Solution #18: Colored Labels
Carol argues as follows:
- If Alice sees two blue labels she will know that her label is red and will
declare this and since a little time has passed without this happening Betty
and Carol cannot both have blue labels.
- Similarly, if Betty sees two blue labels he will know that his label is red
and will declare this, and hence, Alice and Carol cannot both have blue labels.
- Carol can now deduce that if her label is blue, both Alice and Betty
must have red labels. Now Carol knows that both Alice and Betty are
intelligent. If Betty and seen a red label on Alice's hat and a blue label on
Carol's hat, she would know her hat did not have a blue label, because in this
case Alice would have declared her label to be red.
- Since a little time has passed and neither Alice nor Betty has declared she
could deduce the color of her label, Carol knows her label cannot be blue, and
therefore must be red.
Source: Longley-Cook, L. H.