Reference no: EM131834833

Three players enter a room and are given a red or a blue hat to wear. The color of each hat is determined by a fair coin-toss. Players cannot see the color of their own hats, but do see the color of the other two players' hats. The game is won when at least one of the players correctly guesses the color of his own hat and no player gives an incorrect answer. In addition to having the opportunity to guess a color, players may also pass. Communication of any kind between players is not permissible after they have been given hats; however, they may agree on a group strategy beforehand. Verify that there is a group strategy that results in a 3/4 probability of winning. (This puzzle was discussed in the New York Times of April 10, 2001. The hat problem with many players is related to problems in coding theory. The strategy gets far more complicated for larger numbers of players. In the game with 2m - 1 players, there is a strategy for which the group is victorious with a probability of (2m - 1)/2m).