Subj:     MATH PROB. - Five Hats (S448b) 
          From: William Wu of U. C. Berkeley 
          At: http://www.ocf.berkeley.edu/~wwu/riddles/intro.shtml
Solution: http://www.ocf.berkeley.edu/~wwu/riddles/easy.shtml#3hats

There are 3 black hats and 2 white hats in a box.  Three men 
we will call them A, B, & C) each reach into the box and place 
one of the hats on his own head.  They cannot see what color 
hat they have chosen. 

The men are situated in a way that A can see the hats on B & C's 
heads, B can only see the hat on C's head and C cannot see any 
hats.  When A is asked if he knows the color of the hat he is 
wearing, he says no.  When B is asked if he knows the color of 
the hat he is wearing he says no.  When C is asked if he knows 
the color of the hat he is wearing he says yes and he is correct. 
What color hat and how can this be? 


 
 
 
 
 
 

. .
Solution

A sees WW, or WB, or BB.  If A sees WW he knows that he is wearing
     a black hat, therefore A sees WB, or BB.
B sees W, or B.  If B sees W, he knows he is wearing a black hat,
     therefore he sees C wearing a black hat.
Since both A and B did not know their own hat color, C knows he
     is wearing a black hat.