A haberdasher has as grand opening sale and decides to offer a free hat to one of his first three customers. He has five hats on display: three red and two green. Soon after opening, three professors from a near-by university enter the store -- one of whom happens to be blind. To these three men the storekeeper makes the following proposition:

I will select at random three of the hats on display and conceal the remaining two. These hats will be placed on your heads so that no one can see the color of his own hat. The free hat will go the first man who discovers the color of his own hat.

The professors are blindfolded and the hats are then selected and placed in the prescribed manner. After the blindfolds are removed, the professors are asked to name the color of their hats.

The first professor thinks for a few minutes, but then states that he cannot determine the color of his hat. The second professor, after a few moments thought, likewise states that he cannot tell what color his hat is. The blind professor considers the problem briefly and surprisingly, correctly states the color of his hat.

How does he do it?