Need an answer to a math riddle

Question

Three mathematicians are applying for a job. There are five hats, three white, two 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 he has 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 figure it out. 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?

Answer 1

His hat must be white. 

 

We're assuming that given the configuration, both the 2nd and 3rd mathematician are not immediately able to figure out the color of their hat, since there's a long pause and the first guy is the one to answer.

 

So this tells us a couple of things.

 

Clearly the first two are not both wearing black hats, because then the third would know he was wearing white.

So this means the first two are wearing white or black, or both white. 

Let's try giving the first guy black. The second guy seeing this, and knowing that the third guy has not guessed his own hat to be white, would realize that his hat must not be black and it must be white. But he does not realize this, so this must not be the case.

So therefore, the first guy's hat must be white for the given situation to take place.

The first guy knows this because he has taken into account all of these cases and knows that given that no one has answered, none of the above cases can be true, so his must be white.