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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.)
tying together two of the several loose ends. | Comment 43 of 52 |
I'm willing to bet, based on all the talk, that the remark about something being not quite right is the hint to us about C's answer containing the unusual character.  Of course, what this means, l don't know...

I actually like Highway6's answer to this as it fits so nicely with the problem title.  Note that the title uses the proper character in the statement.  I'd be happy with this in fact, if only the puzzle were in liars and knights or even tricks.  But its in cryptography, and that combined with the disguised information cannot be coincidental (mistakes do happen here, some even get through the queue and voting process, but if this were the case here, then the author would have posted a correction/apology by now).  What really gets me, is the difficulty 2.  Not that I've ever gotten a crypto problem, even one of simple replacement variety, but there are some pretty impressive algorithms hacked within this community and nobodys even given first thoughts about where the message might be hidden, let alone some attempts at cracking it.

My next level of scrutiny - there is no indication that the police chief made a comment between the 2 in the first paragraph (separated by a semi-colon) and the 2 in the last paragraph (separated by a period).  This is further complicated by the fact that his third statement is compound - it's truth or falseness depends on both C not being a knight AND there being only one correct answer.

But my final suggestion is this.  This is not a liars and knights problem; in fact the whole construct is a red herring.  Lets see if we can move past the block and think outside the box here.

As far as unusual phrases go (which often can lead to good starting points), this problem is quite well put together.  The only thing that sticks out to me is the "(consecutively)" as this seems intended to indicate whether the questions were asked AABBCCDDEE or ABCDEABCDE, but in fact does not.  I suppose that the "interrogators mention[ing] that something about their statements didn't seem quite right" is a little cumbersome as well, several better ways of phrasing this come to mind.
  Posted by Cory Taylor on 2006-03-07 10:54:00
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