I do not know how to solve it even i have worked for a week :
I have found a paper for this : You can leave your hat on( if you gues its color ) of
Uriel Feige . this is a general method for that kind of hat color game. But i am not a mathtician, so it is hard for me to understand it.
The Rainbow Game is played by a team of seven. Each player gets a hat, which can be any one of the seven colors red, orange, yellow, green, blue, indigo, and violet. The colors of the hats are independent of each other and repetitions are allowed: for instance, it may happen that all the hats are green. Each player can see only the colors of the six hats worn by the rest of the team; no player can see the color of his or her own hat. The players are to guess the colors of their own hats, and if at least one player guesses correctly then the team as a whole wins.
The players may not communicate in any way during the game, and they must all announce their guesses simultaneously. They are, however, allowed to plan out a strategy in advance, and they hope to find a strategy which will guarantee them success for every possible arrangement of hats. Is there such a strategy? Either find one or show that it cannot exist. (As a warm-up, try two players and two colors, or three players and three colors.)
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canh_dieu: A discussion (in Vietnamese) about this interesting problem can be found at http://diendantoanho...showtopic=12494.
Edited by canh_dieu, 21-03-2006 - 00:14.
