My comment got eaten by HN, but I think LLMs should be used as the glue between logic systems like prolog, with inductive, deductive and abductive reasoning being handed off to a tool. LLMs are great at pattern matching, but forcing them to reason seems like an out of envelope use.

Prolog would be how I would solve puzzles like that as well. It is like calling someone weak for using a spreadsheet or a calculator.

Abductive Commonsense Reasoning Exploiting Mutually Exclusive Explanations https://arxiv.org/abs/2305.14618