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

Lable the defendent A, B, and C in the order they are questioned. 

Since each defendant accused someone else, there was at least one lie (the guilty party), and possibly two (A accuses B, B accuses C, and C accuses A), or three lies (everyone accuses one of the innocents).  If there had been three lies, the Red King would have been hopeless to identify the guilty party.  Similarly, if there had been two liars, the Red King would have been helpless to identify who was guilty without knowing who acused who.  However, if only one lie was told, then the liar must be guilty.  Since we are told the Red King could solve the riddle, we can conclude that there must be only one liar, the guilty party.

Humpty Dumpty (HD), realising that there were two truths and one lie told must thefore have asked whether the two truths were consecutive.  If they had been, Humpth Dumpty would not have know if the one lie came first (A) or last (C).  Since Humpty Dumpty was subsequently able to solve the riddle, we can conclude that the two truths were not consecutive.

Therefore, B told the liar and was guilty.

Posted by stan on 2004-04-07 12:09:58