A man named John was trying to find gold. He went to an island where every inhabitant is either a knight or a liar. He met three inhabitants, A, B, and C. A and B made these statements.

A:We are all liars.
B:There is gold on this island.

Then, he asked one of them, "Is it true that you are a knight and there is no gold on this island?" The inhabitant answered, and he could not figure out if there was gold on the island. Then, one of the inhabitants either said that A was a liar or said that B was a liar, and John knew if there was gold on the island.

There is not enough information yet for you to figure out if there is gold on the island. However, if I told you whether the last inhabitant said that A was a liar or said that B was a liar, without telling you which inhabitant said it, then you would be able to figure out if there is gold on the island. Who did the last inhabitant say was a liar, and is there gold on the island?

This is a hard puzzle. There are many possibilities for what the inhabitants could have said.

Posted by Math Man on 2011-01-25 18:08:50