Princeton University
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Computer Science 345 |
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The color of my hatThree players enter a room. The referee puts a white or black hat on each of them. The colors of the hats are determined randomly and independently: each hat is white or black with probability 1/2. Each person sees the hat colors of the other two players, but not his own hat color. Then each of them can either try to guess his own hat color and write it on a piece of paper or pass.
If at least one player makes a correct guess and nobody makes wrong guesses, then the players win. What is the probability that the players win?
Players cannot communicate with each other. But they can discuss their strategy in advance.
Three wise menThree wise men woke up under an olive tree. While they were sleeping, a hooligan soiled their faces. Seeing that the faces of the other two wise men were dirty, they started laughing. Suddenly they stopped laughing. Why?