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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 re: Reply to AvalonXQ | Comment 34 of 52 |
(In reply to No Subject by AvalonXQ)

AvalonXQ: "Of the ten answers to questions listed, only one of them is correct."

Good point !

If "there is only one correct answer" means "only one of the ten answers given by the suspects A through E is correct", then they must consist of four liars and one knave. The only possibility I see then is the one already posted by AvalonXQ:

B and C robbed the bank together.

A is a knave:
  "I didn't rob the bank" = True
  "E robbed the bank" = False
B is a liar:
  "I didn't rob the bank" = False
  "A robbed the bank" = False
C is a liar:
  "I didn't rob the bank" = False
  "I don't know who robbed the bank" = False
D is a liar:
  "I robbed the bank" = False
  "E robbed the bank" = False
E is a liar:
  "I robbed the bank" = False
  "A robbed the bank" = False

["Police have evidence that suggests the perpetrator acted alone" was not a strong enough statement to preclude the possibility of more than one bank robber.]

 

 

 

 

Edited on February 19, 2006, 4:29 pm
  Posted by Penny on 2006-02-19 16:22:24

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