Solving a chess puzzle with Claude and Prolog

Claude AI generated a Prolog program to solve a Martin Gardner chess puzzle requiring placement of two rooks, two bishops, and two knights on a 4x4 board without any piece attacking another. The program found 12 raw solutions, with 2 unique solutions up to symmetry, demonstrating how large language models can assist in writing logic programming code for combinatorial problems.

Prolog is the original logic programming language. The name comes from programming in logic. More specifically, the name comes from programmation en logique because the inventor of the language, Philippe Roussel, is French. Prolog has its advantages and disadvantages. One of the advantages is that the language represents logical problems directly. One of the disadvantages is that the syntax can be quirky. But if an LLM is writing the code, or at least helping to write the code, the syntax doesn’t matter so much. I wanted to see how well Claude Sonnet 4.6, medium effort could solve a chess puzzle https://www.johndcook.com/blog/2025/05/14/another-little-chess-puzzle/ by Martin Gardner that I wrote about a little over a year ago. I chose a relatively obscure problem rather than something like the Eight Queens puzzle because an LLM could simply quote one of countless articles on the puzzle. The puzzle As I stated in the post last year, the task is to place two rooks, two bishops, and two knights on a 4 by 4 chessboard so that no piece attacks any other. There are two basic solutions, twelve if you count rotations and reflections as different solutions. Prolog results Claude wrote an SWI-Prolog program that I ran with swipl -g "run, halt" chess placement.pl and it gave the following output. Total solutions raw : 12 Solutions up to D4 symmetry: 2 Solutions up to D4 symmetry: 2 Solution 1: B . . N N . . B . R . . . . R . Solution 2: . B N . . . . R R . . . . N B . Claude made a nice image of the solutions. Note that you can make eight variations of the first solution by a combination of rotations and flips. There are only four variations of the second solution because two rotations put you back where you started. Prolog source Here’s the Prolog code that Claude generated. % ============================================================ % Non-attacking placement of 2 Rooks, 2 Bishops, 2 Knights % on a 4x4 chessboard % % Run with SWI-Prolog: % swipl -g "run, halt" chess placement.pl % % Or interactively: % swipl chess placement.pl % ?- run. % ?- count solutions N . % ?- count unique N . % ============================================================ :- use module library lists . % ---- Board squares: Row, Col with Row, Col in 0..3 ---------------- square R, C :- member R, 0,1,2,3 , member C, 0,1,2,3 . % ---- Attack predicates ---------------------------------------------- rook attacks R, ,R, . % same row rook attacks ,C, ,C . % same column bishop attacks R1,C1,R2,C2 :- DR is abs R1-R2 , DC is abs C1-C2 , DR =:= DC, DR 0. knight attacks R1,C1,R2,C2 :- DR is abs R1-R2 , DC is abs C1-C2 , DR =:= 1, DC =:= 2 ; DR =:= 2, DC =:= 1 . % attacks +Type1, +R1, +C1, +Type2, +R2, +C2 % True if either piece threatens the other's square. attacks rook, R1,C1, , R2,C2 :- rook attacks R1,C1,R2,C2 . attacks , R1,C1, rook, R2,C2 :- rook attacks R1,C1,R2,C2 . attacks bishop, R1,C1, , R2,C2 :- bishop attacks R1,C1,R2,C2 . attacks , R1,C1, bishop,R2,C2 :- bishop attacks R1,C1,R2,C2 . attacks knight, R1,C1, , R2,C2 :- knight attacks R1,C1,R2,C2 . attacks , R1,C1, knight,R2,C2 :- knight attacks R1,C1,R2,C2 . % ---- All pairs safe ------------------------------------------------- % Check all unordered pairs in a list. no attack pair , . no attack pair T1- R1,C1 , T2- R2,C2 |Rest :- \+ attacks T1,R1,C1,T2,R2,C2 , no attack pair T1- R1,C1 , Rest . all pairs safe . all pairs safe P|Rest :- no attack pair P, Rest , all pairs safe Rest . % ---- Generate a placement ------------------------------------------- % % Placement = rook- R1,C1 , rook- R2,C2 , % bishop- R3,C3 , bishop- R4,C4 , % knight- R5,C5 , knight- R6,C6 % % We enforce an ordering within each pair to avoid counting % same-type duplicates rook1 vs rook2 swapped . % Squares are represented canonically: R,C with R 4+C as index. sq index R, C, I :- I is R 4 + C. placement Placement :- % --- Rooks --- square R1r, C1r , square R2r, C2r , sq index R1r,C1r,I1r , sq index R2r,C2r,I2r , I1r < I2r, % canonical order for the two rooks % --- Bishops --- square R1b, C1b , square R2b, C2b , sq index R1b,C1b,I1b , sq index R2b,C2b,I2b , I1b < I2b, % canonical order for the two bishops % --- Knights --- square R1n, C1n , square R2n, C2n , sq index R1n,C1n,I1n , sq index R2n,C2n,I2n , I1n < I2n, % canonical order for the two knights % --- All six squares distinct --- Squares = R1r,C1r , R2r,C2r , R1b,C1b , R2b,C2b , R1n,C1n , R2n,C2n , all distinct squares Squares , % --- Build placement list --- Placement = rook- R1r,C1r , rook- R2r,C2r , bishop- R1b,C1b , bishop- R2b,C2b , knight- R1n,C1n , knight- R2n,C2n , % --- No piece attacks any other --- all pairs safe Placement . all distinct squares . all distinct squares S|Rest :- \+ member S, Rest , all distinct squares Rest . % ---- Count all solutions -------------------------------------------- count solutions N :- findall P, placement P , Ps , length Ps, N , format "Total solutions raw : ~w~n", N . % ---- D4 symmetry transformations on a 4x4 board --------------------- % Squares R,C in 0..3 transform identity, R, C, R, C . transform rot90, R, C, C, Nr :- Nr is 3-R. transform rot180, R, C, Nr, Nc :- Nr is 3-R, Nc is 3-C. transform rot270, R, C, Nc, R :- Nc is 3-C. transform flipH, R, C, R, Nc :- Nc is 3-C. transform flipV, R, C, Nr, C :- Nr is 3-R. transform flipD1, R, C, C, R . transform flipD2, R, C, Nr, Nc :- Nr is 3-C, Nc is 3-R. apply transform , , . apply transform T, Type- R,C |Rest , Type- NR,NC |TRest :- transform T, R, C, NR, NC , apply transform T, Rest, TRest . % Canonical form: sort pieces within same-type pairs, then sort the % whole list to get a unique representative. canonical placement Placement, Canonical :- findall T, member T, identity,rot90,rot180,rot270, flipH,flipV,flipD1,flipD2 , Ts , maplist transform and sort Placement , Ts, AllForms , msort AllForms, Sorted , Sorted = Canonical| . transform and sort Placement, T, Sorted :- apply transform T, Placement, TPl , msort TPl, Sorted . % ---- Count solutions up to D4 symmetry ------------------------------ count unique N :- findall P, placement P , Ps , maplist canonical placement, Ps, Canonicals , list to set Canonicals, Unique , length Unique, N , format "Solutions up to D4 symmetry: ~w~n", N . % ---- Pretty-print a board ------------------------------------------- print board Placement :- forall member R, 0,1,2,3 , print row R, Placement , nl. print row R, Placement :- forall member C, 0,1,2,3 , print cell R, C, Placement , nl. print cell R, C, Placement :- member rook- R,C , Placement - write 'R ' ; member bishop- R,C , Placement - write 'B ' ; member knight- R,C , Placement - write 'N ' ; write '. ' . % ---- Print all unique solutions ------------------------------------- print unique solutions :- findall P, placement P , Ps , maplist canonical placement, Ps, Canonicals , list to set Canonicals, Unique , length Unique, N , format "~nSolutions up to D4 symmetry: ~w~n~n", N , forall nth1 I, Unique, Sol , format "Solution ~w:~n", I , print board Sol . % ---- Top-level entry point ------------------------------------------ run :- count solutions Raw , count unique Sym , format "~n" , print unique solutions, format "Summary: ~w raw solutions, ~w up to D4 symmetry.~n", Raw, Sym .