Three mathematicians are applying for a job. There are 5 hats, 3 white, 2 black. They're lined up, and a hat is placed on each. The first person in line cannot see any hat; the second in line sees only the hat of the person in front of him; the third person sees only the hats of the two people in front of her. The first person to correctly figure out what color hat they have gets the job; you guess wrong and you are killed. Assume these are INTELLIGENT mathematicians, and that they will do the logically correct thing at each stage -- if something can be deduced, they will. After a long pause, the first person, who cannot see any hats, says he knows the color of his hat. What is the color, and how does he know?