7 Britishmen, 7 Frenchmen, and 7 Italians are invited to play a cooperative game. The game is as follows:

1) The game host puts each of the 21 participants into a separate room, blindfolds him, and places either a red or blue hat on his head.

2) The host then tells each participant the following: how many red hats are there total among each of the other two races, and how many red hats total among the participant's other 6 countrymen. For instance, if the host is talking to a Frenchmen, he would say to the Frenchmen, "Among the 7 Italians, there are a total of x red hats. Among the 7 Britishmen, there are a total of y red hats. Among the remaining 6 Frenchmen, there are z red hats."

3) Each of the 21 participants is then requested to guess their hat color. Each participant has a choice of 'Red', 'Blue', or 'Abstain'.

4) Everybody wins if at least 1 person correctly guesses his hat color, and no person incorrectly guesses his hat. The choice 'Abstain' is considered neutral, and is neither right or wrong. For example, if 1 person guesses the right color, and the other 20 abstain, then everybody wins. If 1 person guesses correctly, 19 abstain, and 1 guesses incorrectly, then everybody lose.

The 21 Europeans above can discuss a strategy before playing the game. Help them determine a strategy that gives as high a winning rate as possible.

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## bushindo 14

7 Britishmen, 7 Frenchmen, and 7 Italians are invited to play a cooperative game. The game is as follows:

1) The game host puts each of the 21 participants into a separate room, blindfolds him, and places either a red or blue hat on his head.

2) The host then tells each participant the following: how many red hats are there total among each of the other two races, and how many red hats total among the participant's other 6 countrymen. For instance, if the host is talking to a Frenchmen, he would say to the Frenchmen, "Among the 7 Italians, there are a total of

xred hats. Among the 7 Britishmen, there are a total ofyred hats. Among the remaining 6 Frenchmen, there arezred hats."3) Each of the 21 participants is then requested to guess their hat color. Each participant has a choice of 'Red', 'Blue', or 'Abstain'.

4) Everybody wins if at least 1 person correctly guesses his hat color, and no person incorrectly guesses his hat. The choice 'Abstain' is considered neutral, and is neither right or wrong. For example, if 1 person guesses the right color, and the other 20 abstain, then everybody wins. If 1 person guesses correctly, 19 abstain, and 1 guesses incorrectly, then everybody lose.

The 21 Europeans above can discuss a strategy before playing the game. Help them determine a strategy that gives as high a winning rate as possible.

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