MATH PROB. - Five Hats (S448b)
From: William Wu of U. C. Berkeley
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
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
When A is asked if he knows the color of the hat he is
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?
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.