Tuesday, July 27, 2010
Hats
N people team up and decide on a strategy for playing this game. Then they walk into a room. On entry to the room, each person is given a hat on which one of the first N natural numbers is written. There may be duplicate hat numbers. For example, for N=3, the 3 team members may get hats labeled 2, 1, 2. Each person can see the numbers written on the others' hats, but does not know the number written on his own hat. Every person then simultaneously guesses the number of his own hat. What strategy can the team follow to make sure that at least one person on the team guesses his hat number correctly?
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They agree on the following strategy:
ReplyDeleteAfter all people have entered the room, each
person will place the other N-1 people by
following these rules:
1. Each person will place the other N-1 people
by reversed entry order (i.e. the last
person who enter the room will be the first
to place the other N-1 people).
2. The person wearing a hat with a number
smaller than the number of another person's
hat, will be positioned on the left.
3. The person wearing a hat with a number
greater than the number of another person's
hat, will be positioned on the right.
4. The person wearing a hat with a number
equal to the number of another person's
hat, will be positioned in front of him.