Board Thread:Fun and Games/@comment-48285-20141118170709/@comment-17259909-20150401211215

A group of three logicians have been asked by the king to play a game. There are three black hats and two white hats, and the logicians must correctly say which hat they have on. The king makes them stand in a single-file line, although he lets them choose the order. The least wise one of the three chooses the back. The second most wise one of the three chooses the middle. The wisest of the three chooses the front. They are blind folded and a hat is put on their hand. The blindfolds are removed, and the one in the back can see the two in front, the one in the middle can see the one in front of him, and the one in the front can see neither. Without directly communicating to each other, they each come to an answer:

The one in the back says, "I don't know."

The one in the middle says, "I don't know."

The one in the front says, "I know," and gives the correct answer.

How did he know?