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?

A can not be a knight. A's second statement indicates that either one or both B and C are knights.  If C was identified by A's coffee-stained statement to be the knight, then C's coffee-stained statement would be either "A and B are both liars",
which contradicts A as a knight, or "A and B are both knights", which is contradicted by B's second statemwnt that identifies A as a liar.

A thus is a liar.  And because A is a liar, B by A's second statement must be a knight.

Because A is a liar his coffee-stained statement can not be a statement about B, as then his second statement that "he is a knight" would not be a lie, thus, by deduction C is guilty.

It is possible by B's coffee-stained statement that A could allegedly be a guilty accomplice, yet it is given that "we know one of them is guilty" -- implying only one is guilty which we know is C. 

Therefore, A made the statements "C is innoncent. He is also a knight."  B made the statements "A is innocent. He is also a liar."  And C stained statement remains a conundrum. 

Edited on April 10, 2007, 12:27 pm

Posted by Dej Mar on 2007-04-10 12:17:01