Hat Colors and People
5 people, Tim, Jim, Slim, Kim, and Jane, are going to play a game. They know that there are 4 hats, 2 red and 2 blue. 4 of them except Jane, will form a circle and be allowed to see where everyone is in the circle. Besides that, they will be blindfolded and get a hat each. Now, Jane will be able to see them but she's only allowed to say one of the two colors, or both, or one of them twice out loud.
Assuming that before the game starts, the players can form a strategy knowing what the game consists of, and assuming that they come up with the best strategy, what would be the minimum number of tries they can get for each of them to know their color?
The answer is 1.
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1 solution
Since they form a circle, they each can agree on the following arrangement:
Tim Jim Slim Kim
List all possibilities:
(1) (2) (3) (4)
R R B R B B R B
B B B R R R R B
(5) (6)
B R R B
R B B R
Then they can follow the next scheme:
R R means (1), R B means (2), B R means (3), B B means (4), R means (5), and B means (6). For example, if Jane says "blue blue," then Tim is wearing red, Jim is wearing blue, Slim is wearing red, and Kim is wearing blue.