Zubon comments on Which Parts Are "Me"? - Less Wrong
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gaffa, have you tried any Raymond Smullyan? If you want logic and mathematical reasoning in a game-like structure, he has several books (like the linked) that present them as riddles. There is no shame in not getting how they work until you read the solution to at least one in each chapter, but you get the pattern of how to think through certain sorts of logical structures.