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."
What we can quickly see, if the police chiefs two hints at the end are both true:
C is a knave (if he is a liar, then he doesn't know himself (unless
this is the catch - maybe he's got multiple personality disorder?) and
he can't be a knight based on the police chief)
D and E are not knights, as their comments cannot be consistently true.
Where I went with this (K=Knight, N1=Truth first Knave, L=Liar):
I assumed A was a knight and tried to find a contracdiction, which led me to A,B,C,D,E= K,N1,N1,N2,L* so I had one solution.
Then I assumed B was a knight and tried to find a contracdiction, which
led me to A,B,C,D,E=L*,K,N1,L,N2, so I had another solution.
I stopped here and tried to eliminate one of the solutions, but
couldn't. There may be (many) more working combinations as these
are the only two configurations I tried. There must be some other
limitation, and some possibolities I see are:
While "Police have evidence that suggests the perpetrator acted alone", maybe this is wrong.
Maybe the police chief is not a Knight and one or two of his hints are not true.
What I have no idea what to do with:
Something important presumably comes from the interrogators opinion of the remarks.
There is no requirement of course that the perpetrator is among A-E,
but assuming either A or B is a Knight requires this anyways.
Thats where I'm at
Immediate Knowledge
