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.