Riddles

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The Three Gods

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.

  1. It could be that some God gets asked more than one question (and hence that some God is not asked any question at all).
  2. 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.)
  3. 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.
  4. Random will answer “da” or “ja” when asked any yes-no question.

What would your three questions be?

Riddle Answer

Nine Lottery Balls

Ali and Zoe reach into a bag that they know contains nine lottery balls numbered 1 to 9. They each take one ball out to keep and they look at it secretly. Then, they make the following statements, in order:

Ali: I don’t know whose number is bigger.
Zoe: I don’t know whose number is bigger either.
Ali: I still don’t know whose number is bigger.
Zoe: Now I know that my number is bigger!

Assuming Ali and Zoe are perfect logicians, what is Zoe’s smallest possible number?

Riddle Answer