A miniature of tribal logic where a single phrase—and what was not heard before—decides everything.
The two islanders
Riddle statement
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?
Show solution
Solution
Let's examine the possible cases.
If both are 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. Then B, by saying "He said no," would be telling the truth, which cannot happen if he is a liar. This case is ruled out.
If A is a liar and B is truthful, the correct answer is still no, so A, by lying, would say yes. But then B could not truthfully say "He said no." Discarded.
If they 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, contradicting his condition as a liar. Discarded.
Only one possibility remains: A and B both belong to the truthful.