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martyb writes:

I just happened to see this story appear in our #rss-bot feed. How to Solve the World's Hardest Logic Puzzle. Given that this is the weekend, I thought it might make for an interesting challenge and discussion.

To set the stage for the puzzle, the author provides some background on Raymond Smullyan, the puzzle's composer:

While a doctoral student at Princeton University in 1957, studying under a founder of theoretical computer science, Raymond Smullyan would occasionally visit New York City. On one of these visits, he met a "very charming lady musician" and, on their first date, Smullyan, an incorrigible flirt, proceeded very logically—and sneakily.

"Would you please do me a favor?" he asked her. "I am to make a statement. If the statement is true, would you give me your autograph?"

Content to play along, she replied, "I don't see why not."

"If the statement is false," he went on, "you don't give me your autograph."

"Alright ..."

His statement was: "You'll give me neither your autograph nor a kiss."

It takes a moment, but the cleverness of Smullyan's ploy eventually becomes clear.

A truthful statement gets him her autograph, as they agreed. But Smullyan's statement, supposing it's true, leads to contradiction: It rules out giving an autograph. That makes Smullyan's statement false. And if Smullyan's statement is false, then the charming lady musician will give him either an autograph or a kiss. Now you see the trap: She has already agreed not to reward a false statement with an autograph.

With logic, Smullyan turned a false statement into a kiss. (And into a beautiful romance: The two would eventually marry.)

Clever! But enough with the setup — What's the puzzle?

The Hardest Logic Puzzle Ever goes like this:

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.

The story's author is, himself, a bit of a puzzle-poser. The story tells how to solve the puzzle, but does not actually provide the solution. Are there any Soylentils up to the challenge?

Original Submission