As before, the police have tracked down three suspects for a murder. They know that one of them is guilty and each one of them can be either a knight or a liar. Each one of them wrote two statements, but parts of them are full of coffee stains and they are not sure which one of the words in the brackets should be under each coffee stain:

A: ███ (B/C) is a liar. He is also guilty.

B: A is a ████ (liar/knight). C too.

C: A and B are both ████ (liars/knights). I'm guilty.

From these statements, can you figure out who is guilty?

If C is guilty, he is a knight, and A and B are of the same type.  A must be a liar, because he either says that B is guilty or that C is a guilty liar. Since A cannot refer to C (who is guilty), A must be saying "B is a liar", but that would be true, instead of a lie. Thus, C is innocent.

C is lying, so A and B are of different types. B says that A and C are of the same type, so A is also a liar.  A cannot say that C is a liar because that would be true, so A says "B is a liar. B is guilty." Since A lies, B is innocent, and A is guilty.

We can tell that A mentioned B in his first statement, and that B said "A is a liar", but we cannot tell what did C say.

Posted by Federico Kereki on 2007-04-20 00:09:21