3 Smart Men and 3 Hats
Inside of a dark closet are five hats: three blue and two red. Three smart men go into the closet, and each selects a hat in the dark and places it unseen upon his head. Each man knows both that the closet contains three blue hats and two red and that the other two men have the same knowledge. 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, and how does he know?
Answer
If the first man is unable to tell, he cannot be seeing two red hats, so men 2 and 3 must be wearing either BB, BR, or RB. When the second man, having heard the first, is still unable to tell, it means he does not see the third man wearing red, otherwise he would deduce his own hat is blue. Therefore the third man must be wearing a blue hat.