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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.)
re(3): Insoluble | Comment 18 of 52 |
(In reply to re(2): Insoluble by Penny)

"There is only one correct answer" is another example of a meaningless addition.  I could use that to add in whatever additional condition I want to make whatever solution I want be the "correct" one.
And I'm still unwilling to make the unwarranted assumption that "I don't know" is precisely equivalent to "I didn't rob the bank".  It could be, for instance, that C knows B is a liar, so when B says, "No," to the first question, C knows that B did it.  The point is we don't know, and you can make up additional conditions all day, but that won't make the problem itself any less insoluble.
  Posted by AvalonXQ on 2006-02-17 17:07:28

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