Answer

“I have a white hat”.

Let’s suppose the winner, you, are A, and the others are B and C.

You could say, by probability, there are more white than black so white is more likely. Or that three identical hats is the only fair test. But that’s a guess, not a deduction.

So, let’s work it out. If two of them have black hats, the third would know immediately he had a white hat, there would be no pause and the problem is over. But that doesn’t happen, so there is at most one black hat.

If you were A and you saw a black hat (say B) and a white hat (C), then you would know you had a white hat, because C does not see two black hats. If he did, he would answer instantly.

If you were A and you saw two white hats (B and C), you would have to put yourself in, say, B’s position. If you (A) had a black hat on, B sees a black (A) and a white (C), realises that C doesn’t know so C must see a black and a white, so B would know the answer and would say he had a white. But he doesn’t, so you don’t have a black hat on, so it must be white.

Puzzle

A wizard is giving his three pupils a final test.

He tells them he has five hats, two black and three white.

The pupils must close their eyes, then each will have a hat put on their head. The remaining two hats will be hidden. Then the pupils can open their eyes.

The first to deduce what colour hat they have will win.

So, they do that. The pupils are not allowed to ask questions, there are no mirrors and they cannot see their own hats.

There is a long pause, and the one says… what?