ou are a logician in training for the police, and the time has come to take the certification test. The police chief brings you the test one morning, and says, "I must warn you, this is your only chance at the certification test; If you fail, you must keep training for another year before you can take it again."
           
- Five suspects were interrogated for a bank robbery.
             
- Each suspect was either a knight, a knave, or a liar.
         
- Knights always tell the truth.
       
- Liars always lie.
       
- Knaves strictly alternate truths and lies with each statement.
                   
- Police have evidence that suggests the perpetrator acted alone.
                   
- Police have evidence that suggests the perpetrator acted alone.

>During the interrogation, two questions were asked (consecutively) of each of the five suspects. Each suspect heard the other suspects' responses, and none of them made a statement between his or her two answers. Here are the two questions and their responses.

"Did you rob the bank?"
A: No.
B: No.
C: No.
D: Yes.
E: Yes.

"Who robbed the bank?"
A: E.
B: A.
C: l don't know.
D: E.
E: A.

The interrogators mentioned that something about their statements didn't seem quite right. The police chief adds, "The only hints I can give you are that C is not a knight and that there is only one correct answer. I'll be back in 24 hours to ask you who robbed the bank."

First, this is Liars/Knights/Knaves world, where anyone can be a Liar/Knight/Knave, including the Police Chief.

Second, remember the two questions were asked consecutively of each suspect. That means that everyone else heard A say he didn't do it and say E did et cetera.

Third, a Liars/Knights/Knaves can not make a statement they are unsure of. That is, anyone who can make a claim as to someone's guilt has to know who did it weather they tell the truth or not.

I'm going to claim that the chief's statement "The only hints I can give you are that C is not a knight and that there is only one correct answer." is a lie since there seems to be more than one answer if we assume C is not a knight. So what if C is a knight?

Then C didn't do it and hasn't been able to deduce who did it from hearing A and B's answers. If C knew A or B was a Knight, he would know the culprit. If C knew A or B was a Liar, he'd also know. So A and B are both Knaves, specifically TF Knaves presuming C knows their classification. This would lead C to exclude all but D from suspicion. So why didn't C accuse D of the crime? Perhaps because the robber may have been none of the above or C is just too slow to have figured it out. Perhaps this is what led to the confusion amoungst the Police. Ahhh, but wait! Only the Police have the information that the robber acted alone. So C could know that A and B are Knaves and think possibly A, B and E collaborated in the crime. This could lead to C's uncertainty and imply D to the Police. Of course if D being the culprit is the unique solution it doesn't diminish the Chief's lie. Only one part of an 'and' statement has to be a lie to make a statement false.

But even if the chief's statement is a lie, it doesn't guarantee that C is a Knight. There could simply be more than one correct answer.

So let's say the Police Chief is a Knight. It sure seems as though there are multiple solutions, but how could A know who did it before speaking unless he knew he did it himself? I guess he could be a witness or something. If A is guilty from this logic I think this is a poorly constructed problem.

...and in regard to the Cryptography categorization, I'd be super impressed to see someone pull out an encryption from this puzzle.

Posted by Eric on 2006-02-18 21:41:35