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Unformatted text preview: h wearing a hat colored red or blue, standing
in a line in order of increasing height. Each person can see only the hats of the
people in front, and does not know the color of his or her own hat. They play
a game as a team, whose rules are simple. Each person gets to say one word:
“red” or “blue”. If the word they say correctly guesses the color of their hat,
the team gets 1 point; if they guess wrong, 0 points. Before the game begins,
they can get together to agree on a protocol (i.e., what word they will say under
what conditions). Once they determine the protocol, they stop talking, form the
line, and are given their hats at random.
Can you think of a protocol that will maximize their score? What score does your
A little bit of thought will show that there is a way to use the concept of parity to enable
N − 1 of the people to correctly decode the colors of their hats. In general, the “parity”
of a set of bits x1 , x2 , . . . , xn is simply equal to (x1 + x2 + . . . + xn ), where the addition is
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- Fall '13