Professor Merle White of the mathematics department, Professor Leslie Black of philosophy and Jean Brown, a young stenographer who worked in the university’s office of admissions, were lunching together.
“Isn’t it remarkable,” observed the one woman in the group, “that our last names are Black, Brown and White and that one of us has black hair, one brown hair and one white?”
“It is indeed,” replied the person with black hair. “And have you noticed that not one of us has hair that matches his or her name?”
“By golly, you’re right!” exclaimed Professor White.
If the woman’s hair isn’t brown, what color is it?
The assumption that the woman is Jean Brown, the stenographer, quickly leads to a contradiction: Her opening remark brings forth a reply from the person with black hair. Therefore, in this scenario, Brown’s hair cannot be black. It also cannot be brown, for then it would match her name. Therefore, it must be white. This leaves brown for the color of Professor Black’s hair and black for Professor White’s. But a statement by the person with black hair prompts an exclamation from White, so they cannot be the same person.
It is necessary, therefore, to assume that either Merle White or Leslie Black is the woman. (All three given names are used for both genders.) Either assumption leads to the conclusion that Black’s hair is white, White’s hair is brown and Brown’s hair is black. The woman’s hair is thus either white or brown. If it isn’t brown, the problem asks, what color is it? Answer: Professor Black is a woman with white hair.
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A version of this puzzle originally appeared in the February 1960 issue of Scientific American.