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."

This entire problem is filled with correct punctuation, spelling, and capitilization.. except for a few places.....   those few places might mean something.


"Each suspect was either a knight, a knave, or a liar"

When "either" is used as a conjunction, in proper english, it needs 'or' to separate the elements... even if there is more than 2 elements.
So.. this could mean.... each suspect was
    a) a knight/ a knave  
or b) a liar.

Which might mean, if a suspect is not lying, then for his first statement he is a knight, and for his second statement, he reverts to being a knave.  
This does not imply if a suspect is not a liar, then he is a truth-first knave.. becasue both statments could be true and he could still be a knight/knave.
This does however imply that, if a suspect is not a liar, his first statment must be true.

The l thing

Every statement in this problem is a sentence, in that they each end with a period and start with a capital letter. Even the bullet items and the responses have periods at the end and start with capital letters.
All except one... the L thing.
If it were a accidental typo..  it would be a capital L, not a lowercase l. It is meant to, at first glance, come off as a capital I, in that its very obviously not a lowercase i. 
Therefore.. i think we have to assume this is no accident.
Also.. if you put the entire thing in MS Word... you can see that it is in fact a lowercase l and not the number 1, and for sure not some I in another font.

what all this means.. I have no clue.

"The only hints I can I can give you are that C is not a knight and that there is only one correct answer....."

One interpretation of this that has not been discussed yet, I dont think, is that the chief means "There is only 1 correct response( answer from suspect)"  Which would mean the chief is telling the testtaker that there is in fact 4 liars, no knights, and one knave.

Of course.. if this were true.. his two statements would be redundant in that he wouldnt have to tell us there were no knights.

Which is all fine and dandy.. but following that logic.. if only 1 of the 10 statements can be a truth..  that leads to two criminals B&C....   which, goes against what the evidence suggests.

Lastly
"two questions were asked (consecutively) of each of the five suspects"

Whoever mentioned earlier that the questions were actually asked AA  BB  CC  DD  EE, I believe is right.
Consecutively means "one after another, without interruption"
it says the "two questions were asked consecutively"....  not "the five suspects were consecutively asked two questions"
Consecutive is worded as such to describe the sets of two questions, not the suspects.

Again though... i dont know what this proves.


Blahh.. i'm starting to not like this problem any more.

Edited on March 7, 2006, 4:01 pm

Posted by Highway6 on 2006-03-07 15:08:18