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 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.

Note that you can ask the same God more than once. You can also think of Random as a god who would give either a truthful or false answer depending on the flip of a coin. You can read the solution in chapter 29 of Boolos's book Logic, Logic, and Logic, published by the Harvard University Press. Link to Google book. You can also find a discussion of the puzzle on Wikipedia.