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You go to an island trying to find gold. Every inhabitant of the island is either a knight or a liar. You meet two inhabitants, A and B.

A:B is a knight and there is gold on this island.
B:A is a liar and there is gold on this island.

What are A and B, and is there gold on the island?

 No Solution Yet Submitted by Math Man No Rating

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They can't both be knights as one is calling the other a liar.

They can both be liars if liars are allowed to make their compound sentences (ANDed sentences) of true and false components (clauses). In this case there is no gold on the island, as the lack of gold is necessary to make B's statement false.

Can A be a knight and B a liar? No, as A claims B to be a knight.

Can B be a knight and A a liar? No, as this would mean that there is indeed gold on the island and both clauses of A's statement would be true, contradicting his being a liar.

So they're both liars and there's no gold on the island.

 Posted by Charlie on 2015-03-26 10:02:29

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