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,
[3] in some order. You do not know which word means which.
Boolos provides the following clarifications:
[1] a single god may be asked more than one question, questions are permitted to depend on the answers to earlier questions, and the nature of Random's response should be thought of as depending on the flip of a
fair coin hidden in his brain: if the coin comes down heads, he speaks truly; if tails, falsely.
[4]