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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.)
Solution A different approach and solution | Comment 38 of 52 |

I don't think anyone tried this line of reasoning yet, forgive me if I'm repeating.

Perhaps the thing that is wrong about the statements is that they are grouped in the wrong order.  Why would the interrogators ask question #1 to each of the five suspects, then go back and ask question #2?  It is more likely that the interrogation went in this order:

"Did you rob the bank?" A: No
"Who robbed the bank?"  A: E
"Did you rob the bank?" B: No
"Who robbed the bank?"  B: A
"Did you rob the bank?" C: No
"Who robbed the bank?"  C: I don't know.

OK, I'm going to stop there.  Assuming the police were telling the truth, C is not a knight and at least one of his statements is false.  His second answer, "I don't know," can't be TRUE because then his first statement "No" would have to be FALSE.  This causes a contradiction - he can't have been the robber and then truthfully say he doesn't know who the robber is.  Therefore he must be lying when he says he doesn't know.  So C knows who the robber is.

Assuming that he has only heard the statements of the first two suspects at this point, there would be no way for him to logically deduce who the robber was from their answers.  Therefore, the only way he could know who the robber was is if he was the robber.

For the sake of completeness:
A is a truth-first knave.
B is a truth-first knave.
C is a liar.
D is a liar.
E is a liar.


  Posted by tomarken on 2006-03-01 11:03:29
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