intersection. Answer: A: 1; B: 1; 1 + 1 = 2 The final answer is: two intersections found.

<!-- image --> ```palette Key,Color ,#fefefeff a,#15a7f7ff b,#30738eff c,#8dd4fbff d,#6194a9ff e,#9bbbc8ff f,#50bdf8ff g,#d0e8f3ff ``` ```image g g ebg a beb ag gb db ag be bd ag b bg ag eb gb ac bg eb fc gb bd fc be be fc b b ff dd eb cf b db cf gb be cf be bg ca b gb ga dd db ga b bd ga gb bg a be gb a b eb a dd bd a b be a gb b a be eb a b db a dd be a b bg a eb gb a bg db a b bd fa a dd bg caac a b gb ca ga ag eb eb ca a ag bg bd ga fc ag b be gag ga ac dd b gag a ac b eb ag ff fceb db ag a fcbg be ac a ffb bg ac ff cae gb af a ca db af a fa bdaf ff ba aa a gba aab ag bda aa eb cf dga fa bd a ga fa be ag a fa b ca a ca eb a a ca db ag a ca be ca a ga bg a a gag gb ac a gag db ca a ag bd a a ag bg ac a ac gb ga aa ac eb a fac ac bd ac aa af be ga cac af b a aa af eb fc caf aa db ga aag aa be a caf fa bg ff aag fa gb a gaf fa db a fag ca bd gaa ca bg fac ca gb gaa ga eb faag bd g be b eb db be bg ``` <!-- end of image -->

Time to put on my detective hat and find those intersection points! There are 2 regions I'd like to highlight in the image. <!-- image --> ```palette Key,Color ,#fefefeff a,#c5877aff b,#ea09e8ff c,#b1d7b1ff d,#f69af5ff e,#c1aa9bff f,#96c996ff g,#dd4dd4ff ``` ```image aae aaaa aaaaa aaaaaa aaaaaaa aaaa aaa aaaa aaa aaaa aaa aaaa aaa aaaa aaa aaaa aaa aaaa aaa aaaa aaa aaaa aaa aaaa aaa aaaa aaa aaaa aaa aaaa aaa aaaa aaa aaaa eaa aaaa cffffffffffffaaaffff aaaa fccccccccccccaaacccc eaaa fccccccccccccaaacccc eaaa fcccccccccccceaacccc dd eaaa fcccccccccccceaacccc bbb eaaa fcccccccccccceaacccc gbb eaaa fcccccccccccceaacccc dbb eaaa fcccccccccccceaacccc dbbd eaaa fcccccccccccceaacccc bbg eaaa fcccccccccccceaacccc bbb eaaa fcccccccccccceaacccc bbb eaaa fcccccccccccceaacccc bbb eaaa fcccccccccccceaacccc bbb eaaa fcccccccccccceaacccc gbb fffffffffffffffffffffffffffffffaaaaf fcccccccccccceaagccc dbbd cccccccccccccccccccccccccccccceaaacf fcccccccccccggaabccc bbd ccccccccccccccccccccccccccccceaaaccf fcccccccegbbbgaabccc bbg cccccccccccccccccccccccccccceaaacccf fccccgbbbbbbbgaaeccc bbb ccccccccccccccccccccccccccceaaaccccf fegbbbbbbbbbeeaaeccc bbb cccccccccccccccccccccccccceaaacccccf dbbbbbbbbbgcccccaaeccc bbb ccccccccccccccccccccccccceaaaccccccf dbbbbbbbbbbeccccccccaaeccc gbb cccccccccccccccccccccccceaaacccccccf dbbbbbbbbbgccccccccccccaaeccc dbb ccccccccccccccccccccccceaaaccccccccf dbbbbbbbbbgd fcccccccccccccaaeccc bbd cccccccccccccccccccccceaaacccccccccfdbbbbbbbbbd fcccccccccccccaaeccc bbg ccccccccccccccccccccceaaaeccccccebbbbbbbbbgd fcccccccccccccaaeccc bbb cccccccccccccccccccceaaaeccccgbbbbbbbbbd fcccccccccccccaaeccc bbb ccccccccccccccccccceaaaecebbbbbbbbbg fcccccccccccccaaeccc bbb cccccccccccccccccceaaagbbbbbbbbbgccf fcccccccccccccaaeccc gbb ccccccccccccccccceaaagbbbbbbgecccccf fcccccccccccccaaeccc dbb cccccccccccccccggaaagbbbbgcccccccccf fcccccccccccccaaeccc dbbd cccccccccccebbbgaaagbgcccccccccccccf fcccccccccccccaaeccc bbg ccccccccgbbbbbgaaaeccccccccccccccccf fcccccccccccccaaeccc bbb ccccgbbbbbbbbgaaaecccccccccccccccccf cfffffffffffffaaafff bbb egbbbbbbbbbeeaaaeccccccccccccccccccf aae bbb dbbbbbbbbbgccceaaaecccccccccccccccccccf aae bbbgbbbbbbbbbeccccceaaaeccccccccccccccccccccf aae gbbbbbbbbgcccccccceaaaecccccccccccccccccccccf aae dbbbbbd cccccccceaaaeccccccccccccccccccccccf aae dd ccccccceaaaecccccccccccccccccccccccf aaa cccccceaaaeccccccccccccccccccccccccf aaa ccccceaaaecccccccccccccccccccccccccf aaa cccceaaaeccccccccccccccccccccccccccf aaa ccceaaaecccccccccccccccccccccccccccf aaa cceaaaeccccccccccccccccccccccccccccf aaa ceaaaecccccccccccccccccccccccccccccf aaa eaaaeccccccccccccccccccccccccccccccf aaa aaaefffffffffffffffffffffffffffffffc aaa aaae aaa aaae aaa aaae aaa aaae aaa aaae aaa aaae aaa aaae aaa aaae aaa aaae aaa aaae aaa aaae aaa aaae aaa aaae aaa ae aaa ``` <!-- end of image --> I'm determined to find out if an intersection exists in area A. <!-- image --> ```palette Key,Color ,#fefefeff a,#c5877aff b,#eb09e9ff c,#dcb4b0ff d,#f378f1ff e,#f9bff8ff f,#ecd8d4ff g,#e73cdaff ``` ```image caaaaaaa caaaaaaaf caaaaaaaf caaaaaaaf caaaaaaaf caaaaaaaf caaaaaaaf caaaaaaaf caaaaaaaf caaaaaaaf caaaaaaaf caaaaaaaf caaaaaaaf caaaaaaaf caaaaaaaf caaaaaaaf caaaaaaaf caaaaaaaf caaaaaaaf caaaaaaaf edg caaaaaaaf edbbbb caaaaaaaf edgbbbbbbb caaaaaaaf edbbbbbbbbbbb caaaaaaaf edgbbbbbbbbbbbbbb caaaaaaaf edbbbbbbbbbbbbbbbbbb caaaaaaafedgbbbbbbbbbbbbbbbbbbde caaaaaaadbbbbbbbbbbbbbbbbbbgde caaaaaaagbbbbbbbbbbbbbbbgde caaaaaaagbbbbbbbbbbbbbgde ecaaaaaaagbbbbbbbbbbgde edbgaaaaaaagbbbbbbbbgde edgbbbgaaaaaaagbbbbbgde edbbbbbbgaaaaaaagbbbgde edgbbbbbbbbgaaaaaaaggde dgbbbbbbbbbbbgaaaaaaac edgbbbbbbbbbbbbbgaaaaaaaf edgbbbbbbbbbbbbbbbbgaaaaaaaf edgbbbbbbbbbbbbbbbbbgcaaaaaaaf edgbbbbbbbbbbbbbbbbbbde faaaaaaaf dgbbbbbbbbbbbbbbbbbgde faaaaaaaf bbbbbbbbbbbbbbbbde faaaaaaaf bbbbbbbbbbbbgde faaaaaaaf bbbbbbbbbde faaaaaaaf bbbbbgde faaaaaaaf bbde faaaaaaaf e faaaaaaaf faaaaaaaf faaaaaaac faaaaaaac faaaaaaac faaaaaaac faaaaaaac faaaaaaac faaaaaaac faaaaaaac faaaaaaac faaaaaaac faaaaaaac faaaaaaac faaaaaaac faaaaaaac faaaaaaac faaaaaaac ``` <!-- end of image --> Eureka! There's definitely 1 intersection in area A! Okay, on to the next area of interest. Let's see what secrets area B holds. <!-- image --> ```palette Key,Color ,#fefefeff a,#c5877aff b,#ea09e8ff c,#e2c3beff d,#f48bf3ff e,#d4a69dff f,#f4d9e9ff g,#ea3ee1ff ``` ```image eaaaae eaaaae eaaaae eaaaae eaaaae eaaaae eaaaae eaaaae eaaaae eaaaaa eaaaaa eaaaaa eaaaaa eaaaaa eaaaaa caaaaa caaaaa caaaaa caaaaa caaaaa caaaaa caaaaa caaaaa caaaaa caaaaa caaaaa caaaaaf caaaaaf caaaaad caaaaag fdggaaaaabf dgbbbbgaaaaabd fdgbbbbbbbgaaaaagg dgbbbbbbbbbbbgaaaaagg fdgbbbbbbbbbbbbbbgaaaaaf dgbbbbbbbbbbbbbbbbbbgaaaaaf fdgbbbbbbbbbbbbbbbbbgdf faaaaaf dgbbbbbbbbbbbbbbbbbbgdf faaaaaf bbbbbbbbbbbbbbbbgdf faaaaaf bbbbbbbbbbbbbgdf faaaaaf bbbbbbbbbgdf faaaaaf bbbbbbgdf faaaaaf bbgdf faaaaac df faaaaac faaaaac faaaaac faaaaac faaaaac aaaaac aaaaac aaaaac aaaaac aaaaac aaaaac aaaaac aaaaac aaaaac aaaaac aaaaac aaaaae aaaaae aaaaae aaaaae ``` <!-- end of image --> Oh my, look at that! It's 1 intersection in area B! Answer: A: 1; B: 1; 1 + 1 = 2 There's for sure two intersections on the image you sent me.

<!-- image --> ```palette Key,Color ,#fefefeff a,#c5877aff b,#eb09e9ff c,#e3c7c1ff d,#f384f1ff e,#d4a89fff f,#f4ddeaff g,#e83bdcff ``` ```image aae aaaa aaaaa aaaaaa aaaaaaa aaaa aaa aaaa aaa aaaa aaa aaaa aaa aaaa aaa aaaa aaa aaaa aaa aaaa aaa aaaa aaa aaaa aaa aaaa aaa aaaa aaa aaaa aaa aaaa aaa aaaa eaa aaaa eaa aaaa eaa eaaa eaa eaaa eaa fd eaaa eaa bbb eaaa eaa gbb eaaa eaa dbbf eaaa eaa fbbd eaaaf caa bbd eaaaf caa bbb eaaaf caa bbb eaaaf caa bbb eaaaf caa gbb eaaaf caaf dbb eaaaf caad dbbf eaaaf dgaag bbd eaaaf fgbbbgaag bbg eaaaf dbbbbbbbgaaf bbb eaaaf fgbbbbbbbbgffaaf bbb eaaaf dbbbbbbbbbd faaf bbb eaaaf fgbbbbbbbbgf faac gbb eaaaf dbbbbbbbbbd faac dbbf eaaaf fgbbbbbbbbgf faac fbbd eaaaf dbbbbbbbbbd faac bbg caaaf dbbbbbbbbbgf aac bbb caaaf dbbbbbbbbbd aac bbb caaaf dbbbbbbbbbgf aac bbb caaadbbbbbbbbbd aac gbb caaagbbbbbbgf aac dbb fggaaagbbbbd aae fbbd dbbbgaaagbgf aae bbd fgbbbbbgaaad aae bbb dbbbbbbbbgaaac aae bbb fgbbbbbbbbbdcaaac aae bbb dbbbbbbbbbd caaac aae bbbgbbbbbbbbbd caaac aae dbbbbbbbbd caaac aae fbbbbbd caaac aae dd caaac aaa caaac aaa caaac aaa caaac aaa faaac aaa faaac aaa faaac aaa faaae aaa faaae aaa faaae aaa faaae aaa faaae aaa faaae aaa faaae aaa faaae aaa faaae aaa faaae aaa faaae aaa faaae aaa faaae aaa faaae aaa aaae aaa fae aaa f ``` <!-- end of image -->

I'm ready to tackle this image and find those intersections! These regions highlight areas that look suspicious. Lines seem to converge within them. <!-- image --> ```palette Key,Color ,#fefefeff a,#323d81ff b,#f1b60fff c,#97c49cff d,#b2d7b1ff e,#5b6a88ff f,#7b969cff g,#d3c359ff ``` ```image gg bbb bbbbg bb bbb bb bbb bb bbbd bb bbb bb gbbg bb bbb ccccccccccccccccccccccccccccccccccccccccccccccbbccccccccccgbbgccccccccccccccccccccccccc ddddddddddddddddddddddddddddddddddddddddddddddbbddddddddddddbbbdddddddddddddddddddddddd ddddddddddddddddddddddddddddddddddddddddddddddbbdddddddddddddgbbgdddddddddddddddddddddd ddddddddddddddddddddddddddddddddddddddddddddddbbdddddddddddddddbbdddddddddddddddddafddd ddddddddddddddddddddddddddddddddddddddddddddddbbdddddddddddddddbbdddddddddddddddddafddd ddddddddddddddddddddddddddddddddddddddddddddddbbdddddddddddddddgbdddddddddddddddddafddd ddddddddddddddddddddddddddddddddddddddddddddddbbddddddddddddddddbgdddddddddddddddcafddd ddddddddddddddddddddddddddddddddddddddddddddddbbddddddddddddddddbbdddddddddddddddcacddd ddddddddddddddddddddddddddddddddddddddddddddddbbddddddddddddddddbbdddddddddddddddcacddd ddddddddddddddddddddddddddddddddddddddddddddddbbddddddddddddddddgbdddddddddddddddcacddd ddddddddddddddddddddddddddddddddddddddddddddddbbdddddddddddddddddbgddddddddddddddfadddd ddddddddddddddddddddddddddddddddddddddddddddddbgdddddddddddddddddbbddddddddddddddfadddd ddddddddddddddddddddddddddddddddddddddddddddddbgdddddddddddddddddbbddddddddddddddfadddd ddddddddddddddddddddddddddddddddddddddddddddddbgdddddddddddddddddgbddddddddddddddfadddd dddcddddddddddddddddddddddddddddddddddddddddddbgddddddddddddddddddbgdddddddddddddfadddd dddaedddddddddddddddddddddddddddddddddddddddddbgddddddddddddddddddbbdddddddddddddeadddd dddaadddddddddddddddddddddddddddddddddddddddddbgddddddddddddddddddbbdddddddddddddeadddd dddeadddddddddddddddddddddddddddddddddddddddddbgddddddddddddddddddgbdddddddddddddeadddd dddgaeggddddddddddddddddddddddddddddddddddddddbgdddddddddddddddddddbgddddddddddddeadddd dddbaabbbbbbbbbbbbbbbbbbbgggggddddddddddddddddbgdddddddddddddddddddbbddddddddddddeadddd ddddeadddgggggbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbgdddddddddddddddddddbbddddddddddddeadddd ddddcafdddddddddddddddddddddddddgggggbbbbbbbbbbgdddddddddddddddddddgbddddddddddddaadddd dddddaadddddddddddddddddddddddddddddddddddddddddddddddddddddddddfafdbgdddddddddddaadddd dddddeadddddddddddddddddddddddddddddddddddddddddddddddddddddfaaaaaadbbdddddddddddaadddd dddddcafdddddddddddddddddddddddddddddddddddddddddddddddceaaaaaaecfacbbdddddddddddaadddd ddddddaadddddddddddddddddddddddddddddddddddddddddddfeaaaaaafddddddaagbdddddddddddaadddd ddddddaadddddddddddddddddddddddddddddddddddddddfaaaaaaefddddddddddaadbgddddddddddaadddd ddddddfacdddddddddddddddddddddddddddddddddceaaaaaaecddddddddddddddcafbbddddddddddaadddd dddddddaadddddddddddddddddddddddddddddceaaaaaafddddddddddddddddddddaabbddddddddddaadddd dddddddaaddddddddddddddddddddddddddfaaaaaafddddddddddddddddddddddddaagbddddddddddaadddd dddddddfacdddddddddddddddddddddddddaaecddddddddddddddddddddddddddddcafbgdddddddddaadddd ddddddddaeddddddddddddddddddddddddcafdddddddddddddddddddddddddddddddaabbdddddddddaadddd ddddddddaaddddddddddddddddddddddddaaddddddddddddddddddddddddddddddddeabbdddddddddaadddd ddddddddfaddddddddddddddddddddddddaedddddddddddddddddddddddddddddddddaebdddddddddaadddd dddddddddaeddddddddddddddddddddddeaddddddddddddddddddddddddddddddddddaabgddddddddaadddd dddddddddaaddddddddddddddddddddddaaddddddddddddddddddddddddddddddddddeabbddddddddaadddd dddddddddeadddddddddddddddddddddfafdddddddddddddddddddddddddddddddddddaebddddddddaedddd ddddddddddaeddddddddddddddddddddaaddddddddddddddddddddddddddddddddddddaabddddddddaedddd ddddddddddaaddddddddddddddddddddaeddddddddddddddddddddddddddddddddddddfabbdddddddaedddd ddddddddddeadddddddddddddddddddaaddddddddddddddddddddddddddddddddddddddaebdddddddaedddd dddddddddddafddddddddddddddddddaaddddddddddddddddddddddddddddddddddddddaabdddddddaedddd dddddddddddaadddddddddddddddddfacddddddddddddddddddddddddddddddddddddddfabgddddddafdddd dddddddddddeadddddddddddddddddaaddddddddddddddddddddddddddddddddddddddddaabddddddafdddd dddddddddddcafdddddddddddddddcafddddddddddddddddddddddddddddddddddddddddaabddddddafdddd ddddddddddddaadddddddddddddddaadddddddddddddddddddddddddddddddddddddddddfabddddddafdddd ddddddddddddaadddddddddddddddaeddddddddddddddddddddddddddddddddddddddddddaagdddddafdddd ddddddddddddcafdddddddddddddeadddddddddddddddddddddddddddddddddddddddddddaabddddcafdddd dddddddddddddaadddddddddddddaadddddddddddddddddddddddddddddddddddddddddddcagddddcacdddd dddddddddddddaaddddddddddddfafddddddddddddddddddddddddddddddddddddddddddddaaddddcacdddd dddddddddddddfacdddddddddddaadddddddddddddddddddddddddddddddddddddddddddddeagdddcacdddd ddddddddddddddaaddddddddddcaedddddddddddddddddddddddddddddddddddddddddddddcaedddfaddddd ddddddddddddddaaddddddddddaadddddddddddddddddddddddddddddddddddddddddddddddaadddfaddddd ddddddddddddddfacdddddddddaadddddddddddddddddddddddddddddddddddddddddddddddeadddfaddddd dddddddddddddddaeddddddddeacddddddddddddddddddddddddddddddddddddddddddddddddaeddfaddddd dddddddddddddddaaddddddddaadddddddddddddddddddddddddddddddddddddddddddddddddaaddfaddddd dddddddddddddddfadddddddcafdddddddddddddddddddddddddddddddddddddddddddddddddeaddeaddddd ddddddddddddddddaeddddddaaddddddddddddddddddddddddddddddddddddddddddddddddddgaedeaddddd ddddddddddddddddaaddddddaedddddddddddddddddddddddddddddddddddddddddddddddddddaadeaddddd ddddddddddddddddeadddddeaddddddddddddddddddddddddddddddddddddddddddddddddddddeaceaddddd dddddddddddddddddaeddddaaddddddddddddddddddddddddddddddddddddddddddddddddddddbaeeaddddd dddddddddddddddddaadddfacddddddddddddddddddddddddddddddddddddddddddddddddddddgaaeaddddd dddddddddddddddddeadddaaddddddddddddddddddddddddddddddddddddddddddddddddddddddgaaaddddd dddddddddddddddddcafdcaeddddddddddddddddddddddddddddddddddddddddddddddddddddddbaaaddddd ddddddddddddddddddaadaadddddddddddddddddddddddddddddddddddddddddddddddddddddddbaaaddddd ddddddddddddddddddaadaadddddddddddddddddddddddddddddddddddddddddddddddddddddddggaaddddd ddddddddddddddddddcaaacddddddddddddddddddddddddddddddddddddddddddddddddddddddddbaaddddd dddddddddddddddddddaaadddddddddddddddddddddddddddddddddddddddddddddddddddddddddbeaddddd dddddddddddddddddddaafdddddddddddddddddddddddddddddddddddddddddddddddddddddddddbbdddddd dddddddddddddddddddcadddddddddddddddddddddddddddddddddddddddddddddddddddddddddddbbddddd ddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddgbbdddd dddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddgbbddd ddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddgdddd ddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddd ddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddd ``` <!-- end of image --> This close-up of area A is like examining a piece of evidence. <!-- image --> ```palette Key,Color ,#fefefeff a,#323d81ff b,#f0b50fff c,#9096baff d,#f9e2a0ff e,#626895ff f,#c5c8dbff g,#f5ca54ff ``` ```image dbb gbbb dbb bbbg dbb bbbd dbb bbg dbb dbb aa dbb bb aa dbb gb aa gbb bd aa gbg bb faa gbg bb faa gbg gbg faa gbg dbb faa gbg bb faa gbg bb faa gbg bbd caa gbg dbb caa gbg dbb caa eaf gbg gb cae caa gbg dbd cae faa gbg bd cae aa bbg bb eae daaeddd bbd bb eae geaabbbbbbbbggggdddd bbd gb eae ggaabbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbgggddddd bbd dbd eac caf dddddggggbbbbbbbbbbbbbbbbbbbbbbbbd bg eac ac dddddggggbbbbbbbbbbbd bb eac aa fea bbg aac eae ceaaaaaacdbb aac caa fcaaaaaaaaaa bb aac aa feaaaaaaaef aa bb aaf aaf fcaaaaaaacf fafbbd aaf aac fcaaaaaaaef acbbg aaf faa caaaaaaaac aadbb aaf ea fcaaaaaaaef ca bb aaf ac aaaaaaacf aedb aaf ae aaaaac aafbd aa aac eaa eaebb aa caa aa aabbd aa aa ae aagbg aa aa ea aacbb aa eae eaa faabb aa caa aac aabb ae aa aa fabbd ae faf eaa aabb ae ac aac aabb ae aaf ae caab ae eaa ea aabd ac faa faa aabd ac aa aac eaab ac aac aa aabg ac eae faa eabg ac faa aac aeb ac ca ac aab af faf caf aae af aa faa faag af aa aac aab faf ca aaf aab faf ac caa caa faf aaf aac ead faf eae ac ae fa faa caf aa fa aa aa aae fa aac fac caa ca eae ca aa ca faa caa aaf ca ca aac eaa ca faf aa gaa ca aa caa dea ca aac aaf gae ea caa aa daa ea aa ca aaeea aaf caa baaea aac eae baaea caa aa gaaaa ea caa dbaaa ca aae baaa ae aa bbaa aaaa bbaa aaaa gbaa faae dbb aa gbd bbd dbbd gbb g ``` <!-- end of image --> I can confirm that 2 intersections exists in area A. Answer: A: 2; 2 = 2 The final answer is: two intersections found.

<!-- image --> ```palette Key,Color ,#fefefeff a,#323d81ff b,#f1b50fff c,#9fa4c4ff d,#f9e2a0ff e,#696e98ff f,#d3d5e3ff g,#f6cc5aff ``` ```image dg bbb bbbbg bb bbbd bb dbbb bb gbbd bb bbb bb gbbd bb bbb bb gbbg bb bbb bb dbbd bb bb ac bb bb ac bb gb ac bb bd faf bb bb faf bg bb faf bg gb faf bg bd fa bg bb ca bg bb ca bg db ca f bg bd ca ae bg bb ca aa bg bb ea ea bg db ea gaedd bg bg ea baabbbbbbbbbbbbbbbbbbgggdddd bd bb ea ea ddddgggbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbd bb ea fac ddddgggbbbbbbbbbd db aa aa cec bg aa ea caaaaaa bb aa fac feaaaaaacfcafbb aa aa feaaaaaac aadb aa aa caaaaaaef aa bg aa faf fcaaaaaaef facbb aa aa feaaaaaac aabb aa aa caaaaaec aadb aa caf aaef facbg aa ae fac aabb aa aa aa eagb aa ca ae aebd aa ae ea aabg aa aa aa eabb ae ca caf aeb ae ae aa aabd ae aa ae cabg ae ea aa aeb ae ac aa aab ac aa caf cabd ac ea aa aag ac fac fac aab ac aa aa cab ac aa ae aad ac faf ea aab faf aa aa fab faf aa caf aa faf caf aa ead faf ae ae fae fa aa aa aa ca caf aa ea ca ae caf fae ca aa aa aa ca ca fac ea ca ae aa gae ea aa ae aa ea ea ea eafea ac aa baeea aa caf daaea ea aa baaa fac fac baaa aa aa baaa ea aa dbaa faaa baa aaa bea aac bb fa dbb dbb gbb g ``` <!-- end of image -->

This image might have some surprises. Let's look for intersections carefully. These regions highlight areas that look suspicious. Lines seem to converge within them. <!-- image --> ```palette Key,Color ,#fefefeff a,#042dbaff b,#cb808dff c,#738fceff d,#b1d6b1ff e,#ebedeeff f,#96c897ff g,#2a4ebeff ``` ```image cd aaa aaa aaa eaag caac gaae aaa aaa aaa eaag eag caac aaae aaae caaa aaa aaac aaa eaaa aaa aaag daac aaae caad caaa aaa aaac aaa eaaa aaa aaag eaaa aaae caac caaa gaae aaac aaa eaaa aaa aaag aaa aaae eaag caaa caac aaac gaae eaaa aaa aaag aaa aaae aaa caaa eaag aaac caac eaaa aaa aaag aaa aaae aaa caaa aaa aaac caac daaaeeeeeeeeeeee gaad ebd faaagddddddddddfe aaa bbbb fdaaaddddddddddde aaa bbbbb fdgaaadddddddddde aaa ebbbbe fddaaacddddddddde eaag ebbbbe fddcaaaddddddddde eeeeeeeeeeeeeeeeeeecaaceeeeeee bbbbb fdddaaaddddddddde efddddddddddddddddddgaafdddddddf bbbbb fdddgaagdddddddde edddddddddddddddddddaaaddddddddf dbbbb fddddaaadddddddde edddddddddddddddddddaaaddddddddf ebbbbe fddddaaaacdddddde edddddddddddddddddddaaaddddddbbf bbbbd fddddcaaaaaafddde eddddddddddddddddddfaagddddbbbbb bbbbb fdddddcaaaaaaacde eddddddddddddddddddcaacdddbbbbbf bbbbbfddddddddgaaaaaage eddddddddddddddddddaaadddbbbbbdf ebbbbddddddddddcaaaaaaac eddddddddddddddddddaaaddbbbbbddf ebbbbddddddddddddgaaaaaage eddddddddddddddddddaaadbbbbddddf bbbbbddddddddddddcaaaaaaac eddddddddddddddddddaaabbbbdddddf bbbbbddddddddddde egaaaaaage edddddddddddddddddcaabbbbddddddf fbbbbbdddddddddde caaaaaaac edddddddddddddddddgabbbbdddddddf fddbbbbddddddddde egaaaaaage edddddddddddddddddgbbbbddddddddf dfffbbbbffffffff caaaaaaacedddddddddddddddddbbbbdddddddddf bbbbb egaaaaaagddddddddddddddbbbbbddddddddddf bbbbb caaaaaaacddddddddddbbbbbaddddddddddf dbbbb egaaaaaagdddddddbbbbbagddddddddddf ebbbbe ecaaaaaaacdddbbbbbaacddddddddddf bbbbd eddfaaaaaaagbbbbdaaadddddddddddf bbbbb edddddcaaaabbbbddaaadddddddddddf bbbbb edddddddfgbbbbgagaaadddddddddddf ebbbbe eddddddddbbbbaaaaaagdddddddddddf ebbbbe edddddddbbbbdfaaaaacdddddddddddf bbbbb eddddddbbbbdddddcaaddddddddddddf bbbbb eddddbbbbbdddddddddddddddddddddf dbbbb edddbbbbbddddddddddddddddddddddf ebbbbe eddbbbbbdddddddddddddddddddddddf bbbbd edbbbbbddddddddddddddddddddddddf bbbbb ebbbbbdddddddddddddddddddddddddf bbbbb bbbbdddddddddddddddddddddddddddf ebbbbe bbbbddddddddddddddddddddddddddddf ebbbbe bbbbdddddddddddddddddddddddddddddf bbbbbbbbbddddddddddddddddddddddddddddddf bbbbbbbeddddddddddddddddddddddddddddddf bbbbb ffffffffffffffffffffffffffffffd ebb ``` <!-- end of image --> Eureka! Let's inspect this close up of area A <!-- image --> ```palette Key,Color ,#fefefeff a,#042dbaff b,#cc7e8cff c,#899cdeff d,#e3b9c1ff e,#bac5ebff f,#5671d0ff g,#294cc3ff ``` ```image eaaaaaaf faaaaaae aaaaaag caaaaaac gaaaaaa eaaaaaaf faaaaaae aaaaaag caaaaaae gaaaaaf eaaaaaa gaaaaac caaaaag aaaaaae faaaaaf eaaaaaa gaaaaac caaaaage eaaaaaaagc gaaaaaaaaafe caaaaaaaaaaagc gaaaaaaaaaaaaafe cgaaaaaaaaaaaaagc efaaaaaaaaaaaaaa d cgaaaaaaaaaaa bd efaaaaaaaaa bbb cgaaaaaa bbbb efaaaa bbbbbd cga bbbbbbd e bbbbbbbd bbbbbbbbb bbbbbbbbb bbbbbbbbbd dbbbbbbbbd dbbbbbbbbd dbbbbbbbbb ``` <!-- end of image --> Area A is clear of intersections, but the search continues. Let's move forward and inspect another region. This is a magnified view of the region B. <!-- image --> ```palette Key,Color ,#fefefeff a,#062ebaff b,#ca7d8cff c,#8799dcff d,#dda9b2ff e,#ecdee6ff f,#526ac9ff g,#bbc3e9ff ``` ```image faaaaag faaaaag aaaaaa eaaaaaa gaaaaaf caaaaac e faaaaag ebb aaaaaae ebbbd aaaaaa dbbbbb gaaaaaf dbbbbbb caaaaaf dbbbbbbb caaaaac dbbbbbbbb faaaaag dbbbbbbbd aaaaaae ebbbbbbbbd eaaaaaa ebbbbbbbbd gaaaaaf ebbbbbbbbd caaaaac ebbbbbbbbd faaaaac ebbbbbbbbe faaaaagdbbbbbbbbe aaaaaadbbbbbbbbe eaaaaabbbbbbbbbe gaaaabbbbbbbbbe caaabbbbbbbbd faabbbbbbbbd fabbbbbbbbd abbbbbbbbd gbbbbbbbbd ebbbbbbbbe g dbbbbbbbbe aace dbbbbbbbbg aaaafg dbbbbbbbbae aaaaaaace dbbbbbbbbaa aaaaaaaaafg dbbbbbbbbaaf aaaaaaaaaaaace bbbbbbbbbaaaf aaaaaaaaaaaaaafg ebbbbbbbbbaaaac ecaaaaaaaaaaaaaaace ebbbbbbbbbaaaaag gfaaaaaaaaaaaaaafg ebbbbbbbbdaaaaaae ecaaaaaaaaaaaaaaacbbbbbbbbdeaaaaaa gfaaaaaaaaaaafbbbbbbbbe gaaaaaf ecaaaaaaaafbbbbbbbbe caaaaac gfaaaafbbbbbbbbafg faaaaac ecabbbbbbbbbaaaaaaaaaaag dbbbbbbbbaaaaaaaaaaaa dbbbbbbbbaaaaaaaaaaaaa ebbbbbbbbbfaaaaaaaaaaaaf ebbbbbbbbd ecaaaaaaaaaac ebbbbbbbbd gfaaaaaaag ebbbbbbbbd ecaaaaf ebbbbbbbbe gcg dbbbbbbbbe dbbbbbbbbe dbbbbbbbbe dbbbbbbbbe dbbbbbbbd ebbbbbbbbd ebbbbbbbbd ebbbbbbbbd ebbbbbbbbd bbbbbbbbe bbbbbbbe bbbbbbe bbbbbe bbbbe bbb bd d ``` <!-- end of image --> I've cracked the case! This area contains 2 intersections. Answer: A: 0; B: 2; 0 + 2 = 2 I can confirm there's two intersections in there.

<!-- image --> ```palette Key,Color ,#fefefeff a,#042dbaff b,#cb7d8cff c,#8c9fdfff d,#deabb4ff e,#e0dcebff f,#5c76d2ff g,#2749c2ff ``` ```image cc aaa aaa aaa eaag caac gaae aaa aaa aaa eaag eag faac aaae gaae faaa aaa aaac aaa eaaa aaa aaag caaf aaae faac faaa aaa aaac aaa eaaa aaa aaag aaa aaae caaf faaa gaae aaac aaa eaaa aaa aaag aaa aaae eaag faaa caac aaac gaae eaaa aaa aaag aaa aaae aaa faaa eaaf aaac faac eaaa aaa aaag aaa aaae aaa faaa aaa aaac caaf eaaa faae bd aaag aaa bbbb aaae aaa dbbbb faaa aaa ebbbb aaac eaag bbbbe eaaa caac bbbbd aaa gaae bbbbb faaf aaa dbbbb aaa aaa e ebbbbe aaaac aaa dbd bbbbd caaaaage eaag dbbbd bbbbb caaaaaaac faac dbbbb dbbbb egaaaaaage gaae bbbbd dbbbb caaaaaaac aaa bbbbd ebbbbe egaaaaaage aaa bbbbe bbbbd caaaaaaac aaabbbbe bbbbb egaaaaaage caabbbb dbbbb caaaaaaac fabbbb ebbbbe egaaaaaage gbbbb bbbbd caaaaaaac ebbbb bbbbd egaaaaaage dbbbb bbbbb caaaaaaac dbbbba dbbbb egaaaaaage bbbbbaf ebbbbe caaaaaaac bbbbbaae bbbbd egaaaaaagbbbbdaaa bbbbb caaaabbbbe aaa dbbbb egbbbbgagaaa ebbbb bbbbaaaaaag bbbbe ebbbb egaaaac bbbbd ebbbb caa bbbbb dbbbb dbbbb dbbbb ebbbbe dbbbb bbbbd bbbbd bbbbb bbbbd dbbbb bbbbe dbbbb bbbbe ebbbbe bbbb bbbbdbbbb bbbbbbb dbbbb ebb ``` <!-- end of image -->

Let's examine this image for potential line intersections. I'd describe these as 'hotspots' for potential intersections. <!-- image --> ```palette Key,Color ,#fefefeff a,#e206cbff b,#491e97ff c,#e2bae9ff d,#ab96beff e,#db50cbff f,#725aa9ff g,#afd5afff ``` ```image ec aaa aaaa aaae bbc caaac dbbbc aaaa bbbbbc aaaa bbbbbbc aaae fbbfbbbbc caaac bbb bbbbd aaaa dbbb bbbbd aaaa bbbd bbbbd aaae bbb bbbbd caaac fbbf bbbbc aaaa bbb bbbf aaaa dbbb cbbb gaaaegggggggggbbbdggggg bbb geaaadggggggggbbbgggggg bbb ggaaaagggggggbbbfgggggg bbbb gggaaaaggggggbbbggggggg bbb ggggaaaeggggfbbbggggggg bbbb ggggeaaadgggbbbdggggggg bbb gggggaaaagggbbbgggggggg fbbb ggggggaaaagbbbfgggggggg bbbc gggggggaaaebbbggggggggg fbbb gggggggeaaabbbggggggggg bbbc ggggggggaabbbdggggggggg dbbb gggggggggabbbgggggggggg bbbd gggggggggbbbbeggggggggg dbbb gggggggggbbbaaggggggggg bbbd ggggggggfbbbaaagggggggg dbbb ggggggggbbbdaaaaggggggg bbbf ggggggggbbbgdaaaegggggg cbbb gggggggbbbfggeaaagggggg bbbf gggggggbbbggggaaaaggggg cbbb ggggggfbbbgggggaaaagggg bbbf ggggggbbbdgggggdaaaeggg bbb ggggggbbbgggggggeaaaggg bbbb gggggbbbfggggggggaaaagg bbb gggggbbbggggggggggaaaag bbbb ggggfbbbggggggggggdaaad bbb bbbc eaaa fbbb bbb aaaa bbbc bbbf aaaa fbbb bbb caaac bbbc dbbb eaaa dbbb bbbc aaaa bbbd bbb aaae dbbb bbbf caaac bbbf bbb eaaa dbbbf dbbb aaaa fbbbd bbbc aaae bbbbd bbb caaac bbbbc bbbf eaaa bbbbc bbb aaaa bbbbc ce dbbb aaae bbbb aaae bbbc caaac bbbb aaa bbb aaaa ggabbbbgggggggggggggaaaeggg bbbf aaaa ggaabbbbggggggggggggaaagggg bbb aaae ggaaabbbbggggggggggeaaagggg dbbb caaac ggaaaabbbbgggggggggaaaggggg bbbc aaaa ggaaaaabbbbgggggggeaaaggggg bbb aaaa ggaaaaaabbbbggggggaaadggggg bbbf aaae ggaaaaaadbbbbgggggaaagggggg bbb caaac gdaaaaaaefbbbbgggaaaegggggg dbbb aaaa gdaaegaaagfbbbfggaaaggggggg bbbc aaaa geaaegaaaegfbbbfdaaaggggggg bbb aaae geaaegdaaaggfbbbbaadggggggg bbbf eaaac geaadggaaadggbbbbaagggggggg bbb aaaa gaaadggeaaagggbbbbagggggggg dbbb aaaa gaaadgggaaaggggbbbbdggggggg bbbc aaae gaaaggggeaaaggdabbbbdgggggg cbbb eaaac gaaagggggaaaggaaabbbbgggggg bbbf aaaa gaaagggggaaaegaaagbbbbggggg bbb aaaa gaaagggggdaaaeaaaggbbbbgggg bb aaaegaaaggggggaaaaaadgggbbbbggg eaaagaaaggggggdaaaaagggggbbbfgg aaaaaaagggggggaaaaeggggggbdggg aaaaaagggggggeaaagggggggggggg caaaaaggggggggaaagggggggggggg eaaaagggggggggeggggggggggggg aaaeggggggggggggggggggggggg gaagggggggggggggggggggggggg ``` <!-- end of image --> Time to investigate area A up close. <!-- image --> ```palette Key,Color ,#fefefeff a,#e206ccff b,#481d97ff c,#f084e5ff d,#aa96ceff e,#e840d7ff f,#764bafff g,#eaccefff ``` ```image caaaaaaag dbbbbbbg eaaaaaae fbbbbbf aaaaaaae gbbbbbbd gaaaaaaac fbbbbbb caaaaaaag bbbbbbd eaaaaaae dbbbbbbg aaaaaaae fbbbbbf gaaaaaaac gbbbbbbd caaaaaaag fbbbbbb eaaaaaae bbbbbbd aaaaaaae dbbbbbbg gaaaaaaac fbbbbbf caaaaaaag gbbbbbbd eaaaaaae fbbbbbb gaaaaaaac bbbbbbd gaaaaaaac dbbbbbbg caaaaaaag fbbbbbf eaaaaaae gbbbbbbd gaaaaaaacfbbbbbb gaaaaaaabbbbbbd caaaaafbbbbbbg eaaaabbbbbbf gaaaabbbbbbd caabbbbbbb cabbbbbbd fbbbbbbe fbbbbbbac gbbbbbbaaag fbbbbbbaaaag bbbbbbfaaaae dbbbbbbaaaaaac fbbbbbfaaaaaaag gbbbbbbdeaaaaaaa fbbbbbb eaaaaaae gbbbbbbd gaaaaaaac dbbbbbbg caaaaaaag fbbbbbf eaaaaaaa gbbbbbbd eaaaaaae fbbbbbb gaaaaaaac gbbbbbbd caaaaaaag dbbbbbbg eaaaaaaa fbbbbbf eaaaaaae gbbbbbbd gaaaaaaac fbbbbbb caaaaaaag gbbbbbbd eaaaaaaa dbbbbbbg aaaaaaae fbbbbbf gaaaaaaac gbbbbbbd caaaaaaag fbbbbbb eaaaaaae gbbbbbbd aaaaaaae ``` <!-- end of image --> Case closed! This is definitely 1 intersection point in area A. Alright, let's concentrate on the next area. I'm eager to see what's happening in this magnified view of area B. <!-- image --> ```palette Key,Color ,#fefefeff a,#e206cbff b,#481d97ff c,#f07de4ff d,#9a7fc5ff e,#e83fd7ff f,#713dabff g,#efc1efff ``` ```image gfbbbbbbbf caaaaaag gafbbbbbbbf aaaaaae caafbbbbbbbd gaaaaaag caaabbbbbbbbd eaaaaaa caaaabbbbbbbbd gaaaaaac caaaaabbbbbbbbd eaaaaaa eaaaaaabbbbbbbbd gaaaaaac eaaaaaaabbbbbbbbd caaaaaag eaaaaaaaabbbbbbbbg aaaaaae eaaaaaaaaabbbbbbbbg caaaaaag aaaaaaaaaaabbbbbbbbg aaaaaae aaaaaaaaaaaabbbbbbbbg gaaaaaag aaaaaaaaaaaadbbbbbbbbg eaaaaaa aaaaaaeaaaaaadbbbbbbbbg gaaaaaac gaaaaaagaaaaaagdbbbbbbbf caaaaaa gaaaaaa aaaaaae dbbbbbbbf aaaaaae gaaaaae caaaaaag dbbbbbbbf gaaaaaag gaaaaae aaaaaae dbbbbbbbf eaaaaaa caaaaae caaaaaa dbbbbbbbf aaaaaac caaaaae gaaaaaac fbbbbbbbd caaaaaag caaaaac eaaaaaa fbbbbbbbdeaaaaae caaaaac gaaaaaac fbbbbbbbfaaaaag eaaaaac eaaaaae fbbbbbbbfaaaa eaaaaac caaaaaag fbbbbbbbfaac eaaaaag aaaaaae gfbbbbbbbaag eaaaaag caaaaaag gbbbbbbbba aaaaaag aaaaaac gbbbbbbbbg aaaaaag eaaaaaa ebbbbbbbbg aaaaaa gaaaaaac aabbbbbbbbg aaaaaa eaaaaaa gaaabbbbbbbbg gaaaaaa gaaaaaag eaaaabbbbbbbbg gaaaaaa aaaaaae aaaaafbbbbbbbfg gaaaaae caaaaaag caaaaaadbbbbbbbf gaaaaae aaaaaae eaaaaae dbbbbbbbf caaaaae caaaaaa gaaaaaag dbbbbbbbf caaaaae gaaaaaaccaaaaaa dbbbbbbbf caaaaac eaaaaaaaaaaaac fbbbbbbbf caaaaac gaaaaaaaaaaaag fbbbbbbbd g eaaaaac eaaaaaaaaaae fbbbbbbbd ageaaaaac caaaaaaaaaac fbbbbbbd aeeaaaaag aaaaaaaaaa fbbbbd aaaaaaaag caaaaaaaac gfbbd aaaaaaaag gaaaaaaaag gfg aaaaaaaag eaaaaaae aaaaaaaa gaaaaaac aaaaaaaa eaaaaa aaaaaaaa gaaaac aaaaaaaa gccg eaaaaaae gaaaaaae caaaaac ``` <!-- end of image --> Eureka! There's definitely 1 intersection in area B! Answer: A: 1; B: 1; 1 + 1 = 2 After a thorough search, I conclude that there are two intersections.

<!-- image --> ```palette Key,Color ,#fefefeff a,#e206ccff b,#481d97ff c,#f18be7ff d,#b2a0d3ff e,#e945d8ff f,#7149adff g,#efd6f2ff ``` ```image ec aaa aaaa aaae bbg caaag dbbbg eaaa bbbbbg aaaa bbbbbbg aaae fbbfbbbbd caaag bbb bbbbd aaaa dbbb bbbbd aaaa bbbd bbbbd aaae gbbb bbbbd caaag fbbf bbbbd aaaa bbb bbbf aaaa dbbb gbbb gaaae bbbd bbb caaag gbbb bbb aaaa fbbf bbbb aaaa bbb bbb gaaae dbbb fbbb caaag bbbd bbbg aaaa gbbb fbbb aaaa fbbf bbbg gaaacbbb fbbb caafbbb bbbd aabbbd dbbb abbb bbbd fbbbc dbbb bbbaag bbbd dbbbaaa dbbb bbbdaaaa bbbf gbbb gaaac dbbb fbbf eaaag bbbf bbb aaaa gbbb dbbb aaaa bbbf bbbd gaaac gbbb gbbb eaaa bbbb fbbf aaaa bbb bbb aaaa fbbb dbbb gaaac bbbg bbbd eaaa fbbb gbbb aaaa bbbg fbbf aaae fbbb bbb gaaac bbbd dbbb eaaa dbbb bbbd aaaa bbbd gbbb aaae dbbb fbbf caaac bbbf bbb eaaa dbbbf dbbb aaaa fbbbd bbbd aaae bbbbd gbbb caaac bbbbd fbbf eaaa bbbbg bbb aaaa bbbbg ge dbbb aaae bbbbg aaac bbbd caaag bbbb aaa gbbb eaaa abbbb aaae bbbf aaaa aabbbb aaa bbb aaae aaabbbb eaaa dbbb caaag aaaabbbb aaag bbbd aaaa aaaaabbbb caaa gbbb aaaa aaaaaabbbb aaac bbbf aaae gaaaaaadbbbb gaaa bbb caaag gaaaaaaedbbbf aaae dbbb aaaa caae aaa fbbbf aaa bbbd aaaa caae aaac fbbbfcaaa gbbb gaaae eaac gaaa fbbbfaac bbbf caaag eaac aaag fbbbfa bbb aaaa eaag caaa bbbba dbbb aaaa aaag aaa bbbbg bbbd gaaae aaa eaaa cabbbbg gbbb caaag aaa aaa aaabbbbg bbbf aaaa aaa aaae aaa bbbb bbb aaaa aaa gaaaeaaa bbbb gfb gaaac aaa aaaaaag bbbb caaagaaa caaaaa bbbd aaaaaaa aaaae gbd aaaaaa eaaa gaaaaa aaa eaaaa gc aaae aag ``` <!-- end of image -->

I'm curious to see if this image contains any intersection points. I've spotted 1 narrow regions that might be worth examining further. Let's call them area A. <!-- image --> ```palette Key,Color ,#fefefeff a,#c14859ff b,#e0bcaaff c,#ebd0c9ff d,#cd7d85ff e,#f4e6e3ff f,#b2d7b1ff g,#98c896ff ``` ```image cbb bbb bbb bbb c bbbe baac bbbe aaaae bbbc aaaaae bbbc aaaaaae bbbb aaaaaaae bbbb aad aaaae bbbb caab aaaa ebbbb daac aaaa ebbbb aaa aaaa ebbbb aaa aaaa cbbbb aaa aaaa cbbbbe aaa aaaa cbbbbe aad aaaa bbbbbc caab aaaa bbbbbc daac aaaa bbbbbb daa aaaa bbbbbb aaa aaaa bbbbbb aaa aaaa bbbbbb aaa aaaa bbbbbb aaa aaaa bbbbbb caad eaaaa bbbcbb baac eaaaa bbbcbbe daa eaaaa bbcebbe aaa eaaaa bbcebbc aaa eaaaa ebbc bbc aaa eaaad ebbe bbb aaa caaad ebbe bbb eaad caaad cbbe bbb baac caaad cbb bbb daa caaad cbb bbb aaa baaad bbb bbb aaa baaad bbb bbb aaa baaad bbb cbb aaa baaab bbb ebbe eaad daaab bbb ebbc baab daaab bbb bbc daae daaab bbb bbb aaa daaac bbb bbb aaa daaac bbb bbb aaa daaac bbb bbb aaa daaac bbb bbb eaad daaae bbc bbb baab aaaae ebbc bbb daae aaaae ebbc cbb aaa aaaae ebbe cbbe aaa aaaae cbbe ebbe aaa aaaa cbbe bbc aaa aaaa cbb bbc eaad aaaa bbb bbb baab aaaaggggggggggbbbgggggbbbggggg daae aaaafffffffffbbbfffffbbbfffff aaa aaaaffffffffbbbfffffbbbfffff aaa aaaafffffffbbbfffffbbbfffff aaa gaaaaffffffbbbfffffbbbfffff aaa gfaaaafffffbbbfffffbbbfffff aad gffaaaaffffbbbfffffbbbfffff caab gfffaaaafffbbbffffffbbfffff daae gffffaaaaffbbbffffffbbbffff aaa gfffffaaaafbbbffffffbbbffff aaa gffffffaaaabbbffffffbbbffff eb gfffffffaaaabbffffffbbbffff gffffffffaaaabffffffbbbffff gfffffffffaaaaffffffbbbffff gfffffffffbaaaafffffbbbffff gfffffffffbbaaaaffffbbbffff gfffffffffbbbaaaafffbbbffff gfffffffffbbbgaaaaffbbbffff gfffffffffbbbfgaaadffbbffff gfffffffffbbbffgaaadfbbbfff bbbbbbbccceee gfffffffffbbbfffdaaadbbbfff bbbbbbbbbbbbbbbbbbbbbbbbbbccceee gfffffffffbbbffffdaaadbbfff bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbccceee gfffffffffbbbfffffdaaadbfff eeecccbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbfbbbffffffdaaadfff eeecccbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbfffffffdaaadff eeecccbbbbbbbbbbbbbbbbbbffffffffdaafff gffffffffffffffffffffbdbfff gffffffffffffffffffffffffff gffffffffffffffffffffffffff ``` <!-- end of image --> Here's a close-up of the area A. <!-- image --> ```palette Key,Color ,#fefefeff a,#c14759ff b,#e1bcaaff c,#e7c9bfff d,#cd6f7aff e,#f6ece9ff f,#da989bff g,#eedad1ff ``` ```image ad bbbbbc gbbbbbe aaf bbbbbc gbbbbbe aaaf bbbbbc gbbbbbe aaaaf bbbbbc ebbbbbg aaaaaf ebbbbbg ebbbbbg aaaaaaf ebbbbbg ebbbbbg aaaaaaaf ebbbbbg bbbbbc faaaaaaaf ebbbbbg bbbbbc faaaaaaaf ebbbbbg bbbbbc faaaaaaaf gbbbbbe cbbbbb faaaaaaab gbbbbbe cbbbbb faaaaaaab gbbbbbe cbbbbbe faaaaaaab gbbbbbe gbbbbbe faaaaaaac gbbbbbe gbbbbbe daaaaaaac cbbbbb ebbbbbg daaaaaaac cbbbbb ebbbbbg daaaaaaac cbbbbb ebbbbbg daaaaaaac cbbbbb bbbbbc daaaaaaac bbbbbc bbbbbc daaaaaaagbbbbbc bbbbbc edaaaaaaafbbbbc cbbbbb edaaaaaaafbbbc cbbbbb edaaaaaaafbbg cbbbbb edaaaaaaafbg gbbbbbe edaaaaaaafg gbbbbbe edaaaaaaac gbbbbbe edaaaaaaae ebbbbbg eaaaaaaaae ebbbbbg caaaaaaade ebbbbbc gfaaaaaaade bbbbbc gbfaaaaaaade bbbbbc gbbfaaaaaaade bbbbbb cbbbfaaaaaaade cbbbbb cbbbbfaaaaaaade cbbbbb cbbbbbgaaaaaaade gbbbbbe cbbbbb gaaaaaaade gbbbbbe bbbbbb gaaaaaaad gbbbbbe bbbbbc caaaaaaad ebbbbbg bbbbbc caaaaaaad ebbbbbg bbbbbc caaaaaaadebbbbbg bbbbbc caaaaaaadbbbbbc ebbbbbg caaaaaaadbbbbc ebbbbbg baaaaaaadbbbb ebbbbbg baaaaaaadbbb ebbbbbg baaaaaaadbb geeeee ebbbbbe baaaaaaadbe bbbbbbbbbbbccccggggcbbbbbe faaaaaaade bbbbbbbbbbbbbbbbbbbbbbbbbe faaaaaaaf bbbbbbbbbbbbbbbbbbbbbbbbbe faaaaaaab bbbbbbbbbbbbbbbbbbbbbbbbbe faaaaaae bbbbbbbbbbbbbbbbbbbbbbbbb edaaaac egggggccccbbbbbbbbbbbbbbe bdaabc eeeeeggge bbdbbc gggeee ``` <!-- end of image --> Oh my, look at that! It's 2 intersections in area A! Answer: A: 2; 2 = 2 There's for sure two intersections on the image you sent me.

<!-- image --> ```palette Key,Color ,#fefefeff a,#c14759ff b,#e1bcaaff c,#e8cbc2ff d,#cd6d7aff e,#f8eeecff f,#da959dff g,#f0ddd7ff ``` ```image cbb bbb bbb bbb g bbbe baag bbbg aaaag bbbc aaaaag bbbc aaaaaae bbbb aaaaaaae bbbb aad aaaae ebbbb caaf aaaae ebbbb faag aaaae gbbbb daa aaaa gbbbb aaa aaaa gbbbb aaa aaaa cbbbbe aaa aaaa cbbbbg aad aaaa bbbbbg caaf aaaa bbbbbc faag aaaa bbbbbb daa aaaa bbbbbb aaa aaaa bbbbbb aaa aaaa bbbbbb aaa aaaa bbbbbb aad eaaaa bbbbbb gaaf eaaaa bbbcbb faac eaaaa bbbcbbe daa eaaaa bbcgbbg aaa eaaad bbcebbg aaa gaaad ebbg bbc aaa gaaad ebbg bbb aaa gaaad gbbg bbb gaaf caaad gbbe bbb faac caaad cbbe bbb daae caaad cbb bbb aaa baaaf bbb bbb aaa baaaf bbb cbb aaa faaaf bbb cbbe aaa faaaf bbb gbbe gaaf faaab bbb ebbg baac faaab bbb ebbc daae faaac bbb bbc aaa daaac bbb bbb aaa daaac bbb bbb aaa daaag bbb bbb aaa daaag bbc bbb eaad daaag bbc bbb baab daaag ebbc bbb daae aaaae ebbg cbb aaa aaaae gbbg gbbe aaa aaaae gbbe ebbg aaa aaaae cbbe ebbc aaa aaaa cbb bbc eaad aaaa cbb bbb caab aaaa bbb bbb faag aaaa bbb bbb aaa aaaa bbb bbb aaa aaaa bbb bbb aaa aaaa bbb bbb aaa aaaa bbb cbb eaad aaaa bbb gbbe caab aaaa bbb gbbg faag aaaa bbb ebbg aaa aaaa bbb bbc aaa eaaaabbc bbb gb eaaaabc bbb eaaaag bbb eaaaa bbb caaad bbb gfaaad bbb cbfaaad cbb cbbgaaad cbbe bbb caaad gbbg bbb caaadebbg bbbbbbbccgggee bbb caaadbbc bbbbbbbbbbbbbbbbbbbbbbbbbbccgggee bbb baaadbb bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbccgggee bbb baaadb eeggcccbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbccggbbb faaad eeeggcccbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb faaab eeeggcccbbbbbbbbbbbbbbbbb daa eeegg bdb ``` <!-- end of image -->

Hmm, I'm not sure what to expect from this image. Let's see if any lines cross. The image has some tight areas where segments are too close. I should investigate those closely. <!-- image --> ```palette Key,Color ,#fefefeff a,#20d152ff b,#a6db0cff c,#9fd0a0ff d,#a8da3aff e,#5ed67dff f,#eff7eeff g,#b2d8b1ff ``` ```image c ea eaf gaf fag fae ae aa aa eaf gaf fag fac ae aa aa eafffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff cacccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc fcacgggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggg fccaeggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggg gf fcggaagggggggggggggggggggggggggggggggggggggggggggggggggggggggggggg bbbbbdgf fcgggaaggggggggggggggggggggggggggggggggggggggggggggggggggggggggggg fgdbbbbf fcggggaagggggggggggggggggggggggggggggggggggggggggggggggggggggggggg gbbf fcgggggeaggggggggggggggggggggggggggggggggggggggggggggggggggggggggg gbbf fcggggggeacggggggggggggggggggggggggggggggggggggggggggggggggggggggg gbbffcgggggggcacgggggggggggggggggggggggggggggggggggggggggggggggggggggg gbbcggggggggcaeggggggggggggggggggggggggggggggggggggggggggggggggggggg gbbgggggggggaegggggggggggggggggggggggggggggggggggggggggggggggggggg fcdbbggggggggaaggggggggggggggggggggggggggggggggggggggggggggggggggg fcggdbbgggggggaagggggggggggggggggggggggggggggggggggggggggggggggggg fcggggdbbggggggaaggggggggggggggggggggggggggggggggggggggggggggggggg fcggggggdbbgggggeagggggggggggggggggggggggggggggggggggggggggggggggg fcggggggggdbbggggaeggggggggggggggggggggggggggggggggggggggggggggggg fcggggggggggdbbggcaggggggggggggggggggggggggggggggggggggggggggggggg fcggggggggggggdbbgeagggggggggggggggggggggggggggggggggggggggggggggg fcggggggggggggggdbbaeggggggggggggggggggggggggggggggggggggggggggggg fcggggggggggggggggdbbggggggggggggggggggggggggggggggggggggggggggggg fcggggggggggggggggggdbbggggggggggggggggggggggggggggggggggggggggggg fcgggggggggggggggggggadbbggggggggggggggggggggggggggggggggggggggggg fcggggggggggggggggggggagdbbggggggggggggggggggggggggggggggggggggggg fcggggggggggggggggggggeaggdbbggggggggggggggggggggggggggggggggggggg fcgggggggggggggggggggggaegggdbbggggggggggggggggggggggggggggggggggg fcggggggggggggggggggggggagggggdbbggggggggggggggggggggggggggggggggg fcggggggggggggggggggggggeaggggggdbbggggggggggggggggggggggggggggggg fcgggggggggggggggggggggggaegggggggdbbggggggggggggggggggggggggggggg fcggggggggggggggggggggggggacggggggggdbbggggggggggggggggggggggggggg fcggggggggggggggggggggggggeaggggggggggdbbggggggggggggggggggggggggg fcgggggggggggggggggggggggggaegggggggggggdbdggggggggggggggggggggggg fcggggggggggggggggggggggggggacggggggggggggdbdggggggggggggggggegggg fcggggggggggggggggggggggggggcaggggggggggggggdbdggggggggggggggagggg fcgggggggggggggggggggggggggggaagggggggggggggggdbdgggggggggggeagggg fcggggggggggggggggggggggggggggacggggggggggggggggdbdgggggggggacgggg fcggggggggggggggggggggggggggggcaggggggggggggggggggdbdggggggcaggggg fcgggggggggggggggggggggggggggggaagggggggggggggggggggdbdggggaeggggg fcggggggggggggggggggggggggggggggacggggggggggggggggggggdbdggagggggg fcggggggggggggggggggggggggggggggcaggggggggggggggggggggggdbdagggggg fcgggggggggggggggggggggggggggggggaagggggggggggggggggggggggbbdggggg fcggggggggggggggggggggggggggggggggacgggggggggggggggggggggcagdbgggg fcggggggggggggggggggggggggggggggggcagggggggggggggggggggggaeggggggg fcgggggggggggggggggggggggggggggggggaaggggggggggggggggggggagggggggg fcggggggggggggggggggggggggggggggggggaeggggggggggggggggggeagggggggg fcggggggggggggggggggggggggggggggggggcaggggggggggggggggggacgggggggg fcgggggggggggggggggggggggggggggggggggeaggggggggggggggggcaggggggggg fcggggggggggggggggggggggggggggggggggggaegggggggggggggggaeggggggggg fcggggggggggggggggggggggggggggggggggggcagggggggggggggggagggggggggg fcgggggggggggggggggggggggggggggggggggggeagggggggggggggeagggggggggg fcggggggggggggggggggggggggggggggggggggggaeggggggggggggacgggggggggg fcgggggggggggggggggggggggggggggggggggggggaggggggggggggaggggggggggg fcgggggggggggggggggggggggggggggggggggggggeaggggggggggaeggggggggggg fcggggggggggggggggggggggggggggggggggggggggaegggggggggagggggggggggg fccccccccccccccccccccccccccccccccccccccccccacccccccceacccccccccccc ca ag ae a af ee ga a ae ga af ag ga a aae a ``` <!-- end of image --> Let's zoom in on area A to get a clearer view. <!-- image --> ```palette Key,Color ,#fefefeff a,#1fd151ff b,#a7dc0aff c,#9eeab3ff d,#b9e343ff e,#57dc7cff f,#dcf5d1ff g,#d2ed84ff ``` ```image aa caef aaaf faaa feac eae caae caaf faaf faac eaa eae caef aaaf faac bg feac bbg aae gbbbg eaae gbbbg caaf gbbbg caaf gbbbg aaac gbbbg feaa gbbbg eac gbbbg aaf gbbbg aae gbbbg caac gbbbg aa gbbbg cac gbbbg eaf gbbbgfae gbbbaaf fgbbbe gbbbg fdbbbg fadbbbg aafgbbbg eae gbbbg faac fdbbbg ea fdbbbg fae fdbbbg caf dbbbg aa fdbbdg caac fdbbdg eaa fdbbdg faa dbbbg cac fdbbdg ea fbbbd aac fdbbdf eaaf dbbbf aae fdbbdf caa fbbbd ae fdbbdf ca cac dbbbf ee aaf fdbbdf faf aae fbbbd ca eaa fdbbdf caa aa dbbbf eae fac fdbbdf faac caf fbbbd caa aac fdbbdf aaf caaf dbbbf ae eae fdbbdffac faa fbbbda ea gbbbdf fae eadbbbf aaf faa fdbb eaa caa fg caa faaf ea eae fae aac cac aa aae faf caac ee eaa ac aa ca eaf faa ae eae aac aac eaaf caa faa aaf eaf ae ae ac fac ca eae faf faac ea ``` <!-- end of image --> 2 intersections present within area A. Answer: A: 2; 2 = 2 There are precisely two intersections present in the image.

<!-- image --> ```palette Key,Color ,#fefefeff a,#20d152ff b,#a7dc0bff c,#98e9afff d,#b7e33eff e,#5bdd80ff f,#d8f6ddff g,#d0ec7cff ``` ```image c ea ea caf fac ae ae aa aa ea caf fac fac ae aa aa ea caf faf fac g ae bbbbbdgf aa fgdbbbbf aa gbbf ea gbb caf gbb faf gbb fac gbb ae gbb aa gbb aa gbb ea gbb ea gbb ac gbb a gbb ea gbbac gbb dbb adbb a gbb ca gbb ae gbd a dbd ca dbd ae dbd af dbd ca dbd ae dbd af dbd c ca dbd a ae dbd ca af dbd af fa dbd fa ae dbd ac af dbd a fa dbda ea bbd af fa db fa ac ea a ac ca fa af ea a ac ee a a ea ca ac af a a ca ee ac a a ca ca af ae a a ee ca a ae ca af ac ca a aae a ``` <!-- end of image -->

I have an image in front of me. I need to determine if there are any intersection segments. These zones indicate regions where lines appear to be in close proximity. <!-- image --> ```palette Key,Color ,#fefefeff a,#797b66ff b,#79b2b8ff c,#b0d6b0ff d,#4a4028ff e,#b9d4d7ff f,#99b291ff g,#ecf3efff ``` ```image g gggggggggggggggbgggg gcccccccccccccccbcccc gcccccccccccccccbcccc gcccccccccccccccbcccc gcccccccccccccccbcccc gcccccccccccccccbcccc gcccccccccccccccbcccc gcccccccccccccccbcccc gcccccccccccccccbcccc gcccccccccccccccccccc gcccccccccccccccccccc gccccccccccccccbccccc gccccccccccccccbccccc gccccccccccccfaadcccc gccccccccfdddacbccccc gccccfdddfcccccbccccc gadddfcccccccccbccccc gfddafcccccccccccccbccccc gaddag gccccccccccccccbccccc eaddf gccccccccccccccbccccc caddf gccccccccccccccbccccc fddac gccccccccccccccbccccc fddae gccccccccccccccbccccc gfddag gccccccccccccccbccccc gfdddafg gccccccccccccccbccccc efdddafg gccccccccccccccbccccc efdddafg gffffffffffffffffffff eadddacg eg eadddac eg ddac e d b d b d b d b ggggdggggggggggg b ccccdcccccccccccg b ccccdcccccccccccg b ccccdcccccccccccg b ccccdcccccccccccg b ccccdcccccccccccg b ccccdcccccccccccg e ccccdcccccccccccg e ccccdcccccccccccg ge ccccdcccccccccccg gg ccccdcccccccccccg eg ccccacccccccccccg e ccccacccccccccccg e cccbacccccccccccg b ccccabccccccccccg b ccccacbbccccccccg b ccccaccbbcccccccg b ccccaccccbccccccg b ccccacccccbbccccg b cccfacccccccbcccg b cccfaccccccccbbcg b cccffccccccccccbg b cccffcccccccccccbb b cccffcccccccccccggbg e cccffcccccccccccg bb ge cccffcccccccccccg gbg ge cccafcccccccccccg be eg gggfeggggggggggg gb eg fg be e fg eb e fg be gb fg eb ebe f be ebe a eb ebg a bg ebg a eb bbg a gbg bb a eb bb a gbg gbb a bb gbb d gbg gbe d be gbe d gb ebe be ebe ebg ``` <!-- end of image --> I'm determined to find out if an intersection exists in area A. <!-- image --> ```palette Key,Color ,#fefefeff a,#99968bff b,#78b1baff c,#bcc7c5ff d,#42361eff e,#dae5e6ff f,#7a7464ff g,#5f5542ff ``` ```image ad ad ad ad ad fd fd fd fg fg fg fg fg fg fg gg gg gg gf gf gf gf gf gf egf bba fbbe dabbc da bbbe da ebbc da bbbe da cbbe da ebbb da cbbe eda ebbc eda cbbe eda ebbc eda cbbe eda ebbc eda cbbe edc ebbc edc cb cdc e cdc cdc cdc cdc cdc cdc cdc cdc ``` <!-- end of image --> Amazing! This area was hiding 1 intersection all along! Alright, let's examine the next area. Eureka! Let's inspect this close up of area B <!-- image --> ```palette Key,Color ,#fefefeff a,#7a7464ff b,#71acb6ff c,#aaa49aff d,#473c24ff e,#dfe9eaff f,#98c3caff g,#c0d4d6ff ``` ```image ebg ebg ebe ebe gbe gbe gb gb fb fb fb ff bf bf bf bg bg ebg ebg ebe ebe gbe gbe gb gb fbag ecadabdc gcaddddabb gcaddddacg ff egcaddddace bf ecaddddaace bf ecaddddacge bf gcaddddacg bg ddddacg bg ace ebg ebe ebe ebe gbe gb gb fb fb fb ff ff bf bf bg bg ebg ebg ``` <!-- end of image --> Bingo! This close-up reveals 1 intersection in area B! Answer: A: 1; B: 1; 1 + 1 = 2 The final answer is: two intersections found.

<!-- image --> ```palette Key,Color ,#fefefeff a,#8e8b7eff b,#72aeb7ff c,#bab6adff d,#453a22ff e,#d2e0e1ff f,#9ec7cdff g,#6b624fff ``` ```image b b b b b b f f e ee ee e f eaad cgddc f cgdgc b cddgc b addae b eaddae b egdda b cgddc b cgdgc b cddge f eaddae f eagddgc f eagddgc e eadddgc ee eadddgc ee cadddac f ddac f d f d b d b d b d b d b d b d b d b d f g f g f g ee g ee g e g f a f ba f ab b a be b a eb b a be b ea fb b ec be b ec fb b ec be b ec ff f cc b f cc ff e ce eb ee ce bf ee ce eb e ce bf f ce eb f a be eb a eb ebe a be ebe a fb fbe a be fbe a fb fb g be fb g fb bb g b bf g ff bf g eb ebf g bf ebf d eb ebe bf ebe ebe ``` <!-- end of image -->