# The Three Gods

Probability Level 2

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 minimum number of 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. What is the minimum number of questions required to determine their identities?

This problem was devised by famous logician George Boolos...

Clarification ---

1) a single God may be asked more than one question,

2) questions are permitted to depend on the answers to earlier questions,

3) The nature of Random's response 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.

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