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Hat puzzles are logic problems that date back to as early as 1961. A number of players, at least three, are each wearing a hat, which may be of various specified colours. Players can see the colours of at least some other players' hats, but not that of their own. With highly restricted communication or none, some of the players must guess the colour of their hat. The problem is to find a strategy for the players to determine the colours of their hats based on the hats they see and what the other players do. In some versions, they compete to be the first to guess correctly; in others, they can work out a strategy beforehand to cooperate and maximise the probability of correct guesses. One variation received some new publicity as a result of Todd Ebert's 1998 Ph.D. thesis at the University of California, Santa Barbara. It is a strategy question about a cooperative game, which has connections to algebraic coding theory.〔(Biography of Todd Ebert at California State University, Long Beach )〕 ==A competitive version== Three players are told that each of them will receive either a red hat or a blue hat. They are to raise their hands if they see a red hat on another player. The first to guess the colour of his or her hat correctly wins. All three players raise their hands. After the players have seen each other for a few minutes without guessing, one player announces "Red", and wins. How did the winner do it? If player 1 sees a blue hat on player 2, then player 1 knows his own hat must be red: if both 2 and 1 had blue hats, 3's hand would not have been raised. Thus any player who sees a blue hat can guess at once. The winner realizes that since no one guesses, there must be no blue hats, so every hat must be red. 抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)』 ■ウィキペディアで「Hat puzzle」の詳細全文を読む スポンサード リンク
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