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."

The key statement is that evidence supported the perpertrator acted alone.  As such, only the bank robber would know who committed the crime.

A can not be a Knight because he claimed to know who did it, therefore he is a Knave or Liar.  

B can not be a Knight because he claimed to know who did it, therefore he is a Knave or Liar.  Since B is not a Knight, A can not be a Liar.  A must then be a Knave.  B must then be a Liar and the bank robber, or a Knave.

As a Liar, A's second statement must be a lie Thus, E would not the bank robber. E would then be a Knave or a Liar.  As he claims to know who did it, he can not be a Knight or even a Knave.  As a Knave he would have to have lied first, because he has been eliminated as the bank robber.  But he could not be telling the truth by identifying anyone else, therefore he would be a Liar.  And thus, A could not be the bank robber.  And B, therefore would be a Liar.

As a Knave, A can not be the bank robber as that would make B a Knight, which he can not be.  Therefore his second statement is a lie and the same observations are true as he had been found to be a Liar -- except that he is Knave and not the bank robber. 

D claimed to know who did it, therefore he is either a Knave or Liar or the bank robber as a Knight.  Because this is his second statement, if he were a Knave his first statement must be true, and he is the bank robber.  If he were a Liar, then his first statement is false, which means someone else is the bank robber, which can only be at this juncture, B or C.

C is given to not be a Knight, therefore he is either a Liar or Knave.  If C is the bank robber, then his first statement is a lie.  If he were a Knave his second statement would be the truth.  As one othe suspects -- A, B, C, D, E -- is given to have robbed the bank, the statement that "l don't know" ("ell don't know) must be a the truth.  As C can not know that "l knows" as the perpatrator acted alone.  Therefore C is a liar and must be the bank robber.

Earlier E was eliminated as the bank robber.  D can not be a Knight as he stated that E did it.

Hmm...I almost forgot the is a not a Logic puzzle but a Cryptography puzzle....I'll have to look further.  

Edited on May 8, 2006, 8:32 pm

Posted by Dej Mar on 2006-05-08 11:26:52