Three men, who are not wearing glasses, are placed in a room without mirrors. The men are told to close their eyes and then a hat is placed on each of their heads. The hat is either red or green in color. Once the hats are in place they are told to open their eyes. They are not allowed to inspect their own hats in any way and are forbidden to talk or communicate in any way except as follows: if they see a red hat, they are to raise their right hand. If they figure out what color their own hat is, they are to leave the room immediately without a word to anyone. They must stay in the room until they figure out what color their own hat is, or until someone else does.
Immediately after having the hats placed on their heads and opening their eyes, all 3 men immediately raise their hands, but no one gets up. Finally, after a few minutes one of the men figures it out and leaves the room. As it turns out, all the hats are red. How did he figure out what color his own hat was?
Answer:
Person A (who figured it out) looked at Person B and Person C and thought to himself, “Both these men are wearing red hats, and each of them sees that the other man and I both have our hands up. If I were wearing a green hat, then person B would look at person C and see that Person C’s hand was up, but not for me — since my hat would be green. Therefore, he would immediately figure out his own hat was red and leave the room. But a few minutes have gone by and neither Person B nor Person C has figured out what would be an obvious conclusion; therefore, they’re stuck because my hat is red, not green.”