Question

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.

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).

To god B: “Does “da” mean ‘yes’ if and only if Pluto is a dwarf planet?” (We supposed B said, “da,” making B True.)

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.