Day 8 - Segment displays

Wow, that's a lot of information.

We are going to have to try to work out how to build a mapping from segment displays back to wires, and it feels a lot like a logic puzzle or a suduko.

But wait, before we get started, what are we actually being asked in part 1?

I've been caught by this before, attempting to solve the asked problem, before realising that the problem can be reduced down to a much smaller problem.

One of the things that we can notice is that for a given digit displayed, there's only a certain number of segments on, as it says, if there's 3 signal wires activated, then there's only 1 possible number that can be displayed, the 7.

I think therefore we don't need to know anything about signals or wires. What we're being asked is to turn the words into frequency counts of the length of words, and then find all the ones that are unique numbers.

That's actually really easy

test_signal_pattern = "be cfbegad cbdgef fgaecd cgeb fdcge agebfd fecdb fabcd edb | fdgacbe cefdb cefbgd gcbe"
import collections

def count_easy_digits(signal_patterns):
    counter = collections.Counter()
    for signal_pattern in signal_patterns:
        outputs = signal_pattern.split(" | ")[1].split(" ")
        for output in outputs:
            counter[len(output)]+=1
    return counter[2]+counter[3]+counter[4]+counter[7]

assert 2 == count_easy_digits([test_signal_pattern])

Great. So in this case, we're counting digital signal lengths, and the digit 1 is just 2 long, the digit 7 is just 3 long, the digit 4 is 4 long and the digit 8 is 8 long. So we can just loop through the example input and see if the total works

test_signal_patterns = """be cfbegad cbdgef fgaecd cgeb fdcge agebfd fecdb fabcd edb | fdgacbe cefdb cefbgd gcbe
edbfga begcd cbg gc gcadebf fbgde acbgfd abcde gfcbed gfec | fcgedb cgb dgebacf gc
fgaebd cg bdaec gdafb agbcfd gdcbef bgcad gfac gcb cdgabef | cg cg fdcagb cbg
fbegcd cbd adcefb dageb afcb bc aefdc ecdab fgdeca fcdbega | efabcd cedba gadfec cb
aecbfdg fbg gf bafeg dbefa fcge gcbea fcaegb dgceab fcbdga | gecf egdcabf bgf bfgea
fgeab ca afcebg bdacfeg cfaedg gcfdb baec bfadeg bafgc acf | gebdcfa ecba ca fadegcb
dbcfg fgd bdegcaf fgec aegbdf ecdfab fbedc dacgb gdcebf gf | cefg dcbef fcge gbcadfe
bdfegc cbegaf gecbf dfcage bdacg ed bedf ced adcbefg gebcd | ed bcgafe cdgba cbgef
egadfb cdbfeg cegd fecab cgb gbdefca cg fgcdab egfdb bfceg | gbdfcae bgc cg cgb
gcafb gcf dcaebfg ecagb gf abcdeg gaef cafbge fdbac fegbdc | fgae cfgab fg bagce""".split("\n")

assert 26 == count_easy_digits(test_signal_patterns)

signal_patterns = """beacf afbd bcead cgefa ecdbga efb gbfdeac ecgfbd acbdfe fb | bf efb bgecdfa egcfa
cbdgef cdfageb cegbd fecba edgf dcfbe dbcafg df fcd dbegca | bgcdef dgbec bfeac fdeg
bgdcfa dgabf bfdec baefd abeg eda afcdge ea bfceadg dfegba | efbad fbdea dae fagbd
cfdabe fcgbe gcdeb ecdfgb bdc cdgf cd cfageb bgdae daebfcg | decbaf cdfg deabg cd
eacgdfb fdbeca agedc cbedf dcfgab bgef gdf fdgec fbcged gf | gf acegd fdeabgc gfd
egcd aebdcf gbeca eg edfcbga gbe cfbag bdeca gadbec bdgefa | caegfbd dgcebfa eg bgdfae
fcgab egafb gedbca gfc cf ceagdf cafbdeg gcafbd dbagc cfdb | dbecga dbgcefa cfg fcg
geacd bg cbfead efgabcd fbace ceabg efbadg gfbc gab geabcf | cfbg fabce bg fdgeacb
bfceg ca baefc caedfb acfedgb cfad edacbg eac debaf bdfage | geadbc bfgeacd efagcdb cefbg
fd dcfbge fcad dfg bgaefc fdcgab fgdceab afdbg cbagf gdaeb | aecdgfb dbcfag cdaf gfecba
dabce gceab fegcab fbdca adeg gcabdfe gedbac ed egdfbc deb | fdegcb acbdf ed gdae
bgcea cbfdage egad ecadb beg befdcg fcgba aecbdf ge abedcg | geb gbe deag eg
bfecag egbdfac abecg gcebf efdagc ca acbf cfbegd eac bgaed | bdcegfa gbfce dbgecaf ac
fcbed dbfegca cdafbe edfgc abfde ebc egcfab dbca fdgbea cb | cb fgedc cb cdfeb
fb fdeacb bfe bfdc ebcgda afdeb acbfge agedf ecbad fdagcbe | gfcdbae fb abcefgd bef
egbca cfe eadbfg baedgfc cf bcfd afbde acebf fecdag edafbc | cfe caedfgb fc eadfgc
gfabc fbcaeg bagd cgbfaed dfecb gfdcb fcedga dg dafbgc dgf | abgd bdgcf ebcdfga fcedbga
cdb abce ebgfdc bfagdec abdcef dbfea gfdca facbd dfaebg cb | cdb cb dbc cdafbeg
afdbe dcfegb gedca adcbe ecfgbad fcadge cb acgdeb cbe agcb | dcage bec cb cb
gafdec cbdg fdgbce dce dfegb fceab becagdf dc dfbce agdefb | dgebf dc bfgde cde
bagfc bdef cgeafd eagfbcd afceb fe cfabde agcdeb cef eabdc | fbdgaec ef ef cafbe
fbage cgfba bdcage edagbf fe agcfdeb gfe adfe dgabe egbfdc | fe gfe geabf dgecab
gdfec bgfc dbgafe gfdebc dbfeg fc fabdcge fcd gedac dcbfea | egadc cfd efbdg gcbf
dacgf dfabc ebgcad daegfcb aedfbc dbgf agd aegfc cbfdag gd | agd gbdf bdafcge bcfegad
gdbea ebacdf adebfgc dfb df fbdea gcfebd fceab bfcgea fdac | gfabecd efdgbc fcebgd fbd
fba gbdcf cbae ebfgca fbcegda ab gbedfa gbacf gface gecdfa | ba bacgfde edfgac ab
fgebda bfgae cfdgba agcbe dbaegcf gbfda ef bfe gcbdfe dfea | ebgfdc eagcb eafd bef
agfecb cabef dafgec adfeb fbc gacb cb afbegdc cfaeg cbdefg | aegbfc fcb cgfdbe fcaged
agf eadfc cegabfd eagdf efdgb cgfbde agbfed gfbcae ag abdg | abdegf gbad baecgf afdbeg
gfbdac bd gcaefd bdcegfa gadbce dgb badf gbfdc fgecb cgadf | bgd fcbgd gdb dbfa
cbgf efcgbd aefdcbg feabd dcf cdebf ebcgda cf egcbd fadceg | dcf cf gcedaf bgfc
bacgfe fbc cgfe bcdagf gebfa cafeb bdcafge afdegb caedb cf | befga cbf gcfe bcf
bgdf geacf acedgb gb aecbfd bdcfa abgcf bgc acgefdb cdgabf | cdbgea gcb fdbg adgefcb
bdacgef fadeb abcg gfcebd gbf afbge egacf dgceaf bg aefgcb | gfb fbg dbgecfa bacg
dcegf bg cdafegb cfdebg fagced bge ecfab dbgace cgbef bdgf | gb gbfd adgefc ebg
gbf fbcdega egdafc bg aefgd gbecfd agbe abcdf edgafb fbdag | cgaefbd dfaeg dafgb dfeagc
beaf aed aecdf aebcgd eafdcb cgfabd ea gfcde cbdfa ceagdfb | fabe bafecd fecgdab ae
bdcfe gbdae bcgafd daegfb aecg cdagbe gfbadec gbc gc edcgb | cdbge efbgcda dagcbe agebdf
ec fdcag aegcbf bagfcd cgfade adecg fdaebcg fecd degba egc | deagc ec ebagd cafgeb
dcgaeb egadc agcfde efac beagdfc fcdagb dgcef gbfde dfc cf | cdf cf febadgc ecgfd
afd df gdafecb bdcf fecba acged edcabf egdbfa egfabc acdfe | cgebaf dacge fdbc decga
ga beafc cgbea dceagf feabdc bfagec abgf cga fdeagbc cebdg | cagbe bgfa gbced gabf
edag cdafb ae efacd eacgbf cedgbf afe fbceadg cdgaef egcdf | eaf cdafb efa ae
eagdbfc cagdf badcge fgec cg cdg bdfca feadg fecdga dfbega | abcfd dgc cgd gdc
beadg ca cdeba gcda acfebg dfbce fcbadge dbafge gdabec cae | gcad eca agbced gdbace
agfcde gdceab dbeaf agfed dg acfegb gaedbfc adg aegcf fgcd | bdefa cgebfad gdfc gd
gafcdb bfgaec daecf bcfgdea bged be dcgfb cfebd fbe dfebgc | fcabge dbfagec gebdfca gbfcd
dcaef agfbec gea ge bged cbdfag fgbade gbdefca abfgd faged | bfdcega aeg bdgaf bedg
dcbfa ag fcaegb fcdaegb gebdf adeg bdfga dgfeba ebcdgf gaf | cbgedfa ag egda ga
bcgdaef fcabde dbfage cfdgb daegf bfe dgefb gfadce egab eb | bfe gfeabd gdbef dagfbec
be egb fgcbde agdbcf gcdfb edbf bagecf ecadg bdefgca bdegc | efcdgab edgbcf efabcg dgecb
bcegfd ceafd gbefca eba dacebfg gebfd baegdf dabg dbfae ab | bae abcgef gbdcefa dbga
dceagfb edac ecfba cbgadf dfbge bcdefa fdc cd fcaegb edcbf | bdface cgfabde cdf cdafeb
cgaedbf acd afbdge afdcg bdcaeg gadfb ac gcbdfa abcf cdgef | gdfac cgdef cgfad cfbedga
gaefdcb debga cd aebcd gceafb afdceb cfabe dfcb dca agdcef | dbcafeg dfecag dbfc efgdacb
abdeg eaf cedfba aefdg gcadfe af gdfaecb gcfa gdfec cbgdef | fea cebfda dfceag fadcebg
bcgdfe fbdce fcdbea bcead adc ca bdgcaf edcgbaf baged feac | ecbad bfdec acd ac
bd aecfgb bfad gdb dgbace fbaegdc egbaf ecdgf egbdf fgadeb | fcageb dgb dgfeb bfad
bfcea dfbcea badge bfegdca gac cafdgb gc aecbgf caebg gefc | fegc bcaeg beafc feadbc
cagef fadgebc fd daf dcfbga ebdgfa cbeadg afdeg abegd ebdf | gbafedc daefg fd gbadec
dfaebc bcgaf bcaeg abecgf eagf dgecb cae ae dcgbafe gbadcf | ea gdecb bfacge gbace
dfbec gcbade fadb df badefcg dbeac cfgeb ebafcd fecdga edf | febcg cfadeg ebcgda dbfa
cadgfe bdfea dgbfeca dab dgbaec afdegb fdgb gaefd db cbfae | dgbf edabf bd dfgb
decbga ebfcgd gcebf cabfe aec cbfad ea eafg adbgcef cebfag | efga ea cgafbed acfdb
dcgefb gafc bagfce ca fcaeb aec dfbae ebgcf bcfdega deacgb | begcdfa ace fdegbac ac
gafc dgafecb cdgeba dbgafc fa bacdg fceabd fbgde afb fadgb | cafgdbe fbedagc adefbc gacefdb
dgfe dfa fd agcfbd bedac gfaec bdfcgae ebgcaf edfac acegfd | adf degf fad fedacgb
efgacdb gedfc eadbfg efd dcagf cfdage gdbacf gcbed fe fcae | eafdgb fdcge cafe dfe
aebg gbfdac dcebfga bdcef ebcfag abcfg acfeb dfcaeg ea eca | bega ace bacfg bgadcf
ceag caefgb agb fbgdc ag cafbg becfa cfeabd deafgb eafcgbd | cgadbef gba ag bag
bdge agbec dgcfae agbedcf gdc gbecad dabgc gd fbadc abefcg | gfcbaed dbge dg acfbd
dcef efb dbcfgae gbecfa fe ebcdag cafedb cadbe afdbe badfg | edcf ef fe fe
cdagfeb fgabc cafd fcb bdagc dfcgeb gbfacd cf baefg bdegac | cf acgbd fdac cdbfega
cefbdg debgca abfeg cebgf fdbgac adcgefb fcde cbe ce cdbgf | bgfae bec cfdebga cfegbd
fcbag gcfbed adgbefc afbdeg adbgf dbea ad cefagd daf debfg | da afd baegdfc afd
ba gbcda degcb bad adbegc fgcad eacb adgefb gdfaecb gcbedf | dgbaec gdbcfe dba ba
cdabf cbdgae facgb fadg acg gfbce ag cgdafb edcfab dbcegfa | dafg bdafec cbfeg facbg
edbaf cfebad aec cdaf ca gfabce cbeda afgebd fbdacge bcgde | ac afgbce dacf fcda
egdba bafeg bd gdfeba bcedfa agcde bad fgdb fceabg gabdefc | fbgae efgacb cadfeb bgdf
fdcgae dcefb cdb fecgabd afecb dbcfeg bgceda bd gfdb cdegf | dgabec cbdgae bcd aedcbgf
beg eg bfcea cdfgeb baefg abgdf fgeabd gcfdba agde dgbaefc | cdabgf dbefgc bdgfa facgebd
dbgef bfecgad egfcd agfbce agbde bf gcebdf dagfce cbdf feb | fbe ebfcdg bcfd fgcdabe
abgdec fgd fcgeb gedabf gfbdc dgaecbf afdc dgcafb fd bgcad | fgd adcf bgfcd fdegba
cafdb acdbge acedb dfbcg af ceadfbg adf adfgec faeb dcfeab | gdabfec bdgfc dcfba feab
dbcgae bcdfeg bfceadg bafgcd dacgb dfac cfgba bfc aefgb cf | dcegbf fc becagd fc
geacb gebfda gbcdafe efgc ge ecabd bcefag gfbcda age gafbc | adbfecg acbge cabedfg gea
gabce feagdb dgb fceadb deagb edbfa gd cbfgde agdbfec afdg | gbd begdcf aegbd bgd
afecbg fgeda dfeabgc cdafe adgb dg dbcegf fabged faebg egd | ged abfgced gd afcde
ec badfec cfe befgd gdacfe bace fgedbac gbcadf fdcba cfedb | ecf ec ce efcdb
dacfgb fd gfdbae ecbdgfa ecbdag cbfeg faed gdf aegbd egdfb | eacdbg gbfdea begfd becfdag
faegbd fgdace acbfeg dfgecba ed dabge fdbe dae badcg eagbf | dfeb dfgabe adcgb de
dbe gbcef acdebf defa geabdc de dfcbag dbgaecf cabfd becdf | eadf adcegb efcbg cfabdg
gcaed adgbce abfeg cb egcba cdba cgadef cgbefda fdbegc ebc | gbeaf cb bcad fadcge
cef fbacd gafedc ec gaecbdf bfedg gdcfeb bfdce cegb bfadeg | ec fbceagd fce fec
gfdae adgb cabfde fgdceb dea gafec bdgafec agdebf ad degfb | bcedgf bedacgf cegfa bcfgead
ec cge dagef eacgbf cdafegb cfgadb gbedca ecagd cdeb agcbd | cfagbd dcega gaecdb bgfaecd
ebgac cegbad dfcegb abegdf gbdec bae dcae efabgdc ea cgfba | ea eba deca bea
dcgfba adgbef feac afedgc dcegf egabfdc fc fdaeg bdceg dcf | beagcfd gdbcafe efac cf
cadfg gb cedagf gbd abgcfd fdcebga acgb febgda fdbec bdgcf | cagb cfagd gbd fegcbad
fgdca afcdeg bcdeagf gc fcaed defabc aedcbg bgfad cdg cfge | gc gdeacf agdbce fbacdge
fea adgeb bgfe fe dcfeag bafegd badcf aedbfgc adefb bcdeag | eafbd abfged begf egfb
gace dagcf fedac fbceagd defab cfe gdcfeb cdfgae ec gbfadc | ecf cagefbd befgdac acge
afc gaedf dfecga bafcdge cf bgdac dafcg eacbfd gbdafe gcef | adbcg fca agdbfce acf
cdfebg dcbe fgbdac bfegd be beagfc gfdea gacfbed fbe cgfbd | gedabfc eb eb aegcbfd
afg dfgec gcfeab ebcfagd fa adfe bagcd gdcfa gfbedc gecdfa | fa eacgdbf fa defa
bfdag gbecd cefg efcbdga fbc cf gbcfd badfec bedfcg egcbda | gadefcb bfc bacfde bgedc
cafde dce dcbfa dgcefb cgea dgafceb fgcdae dagfe gfebad ec | fcdae dbgfec gfdea dfcgeba
gcebad cfgdb cfgeab cdb cd egcdbf gbdaf fcde fgdbcae gfbec | cbd geacdb adbcge dc
afegb adbfg becafdg dg bgd gaebfc fdge cdfba gbcead abfdeg | gd gbd dabfc defg
fabeg gd dfebcg dgfae bfgeca fecad adgb efabgd ecfdbag deg | gd cfead dcfea cbefgda
bfceag dafgb fdce fc cfg gcdebf becgfda dgbec aedcgb cbgdf | fc adfgb dgfab cgbedf
bfeg decaf cegfa ecfgab gcf dbfeacg caedgb aegbc dbcafg fg | bgdcfea fg bfdaegc afgcdbe
eac ae cbdfe cbaedf abcfedg bade aefcbg bdcgef cedaf gdfca | efcdbg ae bdfce cdefa
gdebfca bfgca fda bcafd ad gcda cfgdab fadbeg edfcb gcbfae | cgafdb fad fda acdg
gfbdcae afed gedac facegd bgeac de fgbecd cagfd ged bdgfca | bacge egbacfd adgfc deg
gdafbe dbacgf cbefag cbfdg bfdag fcedg cdbgfae adbc cgb cb | bc gadefb bc acbd
fa egcad acfed ebdcfa dgcbef daf bdecf fgadbc fbae gabdecf | cedfa egdcbfa fa afd
cfd fd gbafc dcagf daecg dbfa cbfage egfdbc bfdgcae cbdfga | ecbdgf df dabf fd
eafbdgc baegd fe bagfed aebfg cabedg efg facgb bdgfec fade | defa ef ef fdae
cfdeagb bdeacf eac gcdbfa egab egacfb cdgfe ea ecfga cgfba | aecfg dfbacge cae ea
aefcdgb bacfg cdg afecd gedbcf afgcbe abgd adbfcg fgdac dg | bagfc gbfcdea gfdac bgda
becf baefgd dcafg cb cdbage dcgfb bcg gdbef edbfcg egbcafd | fbce cbg gcbfde gefabd
gb bgedca fedga cfdeag fegb dcbfa gab afgdb acbgefd bdgaef | bga gb gb ebfg
dca cedbf dcfebga ca egbcad cdaefb fedag efdac acbf cfgdbe | fbcade cebfdag adc acd
bgdeafc gaefd fbeagc cdfa fgc degcf dgbafe gcedaf dgcbe fc | gfc egafd cf bcdeg
dfaeb fae ebacfd egadb fe gadbfc febc gbfeacd fagcde dcabf | beadg adefb fcbe dagfcb
fgaed gd dacgfb egcd gdf acfed adbfceg edbfca dcafeg baefg | decaf bacdgf fgd ebgaf
bcfeadg dfagce fdcgba dfcab gabec gcf gf abgfc bacedf bdgf | bcgfeda bdgf fg gf
ceab gafec cef fcdgba cbfeadg bcagf ce ceagbf agdfe degcbf | efgca efgca cef ebac
abgef abf gbeac gabfcde degcfb efdbga aefd bgdcfa af befdg | afbcdg fa bdfgec dfbgae
gdafce cfb agfbc ebaf fcebdg aegfc cbgfea egbfdca dbgac bf | fb abfe aebf dgecbf
ceadf fecag dcgaeb dgbfcea edc bcafd cdabef ed befd gfcdab | badecf ed egfca edfb
gecdbaf dbag bfade gabfed cedfba gfade cfaebg fgdce ag fga | bafgdce gacbef ga dagb
defbcg gbfce beag gacdf cfbaeg dbcfea ea cefga ceafbgd ace | aefcg ae aegcbf ebga
egbdac fgadb cefdbg aceg gc cedba dcbag ecafdb fgeacdb gcd | cg ecbad egdafbc cgd
bdac ac fcdaebg afbdeg dbagf fbcge acf cadgbf afedgc bgfca | cdab fgceb ac fgbac
ba eacfg cab aefcb cdeabgf ecgdbf dcbfe dbfeac acdbeg dfab | bacef adbf bfda cab
gbfca ceafbd geda gcdfae efbcdg fgced da degbcfa adf cdagf | aegd ad da geabcfd
fgdacb dg efagc gcd cgefab edcgfa cbedf gfdce eabgcfd daeg | dgc gdc cfedga cdg
bcadeg fbgaec ecdag gbafced ba bca edab bgadc fdcgae gdbcf | bcadfge edgacf bac dabgce
aedfb dbfcae caefbdg aefcdg gafcb dfcba bgfeda dc fdc edcb | bdfae cd eafdb cdf
cga afdebc gc adcgefb adbgf acgfde gcabd gbedac ecgb acdeb | gbce ecadb daebcg gc
cdf dcafg df cgade cebgad dcgfea fdacbeg dgbfec afbgc fade | bgeafdc feda edaf fbgac
fagbc dbag feadgc gfa dcebfg gbdcf ag gecafbd ceafb bagcfd | fadegcb gacfed defcbg dgcbaef
cadbfeg dbgace fcagd bedfca cfegd afgb bgdfca ga adg fdabc | dfcag gcedf cefabd fbadc
fgeabd egbca dfage fdagec fb dacbfe badgecf baf gfaeb bdgf | bfdg fdbg ebagc beafg
gbdaefc fa dgafb feda fegbdc dfbeg gaf cegfba gacdb badgfe | bagdf fa afg ebgcdf
bedc fbagd bdage cgdeab eba gcabef afcdge edgca be cfbgeda | geadb be dceb ebdgca
fe fceb acegdfb efg fdgce fagbed bedgc fedbgc dagbce agdfc | febcdg egdcfab dcebgf gef
fagdc ebacgd ecgdb decafgb cefbda geba bagcd bad fbdgce ba | ecdbg abeg dfbeac fgdaceb
decgaf cgab aedbc cbaegd ca bdegc fcegdab efabd cda cdbfeg | aedbf ebdaf cda dca
gafbde ecfda afdegc ecdgb ba cbfa cfadeb edabc bea ecbdfga | eab ecdgb bea ab
gbecaf dbgf facbgde cegabd gebdfa fdaec dfage egf adebg fg | gfe egf becafg abfgedc
gfceabd adgcb bcdf afb gafbd becafg bf dagef agbdec fgcdba | cbagfd fdbga dcbega dfgecba
ba afegdb cdab cfgeb facebdg fcabg cdagf fdgcab gab decgfa | cfbdega dacb agdcfb gabfdc
adebgc bdefcga afegdb bcedf bfg fedbg fg efga dbgea facdbg | gf gf debafg fgb
cegfda gfa ecgf gf ebgdac afcbd ecagd afebgd fcdag begcafd | fcabd dfacgbe fcabedg ceadfg
febgcd fcbda cdgab fcgbad bf fdcea dfb egbadfc bgcdae fbag | cedfa fb fb gabf
ebfag fcbade ad adec bgecdfa afd gebfcd bfdec fbade bgcdfa | adf ecad ebadf bdcgafe
cafbgde bdace cefadg gefcbd ag egdcf gae bcfaeg gcdae adfg | egabcdf cedga cedag adgf
agcef egcab fc dfeagb fce gbaefdc ebcadf aefdg adefcg gcfd | dfgc aebcg egdcfba agbec
db fdbcge dgb gfaced bfacgde dfba egdfba cabge edgfa gebda | eafbgdc db db gdafcbe
cad cdfgea caegbf agbd cbdef gbcdaf gadecbf ad bcafg dacbf | fgecba cgbfeda da dbecafg
bdegaf gfde gf bcadeg dafgcb afg bgaef eagdb cfbeadg fbeac | ebgad gfed debfcag fdge
bgac edgacbf dfbea cgebda gea cfedga agedb ag dcgeb fcedgb | dbage bdgacef cfagdeb deabg
caebd edf edgfbc fe abfegdc cdfea gfdac eacfgd gfacbd gaef | fega fgae gafe cabde
bfadegc dafec dbgaec abdcef fdaegc dag cagf ga aedgf fbedg | bcafedg ag ga adg
dcgfa dgcafeb cfb bf cegafb begcda fdgbce dcebg bfed fcgdb | dgcebaf bedf fb bcged
cbegd edfa fdc gadcfb gbcefad bgacef acfbe ebacfd bfecd fd | fdc dbgafc cefbd cdf
fgd dgbfe gf gcef bdecf dgcfba acfbde gdefbc badge facbdeg | dcfaebg fg fgd fbgced
abdeg adebcg ebafdc bgcadfe gedc ega bgdaf cabed efacbg ge | ge gae age afebgdc
debfa dfbga fagdc fbg cadgfe acgfbd efgcab cgfeabd dbcg bg | fgdba bg gfacbed ecabgf
bc egdba ebdacg cgba dabfec bec defcg cdbefga gbfead becdg | bcefagd bec cebfgda cb
deagbfc agebdc fbedca fa edgafc bfac adcbe gfedb afd efdab | fad dbaef cbfdae af
afgdeb beagd daecbfg gbfedc ecd becad egac agecbd ce fbcda | fbadge eacdbg cde ce
fgabec gefb cdagefb fbacgd dgecba adecf eg cefga egc gcfba | dafgbc gec bfeg gefb
gbcf fceag gb bag bdafge gbeac fdegca cfegdab egfacb daceb | bg cagfeb aedbc cbaeg
gbac fedagb gaf adcbf ceabfd abecgfd bfcdga ga edgcf gfcda | badcf fcedg adbcfg agebfd
gdbfc fbaecd gaef ef efb agebc gabdefc ebcgad facegb bgcfe | cfgdbae faeg efga cdegab
fbacge decgba bcafd fedgab fageb ed efgd ebafd gedbcfa bed | de ed bdafe de
bcgdf badgec de fecgd cfeag dfbe dcgafeb gdacfb ced fdbgce | de de edc gafbdc
gebfa fd dgacb dfgba bfdeca daf becfga edfg afgebcd gfadbe | bdcfea bafecgd acdegfb fgbdea
fgdcb efdcg gcfabd gcdbafe gbf acfb aegcdb edfabg fb gbcda | bgafde gfcbd fb cedbfga
de fadcg befcdg fbeac adcef efd ebgfca cbefadg edba dbaecf | eagbfcd beagfc bcefgd beda
ebcfad fbecgd edgba df adgfcbe dfe bcfaeg bedgf bcefg dgfc | df bcagef df aecfgb
acgdb gdc gcebdaf abcge ecgdfa egbd cbaegf gdacbe fcdba dg | egcfda aebgfc aegcbdf cgd
gc cge cgdb deafbgc dageb cbega agbcde cedgfa gbefad cefab | dabfeg gc eabcgdf gabde
abegc agecf adfcbge bcdaeg fbadec bca cb bcgd egdba gbafde | gbdc begad bfecda cb
daecgb abegd bagedf begfcd fe feag abefd bfe fbgceda fbdac | fbdac gcebdaf egfa fe
eafcbdg abcdg acegf dfcga fgaebc defcbg aefd dfc dfgace df | df adef fd dfea
fdecabg ba agebdc adb gcdea befdg gabc egdba badefc ecagdf | bda gcabde gdaec fgdcae
cdfg dbecf dg caebdf gbd beafg cbegfd ebcgdfa gdfeb agdecb | cedfb gd cbgeafd debgacf
bca cadbfeg gabfcd bcgafe caebg adgfec bc bcfe gefac beadg | cgefab cgfae befc acbegf
cabgdef cgabde efcab degcf gcfdeb da fgda cda feagcd aedcf | adc da cgaedf cgdfbe
dagfbe gaefb efcgadb fbcae fg gbf edbag cbgdae gadfbc gfde | bgf gf acgdfb cfgdba
cbedag edgca bfcagde gfbae gfdea df adfc dafceg fedbcg gdf | adecg gbafe acdbfeg df
ebfc ef gecfad gfdcb egbad gfabcd ecgdafb feg bfgdce dbefg | aegdb bfged ef bafdgc
ce cefd cafdg cdgefa geacbd eca gcbfad gebfa afecg bfedcga | ecgfa cea defc ce
ceb edbgafc fabec cb dfagec fgbea daefcb efdca cebgda bfdc | bec eadfgbc degabc adgfce
cgf aefbdgc gf bagf gedacf ecgfb cdfeb acgbe ebcfga cedbga | gf fbgcade cbegfda acbdfeg""".split("\n")

print(count_easy_digits(signal_patterns))

488

Part 2 - deducing the wires

So we knew this was coming, and this feels really hard.

But let's work from the patterns that we know, and see if we can work out some facts. We're going to use the test line below to work this as an exmaple:

be cfbegad cbdgef fgaecd cgeb fdcge agebfd fecdb fabcd edb | fdgacbe cefdb cefbgd gcbe

We can deduce a 1 from a 7 from a 4 from an 8. If we take the 1 and the 7, the letter in the 7 that isn't in the 1 must be the top line a. Our 1 in this case is be and our 7 is ebd. Therefore d=>a

Now we also have only 2 letters that can result in either c or f lamps being lit. In our case this is be.

One of those letters is the difference between the 6, 9 and 0. All of 6,9 and 0 have 7 digits lit, but the 6 will be missing either the c or the f.
So we're looking at cfbegad, fbgacbe, and we're missing one. Annoyingly, we're missing the 6 in our test case, so we cant determine this.

Whichever one is missing one of the lines that was in the 1, must be the c.

Further the f is lit in every single digit apart from the 2. If we can find a single 5 digit example that has one letter missing whcih is present everywhere else, from the subset from the 1, than that's probbaly the f. In our case fabcd is missing the e, so e=>f.

Going back to our 1, we now know that e=>f, so therefore b=> c

We can use the missing f in 2 to find a 5 long digit that's missing an f. We don't seem to have one in our data set.

We can use the missing c in 6 to find the 6 long digit thats missing a c. We already knew we were missing a 6 though.

At this point I need a lie down... I am struggling to do this once, the fact that the wires and the lamps are boht named after letters is making life really confusing, and even if I can do this once on paper, I'm not confident that I can do this in code.

The problem here is one that I can recognise, it's a form of constraint solving. If I can encode the constraints, like The one and the seven share 2 in common, and the one differnt maps to a then you can feed the system the input and it will reduce down to only the possibilities that match the rules.

The way to program this is to create a dictionary of "possible values" for each lamp, which starts as "all possible values" and then, for exmaple, take the 2 input one, that makes the 1 light up, and modify the possible values for lamps c and f to be only those inputs. You can also then remove those two values from the other possibilities.