Babel on Olympus - Futility Closet

In 1996, MIT philosopher George Boolos published this puzzle by Raymond Smullyan in The Harvard Review of Philosophy, calling it “the hardest logical puzzle ever”:

Three gods A, B, and C are called, in no particular 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.

Boolos made three clarifying points:

It could be that some god gets asked more than one question (and hence that some god is not asked any question at all).
What the second question is, and to which god it is put, may depend on the answer to the first question. (And of course similarly for the third question.)
Whether Random speaks truly or not should be thought of as depending on the flip of a coin hidden in his brain: if the coin comes down heads, he speaks truly; if tails, falsely.

What’s the solution?

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Boolos’ original article includes his own solution; the ensuing years have seen a lively search for improvements. The solution below, by Brian and Landon Rabern, simplifies matters by using embedded questions (“If I asked you x, would you say y?”): Question 1: Ask God B, “If I asked you ‘Is A Random?’, would you say ja?” — If B answers ja, then either B is Random or his answer tells us that A is Random. — If B answers da, then either B is Random or his answer tells us that A is not Random. In either case, God B’s answer to Question 1 has identified a god who is not Random. Question 2: Ask the god who is not Random, “If I asked you ‘Are you False?’, would you say ja?” — If he answers da, then he is True. — If he answers ja, then he is False. Question 3: Ask the same god, “If I asked you ‘Is B Random?’, would you say ja?” — If he answers ja, then B is Random. — If he answers da, then the third god is Random. At this point we’ve established the identities of two of the gods, so we can deduce the third by elimination.

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