Puzzles

This Riddle Has Been Dubbed the Hardest Logic Puzzle Ever

It's no secret that we at Curiosity are huge fans of logic puzzles. It is with great enthusiasm, then, that we present what might just be the grandaddy of all the riddles. How can there be a better challenge than the riddle that earned the title of Hardest Logic Puzzle Ever? Strap on the ol' thinking cap and give this famous head-scratcher a try.

So You Think You Can Logic?

Mathematician Richard Smullyan was called "the undisputed master of logical puzzles" by Bruce Horowitz, one of his former Ph.D. students. One mark of his logic legacy is certainly the Hardest Logic Puzzle Ever. This title was given by a colleague of Smullyan and MIT logic professor, George Boolos. Not only did Boolos have the credibility to lend Smullyan's riddle that superlative title, he had the know-how to solve it. The riddle and solution were published in 1996 in the Harvard Business Review. Hope you're ready for a challenge! The puzzle and solution are below.

Here's the 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 completely random. You must determine the identities of A, B, and C by asking three yes-or-no questions, and each question must be posed to exactly one god. The gods understand English, but will answer all questions in their own language. In their unknown language, the words for "yes" and "no" are "da" and "ja," in some order. You do not know which word means which. How do you go about identifying the gods?

Keep scrolling to get to the solution.

Here's the Answer

Surely you weren't expecting the hardest logic puzzle ever to have an easy, cut-and-dry solution, right? Nautilus does a great job of thinking through this super involved answer, noting that the key is to ask biconditional questions (using "if and only if" statements" within questions). If you just want to get right down to the three question you can ask to solve the puzzle, here they are, as reported by Nautilus:

1. To god A: "Does 'da' mean 'yes' if and only if you are True and if and only if B is Random?" (We supposed A said, "ja," making B True or False).

2. To god B: "Does "da" mean 'yes' if and only if Pluto is a dwarf planet?" (We supposed B said, "da," making B True.)

3. And to god B (True) again: "Does 'da' mean 'yes' if and only if A is Random?" Since B's True, he must say "da," which means A is Random, leaving C to be False.

Still not quite following? We don't blame you. In 2008, a paper was published that claimed to present the simplest solution to this riddle. Check it out here.

Want more puzzle? Check out Raymond Smullyan's "The Gödelian Puzzle Book: Puzzles, Paradoxes and Proofs." Every click helps to support Curiosity.

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Written by Joanie Faletto December 4, 2017