Brainteasers
Brainteaser – The Three Wise Men
The King summoned the three wisest men in his kingdom in order to find out who was the absolute wisest. He blindfolded them all then put a hat on each man’s head.
“In a minute,” he said, “I want you all to remove your blindfolds. Your hats are either black or white. If you can see any black hats, put your hand up. As soon as you know what colour your hat is, say so.”
The men removed their blindfolds. Each man could see the other men’s hats, but no man could see his own hat. All three hats were in fact black, so all the men put their hands up.
After a minute, the wisest man put his hand down and said “My hat is black”.
How did he know?
Because each man raised their hand, they all know that there can’t be two or three white hats (because otherwise at least one man would have seen no black and not have raised his hand). They all know this, and so can all deduce that there is either one white hat, or none.
The wisest man realises that if either of the other two had seen a white hat on his head, they would have known that their own had to be black because it was observed by the other black hat wearer. As they remain quiet, he concludes that his own hat must be black.
