3 Hats Puzzle

Three wise men are told to stand in a straight line, one in front of the other. A hat is put on each of their heads. They are told that each of these hats was selected from a group of five hats: three black hats and two white hats. The first man, let’s call him A, at the rear, can see both other men and their hats. The second man, B, in the middle, can see only the last man and his hat. The last man, C, standing at the front of the line, can’t see either of the men behind him or their hats.

None of the men can see the hat on his own head.

When A is asked if he knows the color of the hat he is wearing, he says no. When B is asked if he knows the color of the hat he is wearing he says no. When C is asked if he knows the color of the hat he is wearing he says, “Yes, my hat is black.”

He is correct. How did he come to this conclusion?

Answer

A must not have seen two white hats on B and C, or he would have known his own hat must be black since there are only two white hats. So A’s answer establishes that at least one of B or C’s hat is black.

Based on A’s answer, B knows that he and C are either both wearing black, or one is wearing black and one is wearing a white hat. If B sees that C is wearing a white hat, then he would know his own hat had to be black. But B does not know what color hat he is wearing, which mean’s C’s hat is not white and must be black.

Since both A and B cannot deduce the color of their own hats, C will know that he is wearing a black hat.

« Previous Riddle