An inhabitant has been killed in Knavesville and the Sheriff has interrogated four suspects. It is known that one of them is the killer. As is expected of Knaves, they alternated between telling the truth and lying (Not necessarily in that order).

Each suspect was first asked if he was the killer, to which the sheriff got the same answer from all the four suspects.

He then asked them, 'Who was the killer?' The answers to which are shown below.

Abbey said: Bart is the killer.
Bart said: Dean is the killer.
Cody said: Bart is lying when he says Dean is the killer.
Dean said: If Abbey did not kill him, then Bart did.

Who was the killer?

I came across two possible solutions (unless I've made some mistake over the process):

Solution 1 - C is the killer

Let's presume everybody answers No to the first sheriff's question. As one of the four suspects is the killer, one of them must be lying. So, during next round, three of them will be lying, and that one, the killer, will tell the truth. So, neither A nor B can't be the killers, because if they were, they would be now telling the truth and answering "I'm the killer". Instead, they accuse someone else. So they're lying and they're not the killers. And if B is lying that means D can't be the killer also. So we end up with C as being the killer and you can verify that he is in fact the only one who's telling the truth now.

Solution 2 - B is the killer

On the contrary, we may suppose now that everybody answered Yes to the sheriff's first question. That means that three of them are lying and will tell the truth the next round. Now, A and B, for instance can't be telling the truth simultaneously in this second round. One of them must be lying. That leaves us assured that C and D are telling the truth. Then, by C's statement we get that B is the liar. So he is the killer, as he was the only one to lie during the first sheriff question. Everyone's else is telling the truth and every statement checks ok...

Have I made any mistake around here?

Posted by vj on 2007-03-08 07:09:07