#35

There are three wise men on top of a mountain that are arguing about who is the wisest of them all. A stranger comes along and says he can solve their debate. The stranger has 5 hats, two black and three white, as shown below. He says "I will put a hat on each one of you when your eyes are closed and take the remaining hats away. When you open your eyes you will be able to see the other two mens hats but not your own. The first person to definitevly say what color hat he has wins." The wise men sat for a long time and finally one said "I know what color hat I have!" Remember they are wise men and do not take guesses so the wiseman knew for sure what hat he had. What color are the hats on each wiseman and how did the one who spoke arrive at his conclusion?

Answer:

The 3 wise men all had white hats.

Lets consider 3 cases for the wisemen A,B and C. 1) 2 hats are black and 1 is white 2) 1 hat is black and 2 are white 3) all 3 are white hats. If any of the 3 wise men saw 2 black hats he would know that his hat is white. Again, they were thinking for a long time and nobody saw a white and a black. If A saw 2 white hats he would know his hat is not black because B would see a black and white and deduce he has white.Since they were sitting for a long time each saw 2 white hats which means they all had white hats.