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."

Because each is asked only two questions and there is no quota of knaves, knights, and liars, the problem is insoluble.  Any answer can be either true or false without giving anything away or invalidating any individual.
Solution 1: A did it.  A is a liar, B is a knight, C is a knave (true first), D is a liar, E is a knave (false first).
Solution 2:  B did it.  A is a knave (true first), B is a liar, C is a knave (true first), D is a liar, E is a liar.
Solution 3:  C did it.  A is a knave (true first), B is a knave (true first), C is a knave (false first), D is a liar, E is a liar.
Solution 4:  D did it.  A is a knave (true first), B is a knave (true first), C is a knave (true first), D is a knave (true first), E is a liar.
Solution 5:  E did it.  A is a knight, B is a knave (true first), C is a knave (true first), D is a knave (false first), E is a knave (true first).
I'm pretty sure there is nothing in problem inconsistent with ANY of my solutions, thus, the problem is insoluble.
Please refute.

Posted by AvalonXQ on 2006-02-17 04:23:59