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."

1. The Police chief is not a knight (Proof: His first two statements are contradictory: "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.") The implications of this are that at least one of his two statements at the end is a lie: "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." If the Police chief is a truth-first knave, he will likely be back at some point other than 24 hours*, but his hints are true. If the chief is a lie-first knave, you will have another shot at the test a year from now (I don't think that gives us any extra information) and we do have 24 hours to think about it, which is an awfully long time, but the hints are false, which translates to: "C is a knight or all answers are incorrect or there is more than one correct answer" (regardless of whether "answers" is interpreted to be the answers of the suspects or the answer to the test. If the police chief is a liar, the same applies.

2. This problem is listed under Cryptography. The implications of this have yet to be determined.

3. C's second response is 'l don't know' as in the lowercase letter L don't know. The implications of this have yet to be determined.

4. The suspects each heard each other's response. This has been taken into account in AvalonXQ's answer, although the other factors listed above don't seem to be taken into account which makes me think it is at best only partially correct.

For 3, what about the idea that the 'l' corresponds to Liars? As in the Liars don't know who the bank robber is?

Another thought: if the police chief is not necessarily a knight, are the stipulations of the problem in the bullet points all true? Also, can we suspect the police chief himself, or the general possibility that the bank robber is not one of the questioned suspects?

Has anyone taken into account anything to do with letters or codes in the puzzle? Especially given the random 'l' in C's answer. "EAlEA' doesn't seem to mean anything...

* NOTE: after typing this, I realized that the lie interpretation of the chief's last statement could be taken to mean that the police chief will return in 24 hours, but NOT to ask who robbed the bank! So it could be that we have been attempting to answer the wrong question all along!

Posted by Avin on 2006-02-21 15:20:48