# “I know”?

Score Points: 2Solvers: 8

There are three people standing in a queue so that the last person can see both people in front, the middle person can see one person in front, and the first person can't see anyone. Three hats, chosen out of three red and two blue hats, are placed one each on their head. The last person is asked the colour of hat on his head, and he says "I don't know". The middle person is asked the same and he also says "I don't know". Is it possible for the first person to answer “I know”? If yes, enter 0. If no, enter 1.

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Go through several scenarios of different placements of hats and see what all scenarios are ruled out by the first two statements.

Since the last person says he doesn't know, the front two have at least one red hat between them (else the blue hats would be exhausted and the last person would know he has a red hat). Given that the front two have at least one red hat, the fact that the second person says he doesn't know means that the first person has a red hat (otherwise the second person would know he is the one who has a red hat). This makes it obvious that the first person has a red hat, and if he is a logical being, like we have presumed, then he will say “I know”.

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