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

The second defendant was guilty. Then two consecutive statements were not true, because the first  defendant truthfully accused the second, the second falsely accused the first (or the third) and the third truthfully accused the second. Humpty Dumpty must have asked whether two consecutive statements were true, and the White Knight  must have said no. Otherwise Humpty Dumpty could not have solved it.

The Red King is a red herring.  

If the White Knight had told Humpty Dumpty that two consecutive statements were true, then either the first or the third defendant was guilty. If Humpty Dumpty had asked if two consecutive statements were false, the White Knight would have said no, and any of the three could have been guilty.

I guess this assumes that both of the innocent defendants were telling the truth. We know that the guilty defendant was lying, since everyone accused someone else. No one accused himself.

Even if when the White Knight was conversing with the narrator, he could not remember who had been accused by whom, or how he had answered the Red King, he must have known who the guilty defendant was when he was conversing with Humpty Dumpty, in order to have answered Humpty Dumpty's question. He didn't tell Humpty Dumpty that he couldn't remember who had been accused by whom, or that he didn't know which defendant was guilty, only that he couldn't remember how he had answered the Red King. 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Edited on April 6, 2004, 8:12 pm

Posted by Penny on 2004-04-06 16:59:12