An employer was very anxious to find the most intelligent of the three men who had applied for a job. So he told them: ‘here are five conical hats. Three are white and two are black. I shall place a hat on each of your heads. When you turn around, you will be able to see the others’ hats but not your own. The first one to tell me the color of his own hat will get the job.’ He then placed a white hat on each man’s head. When the three men turned to face each other there was a long silence. Then, suddenly, one of the candidates said, ‘Mine is white.’
How did he know?
Clue for the Puzzle:
There are three possible combinations: two men had black hats and one a white one (this must be excluded because if one man had seen two black hats, he would immediately have known his was white); two had white hats and one had a black one; all three had white hats.
The secret is to work out the color of one’s own hat from what the other people must able to see.
Answer for the Puzzle:
He could see two white hats. Therefore he might have had on either a white or a black hat. He then reasoned like this: Suppose my hat is black. If it is, my two rivals A and B can each see a black hat and a white hat. One of them (A) might then work out that his own hat could not be black because, if it were, B would see two black hats and would know that his own hat must therefore be white. B says nothing however. A might therefore conclude, if my hat is black, then his own hat must be white. But since he does not come to this conclusion, then my assumption that my hat is black must be false. Therefore my hat must be white.