Even harder than The Hardest Logic Puzzle Ever

by Tom Ellis


George Boolos coined the title The Hardest Logic Puzzle Ever for a puzzle that Wikipedia gives in this form:

Three gods A, B, and C are called, in some order, True, False, and Random. True always speaks truly, False always speaks falsely, but whether Random speaks truly or falsely is a completely random matter. Your task is to determine the identities of A, B, and C by asking three yes-no questions; each question must be put to exactly one god. The gods understand English, but will answer all questions in their own language, in which the words for yes and no are 'da' and 'ja', in some order. You do not know which word means which.

I have some comments on that definition:

Clearly the former leads to (on the face of it) an easier problem, and I suspect that's what the definition intended.

A logic puzzle harder than the hardest ever

Now I wish to extend the puzzle and make it even harder! Then I'll demonstrate how to solve it.

(The "castle" question is arbitrary. It's just a question you don't originally know the answer to.)

How can we solve this puzzle?

If you'd like to know how to solve this puzzle, you will find the answer on a separate page.



Thanks to Jon Pretty and Richard Smith without whose input I would never have written this article. Thanks to Brian Rabern for his comments on use-mention.