Black Hair Red Hair

A man and a woman were the only two people walking along a beach. “I’m a man,” said the one with black hair. “I’m a woman,” said the one with red hair. At least one of them was lying. What was the color of the woman’s hair?
Source: NCTM Mathematics Teacher, January 2006

Solution
If the red hair person was lying, then red hair is a man.
If the black hair person was lying, then black hair is a woman.
If either one of them was lying or both of them were lying, the woman’s hair was black.

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About mvtrinh

Retired high school math teacher.
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