Xah Talk Show 2025-12-18 Ep727 Wolfram Language, Advent of Code 2025, Day 3, take 2

https://youtu.be/nWPN0jzuRQI

Video Summary (Generated by AI, Edited by Human.)

Solving Advent of Code 2025, Day 3 (0:04), I'm working in Wolfram Language to extract two digits from a given number that form the largest possible number (1:53-2:10).

First, I convert the number to a list of digits using IntegerDigits (4:08).
Then, I find the largest digit, excluding the last one, from this list using Drop and Max (7:33-8:25).
I get its Position (9:02) and use it to select the remaining digits, finding the second largest digit from those (10:09-12:20).
Finally, I combine these two chosen digits into a number using FromDigits (12:06).
I built an extractMaxTwoDigits function (13:02) and tested it with examples (23:34). After a fix for how Position handles duplicate digits (31:43), the code produced the correct sum for the sample inputs (25:00). I then used the larger official input (26:27), and the solution (17766) was successfully submitted (36:02). I also showed a more "pure functional" version of the code, eliminating local variables (38:50).

https://adventofcode.com/2025/day/3

(* algo steps.
First, pick the largest digit in the number, but not the Last digit.
then, pick the largest digit, from the digit pool that is to the right of the digit you picked.
 *)

IntegerDigits[78129]
(* {7, 8, 1, 2, 9} *)

Drop[{7, 8, 1, 2, 9},-1]
(* {7, 8, 1, 2} *)

Max[{7, 8, 1, 2}]
(* 8 *)

Position[{7, 8, 1, 2}, Max[{7, 8, 1, 2}], {1}, 1]
(* {{2}} *)

Drop[{7, 8, 1, 2, 9}, 2]
(* {1, 2, 9} *)

Max[{1, 2, 9}]
(* 9 *)

FromDigits[{8,9}]
(* 89 *)

advent_of_code_2025_day_3_input.txt

xinput= {987654321111111, 811111111111119, 234234234234278, 818181911112111};

extractMax2Digits = Function[x,
Block[{ xdigitList, xdigit1, xdigit1Pos , xdigit2},
 xdigitList = IntegerDigits[x];
 xdigit1 = Max @ Drop[xdigitList,-1];
 xdigit1Pos = Position[ xdigitList, xdigit1, {1}, 1];
 xdigit2 = Max @ Drop[xdigitList, Flatten[{1, xdigit1Pos }] ];
 FromDigits[{xdigit1, xdigit2}]
]];

Total @ Map[ extractMax2Digits, xinput]
(* 357 *)

Position[ {5,2,1,0,0,5,7}, 5]
(* {{1}, {6}} *)

Position[ {5,2,1,0,0,5,7}, 5, {1}, 1]
(* {{1}} *)

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1225222172436272232152224472436378228238344252537321232143222162232422241622442237322439142322224332,
2134222222621363445321422363333314221122222223244313241224232522243214274432346243462431342212242424,
2121443212224135231222223113432432222232318221222214222213222221232362211212122222447213222412414122,
1566355333393336334172656442374316389732383778336895623949463733633559423424688358375253739713963278,
2341254222222332212427223222222642221332224111722741226322434121222243214226221723244132622112112222,
6644642354573624554464472324223453542555645455422354444343626843445234444444464232522646245432242461,
3247436536134438548873464346333532755684353334675455432343435333344342364244863454955333432551323333,
1235215233244313532333113423336323344236333333463553332363232223353134733242353532332532433235323331,
9222226122322232272232261242721521223265414242325421722226222125122232222231213222672252242812254326,
1321222223122222222232223523415321322322222244221222222232233212323122123122223221232542424214322539,
3444232433344233344454133423435235333414322363245333434435335434413545373344433431434333433325353439,
2212231212222123222222225221229521332221225212351322113133232211222223562322313223231212312212132342,
3446665745854144677546554847575954733732467444426485447556754446464596854754334252247464584775744424,
4346262565225353555549454323452344542464454435533544545555222345534465553645355534534534542354335354,
1335222241344263233453344231323221127323221184223234423232221222322332323423213224332341222223121326,
5344331336363574334353641632133233443333323413442443343323633245842438635472374733453364333646334433,
9444334434444244644444345323745554354344344442435442435432433266524353434344383446433135455453554445,
4533434334344535345534333423444431344333442423245543134433552254344459432435544425422436135444413644,
2221322532223525175451345547567432822312232752333534963253638162474322348231743243225235335422414474,
5254537535635118228352459323444144421232545422514324214363242754457442221353275325294663252333452344,
2413222233253222363233382222333233152212233222212337331353332323322443221324233422332213312322322133,
2222353561222523135513522223232521222522222242432335222215412222223212333534452236531127122125221212,
2442384334158465433823365235674363435555433458234364573525766645443242362442362654345585533525374685,
3333362346234532333524724934541315323533324353333233612233443433323533333394347536227433666337336345,
3322344485213336532312332343343333354224833344334424424445333432633913344243324113436484424263233322,
3342333423262333433223332234432223332323323233423328434732342233331733323332432433321152213332433334,
3333313232317322332533333233335133721333233433822273382244353338333441233242825341253133329383633221,
2322243422312132242231323224322324422135322335433593322322522123323251242522132231334321332322335223,
5635623236946239558355233633854435593532134143353443243324233533164555442233345444454463345533536943,
3544244193244226529332426724342221335632234551423312214452252222623354242453451522223552173531454254,
8316113362363225333531324323422213323312453324252323432416222221353339564652322435137224342323323333,
7342633555612222253253223233314222132543262332234425246244543534553653523375332342323242224241345132,
2426443634943333523434526234444346524431545314136223423324424436344554416413323244144424537235436263,
2422345222227262832125222262122535563213221362163123126225342722332424326626434424452442652213242233,
2695512227221334661242722252244682332252321214131628211624213412225241322622222125224122222215272282,
8352222447535225362515335225152142332257652128665342313311225323322435782254832283123285572331272623,
2522423322322452621212352246423223132352222625543322132323122213622223136386123225124222253232522212,
6233333553433344335534335441536333444432144432234444434333424533233441434443342335444542211343343443,
4353732444512234333345235313431332543323433323223443373336442333335434932835543135333462635233343534
};

extractMax2Digits = Function[x,
Block[{ xdigitList, xdigit1, xdigit1Pos , xdigit2},
 xdigitList = IntegerDigits[x];
 xdigit1 = Max @ Drop[xdigitList,-1];
 xdigit1Pos = Position[ xdigitList, xdigit1, {1}, 1];
 xdigit2 = Max @ Drop[xdigitList, Flatten[{1, xdigit1Pos }] ];
 FromDigits[{xdigit1, xdigit2}]
]];

Total @ Map[ extractMax2Digits, xinput]

(* 17766 *)

xinput= {987654321111111, 811111111111119, 234234234234278, 818181911112111};

extractMax2Digits =
Function[x,
Block[{ xdigitList, xdigit1, xdigit1Pos , xdigit2},
 xdigitList = IntegerDigits[x];
 xdigit1 = Max @ Drop[xdigitList,-1];
 xdigit1Pos = Position[ xdigitList, xdigit1, {1}, 1];
 xdigit2 = Max @ Drop[xdigitList, Flatten[{1, xdigit1Pos }] ];
 FromDigits[{xdigit1, xdigit2}]
]];

(* alternative code. pure functional programing supreme.
 without using any local variable or constants *)
extractMax2Digits =
Function[x,
 Function[xdigitList,
 FromDigits @ ( ({ #, Max @ Drop[xdigitList, Flatten @ {1, Position[ xdigitList, #, {1}, 1] } ] } &) @ (Max @ Drop[xdigitList,-1]) ) ] @ IntegerDigits @ x
];

Total @ Map[ extractMax2Digits, xinput]
(* 357 *)