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The hat

Adam, Brian and Charlie are in a room together; Adam and Brian have perfect eyesight but Charlie is totally blind. On a table in front of them are 5 hats: 3 red, 2 blue, otherwise identical. They all know what's on the table.

While Adam and Brian close their eyes – they don't cheat – the hats are mixed up, each of them takes one hat and puts it on and the remaining 2 hats are taken away.

Adam looks at Brian and Charlie and says, "I can't tell what colour hat I have on."
Brian looks at Adam and Charlie and says, "I can't tell what colour hat I have on."
Charlie says, "I'm wearing a hat."

Charlie was right. What colour did he say and how did he know?

Tom Braider Wed 03/09/08 20:06

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Tom Braider
Wed 03/09/08
20:08

Question Author

I meant to write, "Charlie says, "I'm wearing a red / blue hat." Anyway, Charlie says he knows what colour his hat is.

gen2
Wed 03/09/08
22:26

Yes. Charlie declares he is wearing a RED hat.

The only combinations where Adam and Brian cannot deduce a color for themselves are

Adam - Red, Brian - Red, Charlie - Red
and
Andam - Blue, Brian - Blue, Charlie - Red

In both cases Charlie is Red and declares it.

Gizmonster
Wed 03/09/08
22:31

C must be wearing a red hat.

Explanation:

A looks at B and C. The only way A would know what colour hat he was wearing, would be if B and C both had a blue hat on - leaving only red hats remaining. A doesn't know what he is wearing so we know that B and C are not both wearing blue hats.

B looks at A and C and also states that he does not know the colur of his own hat. By the same assumption that we used for A, we know that A and C are not both wearing a blue hat.

Let's assume that C is wearing a blue hat. If this is the case, then B is not wearing a blue hat, otherwise A would know that he is wearing a red hat. B knows this, so if A states that he does not know the colour of his own hat, then B would know that his own hat must be red.

However, since B states that he did not know the colour of his own hat, C must be wearing a red hat.

Gizmonster
Wed 03/09/08
22:32

*sigh*

It took so long to type the answer, gen2 beat me to it lol :(

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