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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.)
Coin toss / hats recieved | Comment 4 of 16 |
(In reply to by Cory Taylor)

This strategy works only if one color is designated to either heads or tails. Another part of it is it will only work if the color stays on either heads or tails for all the players. When the coin is flipped for another player, you look to see if it's a head or a tail. Then look at what color they recieve. Then when it is your(you're a player) turn, you will see what you get, heads or tails, and figure out the color by comparing it with the other players head/tails and color

e.g. player 1: heads blue
Player 2: heads blue
Player 3: tails red

once player 3 knows heads gives him blue, he knows tails will give him red and when he finds out what he gets, heads or tails, he will easily figure out which hat he has.

  Posted by abu on 2002-12-10 14:40:40

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