BRAINTEASERS: THE AFTERMATH
PROBLEM: A king wants to hire a royal adviser, so he invites his kingdom's three wisest men to engage in a contest of wits. He sits them down facing one another and walks behind them, putting a cap on each man's head. He tells them that he has given each of them a red cap or a white cap; in fact, he has placed red caps on all three heads. No one can see what he himself is wearing; there are no mirrors or other ways to cheat. The king says, "Raise your hand if you see someone wearing a red hat." All three men raise their hands. Then the king says, "All right, now, if you know what color your cap is, stand up."
For several minutes, no one moves. Then wise man No. 3 stands up. "I am wearing a red cap!" he proclaims. How did he know?
ANSWER: Wise man No. 3 first imagined himself wearing a white cap. "If I have a white cap," he reasoned, "then when wise man No. 2 raised his hand he must have been looking at wise man No. 1's red cap. Wise man No. 1, being smart, would have realized immediately that the red cap seen by No. 2 had to be his, and he would have stood up. Wise man No. 2 would have reached the same conclusion and he would have stood up quickly as well. Since neither of the others stood up, I must not be wearing a white cap. I must be wearing a red one."
SUBSEQUENTLY: Wise man No. 3 is made the king's royal adviser. Two days later, the king consults with him. "The people of my kingdom are unhappy," he says. "There is much misery and disease, farmland lies fallow, and war may be imminent. What shall I do?"
The wise man thinks for a moment. Then he says, "Sire, do any of those people happen to be wearing a red hat