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The White Knight who couldn't quite remember II (Posted on 2004-05-12) Difficulty: 4 of 5
"Good job on that last puzzle!" said the White Knight.

"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.

No Solution Yet Submitted by Sam    
Rating: 4.1429 (7 votes)

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Solution Solution | Comment 1 of 13

If the first and third defendants were in agreement, they must both be lying. From this, the Jabberwock could have discovered the answer only if the first had claimed innocence (and therefore been guilty), since it is unknown whether the second was lying or telling the truth.

Had they contradicted each other, the second must have been lying, and the Jabberwock could only have worked out the answer had he also claimed innocence.

Therefore either: the first and third were in agreement and both said the first was innocent; or the first and third were not in agreement and the second claimed innocence.

Possibilities for the statements are:
1) I am innocent 2) Either 3) 1 is innocent
1) I am innocent 3) I am innocent 3) 1 is guilty
1) I am guilty 2) I am innocent 3) 1 is innocent

Since Tweedledee was unable to work out the case from what the first defendant said, he must have said that he was innocent, else Tweedledee would have solved the case.

Had the Knight told Tweedledum that 3 had said that 1 was guilty, Tweedledum would have solved the case. He would also have solved the case had the Knight told him that the 2nd had said he was guilty. So the Knight told Tweedledum that either the second had claimed innocence or that the third had said that 1 was innocent.

Humpty Dumpty could not have solved the case if the Knight had told Tweedledum of the second defendant's statement, so the Knight had said (to Tweedledum) that the 3rd had said that 1 was guilty. Therefore the statements at the trial were as follows:

1) I am innocent 2) I am innocent 3) 1 is guilty

This means that 2 is guilty.

  Posted by Iain on 2004-05-12 17:20:05
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