A judge visits an island where everyone belongs to one of two tribes: the truthful, who always tell the truth; the liars, who always lie. He meets two islanders, A and B. He asks A: “Are you both liars?” A responds in a low voice, and the judge cannot hear him. Then B says: “He said no.” What tribe does each one belong to?

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The two islanders

A miniature of liars and truth-tellers where the real twist is not having heard the first answer.

A judge visits an island where everyone belongs to one of two tribes:

the truthful, who always tell the truth;
the liars, who always lie. He meets two islanders, A and B. He asks A:

“Are you both liars?” A responds in a low voice, and the judge cannot hear him. Then B says:
“He said no.” What tribe does each one belong to?

Solve this riddle

Hints

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Ask yourself what A might answer if they were both liars.
Then check whether B's sentence can be true or false in each case.
Only one combination of tribes fits both interventions.

Solution

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Let's examine the possible cases. If you are both truthful, the correct answer to “are you both liars?” It's no.

A would say no. B says “He said no,” which is true.

This case fits. If A is truthful and B is a liar, A would say no.

So B, by saying “He said no,” would be telling the truth, which cannot happen if he is a liar. If A is a liar and B is truthful, the correct answer is still no, so A, by lying, would have to say yes.

But then B could not truthfully say “He said no.” If you are both liars, the correct answer to “are you both liars?” it would be yes. A, by lying, would say no.

But then B, by saying “He said no,” would be telling the truth. There is only one possibility: A and B are truthful.

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