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 Return of the hats (Posted on 2002-12-10)
Three players enter a room and a red or blue hat is placed on each person's head. The color of each hat is determined by a coin toss, with the outcome of one coin toss having no effect on the others. Each person can see the other players' hats but not his own.

No communication of any sort is allowed, except for an initial strategy session before the game begins. Once they have had a chance to look at the other hats, the players must simultaneously guess the color of their own hats or pass. The group shares a hypothetical \$3 million prize if at least one player guesses correctly and no players guess incorrectly. What strategy should they use to maximize their chances of success?

(From - http://www.princeton.edu/~sjmiller/riddles/riddles.html)

 See The Solution Submitted by Raveen Rating: 3.6923 (13 votes)

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 Probability | Comment 5 of 16 |
If they can't signal one another, and the hats are random, then they can't be completely certain of winning, but there is a best stategy. I am not absolutely certain that this is it, but it's my best shot.

You need to realize two things

At least two of the men will have the same color.

There is only a 1/4 chance that they will all have the same color.

So if each person passes if the other two are wearing different colors, and guesses the red if he sees two blues (or vice versa), then three times out of four, two will pass and the third will guess correctly, the fourth time, all three will guess incorrectly.
 Posted by TomM on 2002-12-10 16:05:59

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