You get a note from the police station. Unfortunately, it is full of coffee stains.

We have tracked down three suspects for a murder. We 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 a statement or two, but parts of them are full of coffee stains and we are not sure which one of the words in the brackets should be under each coffee stain:

A: ███ (B/C) is innocent. He is also a knight.

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

C: A and B are both ████ (liars/knights)

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

Since B says that A is a Liar, A & B cannot be of the same type. If they are both Knights, then B cannot say that A is a liar. Likewise, If both are Liars B again cannot say that A is a Liar, as then B would be saying the truth.

Following this, C is certainly a Liar as he says that both A & B are of the same type.

Hence, we are left with just 2 possible combinations
A - Knight, B - Liar, C - Liar
A - Liar, B - Knight, C - Liar

If, A - Knight, B - Liar, C - Liar
...Then A cannot say that there is another Knight.

Therefore, A is a Liar, and either B or C is Guilty.

Now the only combination left is... A - Liar, B - Knight, C - Liar
Then A's statement should be about C, else he would be saying the truth that B is a Knight

... Hence C has to be the Guilty one.

Posted by Syzygy on 2007-04-11 02:49:32