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Very Difficult Logic Problems
Colored Hats

Tue Aug 30, 2016 4:48 am  by tartle

A warden lines up a group of 30 prisoners so they can see everybody in front of them and nobody behind them, then places either a red or a blue hat on each of their heads, randomly. He then goes from the back of the line to the front, telling each prisoner to guess the color of their own hat. Each who guesses correctly is freed. The prisoners cannot see the color of their own hat, and cannot communicate with each other, but can hear each others' guesses and can strategize beforehand. What strategy saves the greatest number of prisoners?
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