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."

Possible correct answer (stated before), but with correct(?) logic

You are a logician, so no unstated assumptions, and words/sentences need to be taken literally, or conjectures must be proven with facts at hand

1) C cannot be a Knight - so at least one of his statements is false. 2) C cannot be a F-first knave - then his statements are inconsistent. 3) C can therefore be a T-first Knave or a Liar.

Assume C is a T-first Knave - then valid solutions exist for any of the others being the crook.  And, C knows who that crook is (so what?).  Multiple answers violates the "one solution" clause.  Additioanlly, each hearing the other's statments does not eliminate any of these possibilities.  So, conlcude that C cannot be  T-first knave.

Therefore, C is a Liar, and he did it.  Also, for the C=Liar solution, all the suspects tell at least one lie.  Thefore, that is the "something is not right" bit that the interregaotrs noticed - they have good instincts.

Edited on March 2, 2006, 6:15 pm

Posted by Kenny M on 2006-03-02 18:15:17