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

(In reply to re(2): Through the looking glass...... by Penny)

Well, since you're expecting about ten replies...
I don't always post the solutions I come up with, because I'm often lazy.  I think this is an interesting puzzle.

The White Knight went to a trial with three defendants and each one accused one of the others.  The Red King could tell who was guilty just by knowing which were lies.

If the White Knight told the Red King said that a defendant told the truth, the Red King can deduce that that defendant was innocent (assuming only one is guilty).  If the defendant lied, the Red King can't deduce anything.  For the Red King to deduce the guilty one, the White Knight needed to say that one lied and the others told the truth.  Then, the liar must be guilty.

Since two defendants told the truth, Humpty Dumpty could not have asked if two consecutive lies were told--he would receive a "no" no matter who was guilty.  He asked if there were consecutive truths, and the answer was no--or Humpty would not know whether the first or last was guilty.  Therefore, the first and third told the truth, while the second lied.  The second defendant was guilty.

... that was a little longer than I expected.

Posted by Tristan on 2004-04-07 15:35:46