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

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

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

Suppose B is a liar. Then it must be the case that there is no gold on the island AND A must be a knight, otherwise B's statement would be true. But if B is a liar and there's no gold, then A's statement is false, making A a liar. Since this contradicts, B can't be a liar and so must be a knight.

If B is a knight, then A's statement is true, so A is also a knight.

As a knight, B's statement must be true. And since the first part is false (A is not a liar), the second part of the "or" must be true, so there is indeed gold on the island.

Any other combination of A's and B's type or whether there's gold results in a contradiction.

Posted by Paul on 2015-04-22 19:13:20