# 345 logic/smullyan/black.hat.p

## Description

This article is from the Puzzles FAQ,
by Chris Cole chris@questrel.questrel.com and Matthew Daly
mwdaly@pobox.com with numerous contributions by others.

# 345 logic/smullyan/black.hat.p

Three logicians, A, B, and C, are wearing hats, which they know are either

black or white but not all white. A can see the hats of B and C; B can see

the hats of A and C; C is blind. Each is asked in turn if they know the color

of their own hat. The answers are:

A: "No."

B: "No."

C: "Yes."

What color is C's hat and how does she know?

logic/smullyan/black.hat.s

A must see at least one black hat, or she would know that her hat is black

since they are not all white. B also must see at least one black hat, and

further, that hat had to be on C, otherwise she would know that her

hat was black (since she knows A saw at least one black hat). So C knows

that her hat is black, without even seeing the others' hats.

Continue to: