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Logic Level 1

You are on an island where there are two kinds of people: those who always tell the truth, and those who always lie. Half of the islanders have brown hair and the other half have blond(e) hair. What hair color you have has no relation to whether you are a truth teller or a liar.

One scorching day, you duck inside a cool alcove to see two natives deep in the shadows. You can't see their hair color.

"Hey!" you call out. "Are you liars, and what color is your hair?"

Native A says: "Both of us have brown hair."

Native B says: "Both of us are liars."

What are they?

A -- blond(e) hair, liar B-- blond(e) hair, liar A -- brown hair, truth teller B -- blond(e) hair, liar A - brown hair, truth teller B -- brown hair, liar A -- brown hair, liar B -- brown hair, liar A -- brown hair, liar B -- blond(e) hair, liar A -- blond(e) hair, truth teller B -- blond(e) hair, liar A -- blond(e) hair, truth teller B -- brown hair, liar A -- blond(e) hair, liar B -- brown hair, liar

2 solutions

Denton Young
Jun 18, 2015

Clearly, native B's statement cannot be true, because then both of them WOULD be liars and B, a liar, would have made a true statement. So B's statement is false, and both of them are not liars. But since he made a false statement, B is a liar. Therefore A must be a truth-teller.

Since A is a truth-teller, his statement is true. Therefore both of them have brown hair.

So the full categorization is: A has brown hair and is a truth teller. B has brown hair and is a liar.

Varun M
Jun 18, 2015

B is a liar because his statement cannot be correct because then both would be liars and his statement would become true which is contradictory.So A is the truth tellur and both have brown hair.

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2 solutions

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