# Answer to Riddle #12: Three Men and Red & Blue Hats

12. Inside of a dark closet are five hats: three blue and two red. Knowing this, three smart men go into the closet, and each selects a hat in the dark and places it unseen upon his head.

Once outside the closet, no man can see his own hat. The first man looks at the other two, thinks, and says, "I cannot tell what color my hat is." The second man hears this, looks at the other two, and says, "I cannot tell what color my hat is either." The third man is blind. The blind man says, "Well, I know what color my hat is." What color is his hat?

This is one of those problems that sort of gives you brain ache, you can work out the answer but explaining it clearly is more difficult...

We will call the people A, B & C in the order that they speak.

A does not know what colour hat he is wearing. A would only know what colour hat he was wearing if he could see that B & C were both wearing red hats, (as there were only two red hats in the cupboard.) This is not the case so either:-
B & C are both wearing blue hats
OR
one of B & C is wearing red and the other is wearing blue
When B speaks we obviously assume he has thought of all of this. When B looks at C if C were wearing red then he (B) would know that he (B) must be wearing blue as they can't both be wearing red. But this does not happen so C must be wearing blue, causing B not to know if he is wearing red or blue:

The third person (C) must be wearing a BLUE hat.

## Assumptions

Implicitly we have assumed that all the people in the puzzle can solve the riddle as we can. Possibly if you want to take it a step further, we have assumed that the first two people are not blind.

Bard got this one completely wrong ChatGPT got it right and for the right reasons.

If you're curious what Bard made of this puzzle...

If you're curious what ChatGPT made of this puzzle...

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