All of them know the color of their hats. This is assuming that all five of them know whether a person was able to tell the color of his/her hat or not. Here's how: Notation: 1B = the first person has a black hat. Condition 1: If the fifth hat is a WHITE one Then the condition will be something like: 1B, 2B, 3W, 4W, 5W (Here, the order of the hats does not matter. ) Now, when 1 looks at other people, he can only see one black hat. So, he instantly knows that his MUST have a black one too. Same logic with 2 too; So 2 also knows that he has a black hat. When 3 looks at other people, he can see two white hats and two black hats. But he knows that if he had a black hat, then 1 and 2 would not be able to tell the color of their hats. But since 1 and 2 know the color of their hats, 3 must have a white hat. Same logic with 4 and 5 too, and hence they know that they have white hats too. Condition 2: If the fifth hat is a BLACK one. Its the similar logic. We will then have condition like: 1W, 2W, 3B, 4B, 5B.