Question of Logic. Can you answer this?

Question

3 people are standing in a row, one behind the other, all facing the same direction. A man tells them that he has 5 hats, 3 white and 2 black. He will place one on each of their heads. Only the one in the back can see the two in front, and the middle person can see the person in front, but the person in front cannot see the others although they can all hear each other and the man. He tells them how many hats he has and what color they are and they can also hear each other. The woman in the back when asked what color hat he placed on her head says she does not know, the middle woman says the same, but the woman in the front of the row knows exactly which hat she has on her head. What color hat does she have on her head and how does she know this?

Answer 1

does she have a mirror? did she say what color she wanted??

Answer 2

If the person in the back doesn't know the color of her hat, then the hats on the other people can't both be black. They're either both white, or they're mixed.

The 2nd person knows that at least one of them has a white hat. If the person in the front had a black hat, the 2nd person would know that she must have a white hat.

Because she isn't able to determine her hat's color, the only options left are:

Front: White hat, Middle: White hat

Front: White hat, Middle: Black hat

No matter which is true, the person in front must be wearing a white hat.

Answer 3

d**n. I haven't done these in forever - probably since the 5th grade.

I have no idea.

Answer 4

3rd doesn't know his hat color, therefore 1st and 2nd must have hats of different colors or both have to have white hats. Because 2nd knows that the 3rd does not know his color, therefore 2nd knows he and 1st have different colors or whites. 2nd does not know his color, therefore 1st has to have a white hat. Since 1st is listening and drawing the same conclusions he knows he has a white hat.

Answer 5

is the woman in the front, standing in front of a mirror?