Three highly intelligent sophomore women, whose names begin with A, B, and C, are trying out to be cheerleaders. They sit in a triangular arrangement to try a puzzle. Each is wearing either a red or gold hat put on her head by the head cheerleader. Each woman can see the other two women’s hats but not her own. The head cheerleader tells them that at least one of the hats is red. Each woman is to look at the other two hats and say nothing, unless she can deduce what color her own hat is. Well, C has been sitting there with her eyes closed the whole time. She never even looks at the other women’s hats. After a few moments of silence, she announces that her own hat must be red. How did she figure it out?
If any of the women sees two gold hats, then she knows her own is red. Since neither A nor B concludes that her own hat is red, it must be that both of them are seeing at least one red hat. If C’s hat were gold, then both A’s and B’s hats must be red, and they would figure that out and announce their hats were red. Since neither of them is saying anything, C’s hat must not be gold. It must be red.