Solving a "Layton Puzzle" with Prolog

Summary

April 8, 2025 Solving a "Layton Puzzle" with Prolog I have a lot in the works for the this month's Logic for Programmers release. Among other things, I'm completely rewriting the chapter on Logic Programming Languages. I originally showcased the paradigm with puzzle solvers, like eight queens or four-coloring. Lots of other demos do this too! It takes creativity and insight for humans to solve them, so a program doing it feels magical. But I'm trying to write a book about practical techniques and I want everything I talk about to be useful. So in v0.9 I'll be replacing these examples with a couple of new programs that might get people thinking that Prolog could help them in their day-to-day work. On the other hand, for a newsletter, showcasing a puzzle solver is pretty cool. And recently I stumbled into this post by my friend Pablo Meier, where he solves a videogame puzzle with Prolog: Summary for the text-only readers: We have a test with 10 true/false questions (denoted a/b) and four student attempts. Given the scores of the first three students, we have to figure out the fourth student's score. bbababbabb = 7 baaababaaa = 5 baaabbbaba = 3 bbaaabbaaa = ??? You can see Pablo's solution here, and try it in SWI-prolog here. Pretty cool! But after way too long studying Prolog just to write this dang book chapter, I wanted to see if I could do it more elegantly than him. Code and puzzle spoilers to follow. (Normally here's where I'd link to a gentler introduction I wrote but I think this is my first time writing about Prolog online? Uh here's a Picat intro instead) The Program You can try this all online at SWISH or just jump to my final version here. :- use_module(library(dif)). % Sound inequality :- use_module(library(clpfd)). % Finite domain constraints First some imports. dif lets us write dif(A, B), which is true if A and B are not equal. clpfd lets us write A #= B + 1 to say "A is 1 more than B". We'll say both the student submission and the key will be lists, wh...