Three gods: The hardest logic puzzle ever (2024)


Tackle this logisticians’ parlour game and you may be a bit closer to understanding the nature of truth itself

By Richard Webb

Three gods: The hardest logic puzzle ever (1)

NEED something to mull other than wine as you atrophy there in the armchair? Then set your grey cells humming with this puzzle.

“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.”

Welcome to the “Hardest Logic Puzzle Ever”. If you should happen upon three questions that will unmask the gods, don’t stop there. Your next task: make the puzzle even harder.

This is a parlour game played by logicians since the Hardest Logic Puzzle Ever was first so named – and solved – by US logician George Boolos shortly before his death in 1996. Find a solution, and you understand a little more about how to extract truth in a world where imperfect information abounds – and perhaps, by the by, about the nature of logic itself.

Boolos always had an individual take on the world. He once delivered a public lecture explaining Kurt Gödel‘s second incompleteness theorem, a seminal result in mathematical logic, entirely in words of one syllable, and was wont to pace the corridors of the Massachusetts…


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Three gods: The hardest logic puzzle ever (2024)


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