Problem #18: Colored Labels
Three intelligent women, Alice, Barb and Carol, sit down to try out a test
in logical reasoning. They are so arranged that each can see the color of a
label which is either red or blue, attached to the hats worn by the other two
but no one of them can see the color of the label attached to her own hat.
They are told that at least one of the labels is red. If any one of them can
logically deduce the color of the label on her hat, she is to declare it.
Carol decides to play this game with her eyes closed, knowing that the other
two women have their eyes open. After a little time Carol, who has not seen
the label on any of the hats declares her label is red.
How can she deduce this?