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I don't know. (Posted on 2006-02-16) Difficulty: 2 of 5
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."

No Solution Yet Submitted by Dustin    
Rating: 3.3333 (6 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
Another tack.. | Comment 20 of 52 |
Not sure  what to think about the problem category, but maybe it is important.

From AvalonXQ and others, there are five valid solutions, 1 each for A-E. 
For A, B, D, or E to be guilty, C MUST be  a truth first Knave (C can never be a liar first Knave, since that is inconsistent with his statements).

If A, B, D, or E is guilty, then it MUST follow that C KNOWS who is guilty, since his second statment must be a lie ( not sure I saw this  stated before - thx Vernon)
 
If C is guilty, he must be a liar (stated before).

If C knows who is guilty, then is he indeed involved? Not sure.

Assume that 2 suspects are guilty (the evidence only "suggests' one, it is not "certain") Also assume ( I am new to Liars and Kinghts, so help me here) that a partial truth is not a "truth"(?).

Taking this all in and analyzing, C&A cannot be guilty together due to partial truths from E and B.  C&B could be guilty, C alone could be guilty,  C&D could be guilty, C&E could not due to partial truths from A & D.  Next??

OR

Could one analyze how a Knave might decide to be lie-first or truth-first, based on what he heard from those speaking before him?  That is a conspicuous part of the problem - that they all heard each other's statements in order.



Edited on February 17, 2006, 5:42 pm
  Posted by Kenny M on 2006-02-17 17:40:09

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