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Return of the hats (Posted on 2002-12-10) Difficulty: 3 of 5
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 -

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

Comments: ( Back to comment list | You must be logged in to post comments.)
re: Proving best strategy Comment 16 of 16 |
(In reply to by Cheradenine)

This is a good way to show this is the best strategy. It also is quite helpful in reconciling the two viewpoints ("3/4 is the answer" and "coinflip and no communication should imply 1/2 as the answer").

From reading the problem, you get the feeling that there is no solution that will let them win all the time. This can be proved because even if they could go in turns, the first person has no information to tell red or blue (and thus couldn't be sure either way, so must pass).

Since the first person always passes regardless of what he sees, the second person is in the same situation and must pass, and then so is the third person.

  Posted by Gamer on 2008-07-12 16:57:03

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