There are 6 prisoners and 36 hats of differents colors
(6 red hats, 6 orange, 6 yellow, 6 green, 6 blue, and 6 violet).
Each prisoner gets a hat, which can be any one of those six colors.
The colors of the hats are independent of each other and repetitions
are allowed. For instance, it may happen that all the hats are green.
Each prisoner can see only the colors of the five hats worn by the rest
five prisoners. No prisoner can see the color of his or her own hat.
The prisoners are to guess the colors of their own hats, writing down
their guesses on sheets of paper. No prisoner can see what other prisoners
are writing. No communication between the prisoners is allowed.
If at least one prisoner guesses correctly then all six prisoners go free.
The prisoners are allowed to plan out a strategy in advance,
and they hope to find a strategy which would guarantee them success
for every possible arrangement of hats. Is there such a strategy?
Either find one or show that it cannot exist.
2006-07-10
23:18:01
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7 answers
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asked by
yakart
1