The White Knight was recounting the story of one of the trials he had recently attended:

“Ah yes, it was a fine trial. Let’s see if I can remember it… If I recall there were three defendants. Each of them made one statement accusing one of the others, I think, but I’m afraid I can’t remember who accused whom. Can you work out who was guilty?”

“Of course not!” you reply. “You haven’t told me anything yet! Could you at least tell me who lied and who told the truth?”

“Hmmm... Interesting that you should ask that. When I was describing the trial to the Red King he asked me the same question. When I told him the answer, he worked it out. Unfortunately I’ve now quite forgotten what I said.”

“Well, I guess it’s hopeless for me then…” you sigh.

“Interesting that you should say that, too. When I was describing the trial to Humpty Dumpty he asked me the same question, and when I told him I had forgotten what I told the Red King, he too claimed to be at a loss. But then he asked me another question, I can't quite remember what, but when I told him the answer he was able to solve it. I think he either asked me whether two consecutive statements were true, or whether two consecutive statements were false. Unfortunately I can neither remember which one he asked, nor what I answered. I think I’ve given you quite enough information now though, so tell me: who was guilty?”

    Adapted from Raymond Smullyan's Alice in Puzzleland

It must first be assumed that one, and only one of the defendants is guilty.  If this were not the case, then no answer to the king's question would allow him to determine which among them (if any) were guilty.

This only leaves one type of answer that would allow him to determine which one of the defendants is guilty.  Only one of them lied, and he is the guilty party.  The two truth-tellers accuse the guilty party, who lies in accusing one of the others.

They could not all have told the truth, for the guilty party accused one of the others.
Had they all lied, any one of them could be the guilty party.
Had two lied, either one could be the guilty party.

Humpty Dumpty's question was whether two consecutive statements were true.  It could not have been whether two consecutive statements were false, because there was only one false statement, so the answer would surely be 'no', and this would gain no one any new information.

The answer was 'no'.  Had it been 'yes', the liar could have been either the first or last defendant, so Humpty Dumpty wouldn't know which, and couldn't solve it.

This leaves the second defendant as the guilty party.

Posted by Galendir on 2004-04-19 04:51:32