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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)

Comments: ( Back to comment list | You must be logged in to post comments.)
Solution re(2): Solution | Comment 6 of 13 |
(In reply to re: Solution by platosadvisor)

I agree -- well, with the ultimate conclusion. Here is the logic I used to arrive at that end.

First, we know there are 8 possible permutations:
III, IIG, IGI, IGG, GGG, GGI, GIG, GII

When the 1st and 3rd defendants disagree in their statements, it means that one of them is lying while the other is telling the truth. Only one person, at most, can tell the truth; therefore, the second defendant must be lying.
IIG, IGG, GGI, GII 
No person is going to say that he is guilty when in fact he is innocent. Therefore, we can eliminate the two permutations above that have the second defendant indicating he is guilty. (If we kept them, and the second defendant is lying, then he would be innocent).
This leaves us with: IIG and GII
In both cases the 2nd defendant is guilty.

However, we still have another category: when the 1st and 3rd defendants agree in their statements. They must then both be lying as no more than 1 person can tell the truth. From this information, we do not know if the 2nd defendant is also lying or is telling the truth.
III, IGI, GIG, GGG
According to the problem, only one defendant is guilty ("who the guilty party was").
III --> 1 & 3 lying, so 1 is guilty
IGI --> 1 & 3 lying, so 1 is guilty
GIG --> 1 & 3 lying, so 2 is guilty
GGG --> 1 & 3 lying, so 2 is guilty

Now, we have 6 permutations (# in parentheses in the guilty defendant)
III (1)
IGI (1)
GIG (2)
GGG (2)
IIG (2)
GII (2)

Tweedledee knew what the 1st defendant said. Based on the above list, if the 1st defendant said he was guilty, then Tweedledee would have known the 2d defendant was the guilty one. Therefore, the 1st defendant must have said he was innocent. III (1), IGI (1), IIG (2)

Tweedledum did not know of his twin's efforts, so he was also working with the 6 permutations. If he was told the 2nd defendant said innocent III (1), GIG (2), IIG (2), GII (2) he would have been confused. If he was told the 2nd defendant said guilty IGI (1), GGG (2), he would also have been confused. If he was told the 3rd defendant said innocent III (1), IGI (1), GII (2) he would have been confused. Finally, if he was told the 3rd defendant said guilty GIG (2), GGG (2), IIG (2) he would have known the 2nd defendant was guilty. Therefore, he was not told that the 3rd defendant said guilty.

Humpty-dumpty knows about both twins' efforts. Thanks to Tweedledee, the six permutations are now reduced to 3 III (1), IGI (1), IIG (2). Based on Tweedledum's efforts, we know that the third defendant could not have been guilty, so we are now reduced to 2 permutations III (1), IGI (1). It doesn't matter which were the actual statements because both result in the 1st defendant being guilty.

The statement must have been III using logic from the beginning: no innocent defendant is going to lie and say he is guilty (IGI).

  Posted by alexandra thomas on 2004-06-04 23:49:34

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