"Let's see now... I do remember that there was another trial. A quite interesting one, if I recall...

"Again there were three defendants. The first defendant either claimed he was innocent or guilty, but I can't remember which. The second also either claimed he was innocent or he was guilty. The third defendant... hmmm... Well he either accused the first defendant, or claimed that the first defendant was innocent. The one thing I do remember, however, is that at most one of the statements was true.

"Now then, last month I recounted the trial to the Jabberwocky, and at that time I remembered what each of the defendants said at the trial. The Jabberwocky quickly worked out who the guilty party was.

"Three weeks ago I was trying to recount the trial to Tweedledee, but unfortunately at that time I could only remember what the first defendant had said. I also told him that the Jabberwock had solved the case. Poor Tweedledee was left quite baffled, though.

"Two weeks ago I was telling Tweedledum about the case. I told him about the Jabberwock solving the case, but I forgot to tell him about Tweedledee's attempt. I had at this time forgotten what all the defendants had said at the trial, except for either the second defendant's statement or the third defendant's statement. Whichever I told Tweedledee, he was left just as baffled as his brother.

"Finally, just last week, I was recounting the case to the brilliant logician, Humpty Dumpty. I told him all about the Jabberwock solving the puzzle, and about the two twins being stumped. Humpty Dumpty worked on it for a while, and finally asked me if I could just remember which defendant I had told Tweedledum about. Fortunately at the time I did remember, and so I told Humpty Dumpty, who was able to solve the case.

"So tell me now, who was guilty?"

    Adapted from Raymond Smullyan's Alice in Puzzleland.

#2 is guilty.

There are only three combinations that result in a single guilty party:

1. #1 - I'm innocent (lying), #2 - I'm guilty (lying), #3 - #1 is innocent (lying) = #1 Guilty

2. #1 - I'm innocent (truth), #2 - I'm innocent (lying), #3 - #1 is guilty (lying) = #2 is Guilty

3. #1 - I'm innocent (lying), #2 - I'm innocent (truth), #3 - #1 is innocent (lying) = #1 is Guilty

In all cases: #1 claims to be innocent therefor Humpty knows his statement is innocent. Humpty also knows #3 is always lying.

If the unknown person was # 2, that would not be enough information to solve the problem (for Tweedledum).  If #2 said they were innocent or guilty, the real guilty person could be either #1 or #2. 

If the unknown person was #3 then claiming #1 was innocent would mean that the guilty party is #1.  Claiming #1 was guilty would mean #2 was guilty.

This only leaves one case where it the guilty party can be determined based on WHO gave the statement.  That is the case where #2 is guilty.

Chart:

1,2,3,Guilty<o:p></o:p>

G,G,G,<o:p></o:p>

F,F,F,3<o:p></o:p>

T,F,F,NP<o:p></o:p>

F,T,F,2<o:p></o:p>

F,F,T,NP<o:p></o:p>

G,G,I,<o:p></o:p>

F,F,F,NP<o:p></o:p>

T,F,F,1<o:p></o:p>

F,T,F,NP<o:p></o:p>

F,F,T,3<o:p></o:p>

G,I,G,<o:p></o:p>

F,F,F,2<o:p></o:p>

T,F,F,NP<o:p></o:p>

F,T,F,3<o:p></o:p>

F,F,T,NP<o:p></o:p>

G,I,I,<o:p></o:p>

F,F,F,NP<o:p></o:p>

T,F,F,1<o:p></o:p>

F,T,F,NP<o:p></o:p>

F,F,T,2<o:p></o:p>

I,G,G,<o:p></o:p>

F,F,F,NP<o:p></o:p>

T,F,F,3<o:p></o:p>

F,T,F,NP<o:p></o:p>

F,F,T,1<o:p></o:p>

I,G,I,<o:p></o:p>

F,F,F,1<o:p></o:p>

T,F,F,NP<o:p></o:p>

F,T,F,NP<o:p></o:p>

F,F,T,NP<o:p></o:p>

I,I,G,<o:p></o:p>

F,F,F,NP<o:p></o:p>

T,F,F,2<o:p></o:p>

F,T,F,NP<o:p></o:p>

F,F,T,NP<o:p></o:p>

I,I,I,<o:p></o:p>

F,F,F,NP<o:p></o:p>

T,F,F,NP<o:p></o:p>

F,T,F,1<o:p></o:p>

F,F,T,NP