Wednesday, May 22nd

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100 prisoners and hats

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100 prisoners are lined up in a row by the jailor. The jailor puts red and blue hats on them. They can't see their own hats, but they can see the hats of the people in front of them. The jailor starts in the back and says “what color is your hat?”. The prisoner can only answer "red" or "blue". The prisoner is killed if he gives the wrong answer; then the jailor moves on to the next prisoner. The prisoners in front get to hear the answers of the prisoners behind them, but not whether they live or die. They can consult and agree on a strategy before being lined up, but after being lined up and having the hats put on, they can't communicate in any way other than those already specified. What strategy should they choose to maximize the number of prisoners who are guaranteed to be saved ?


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