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        riddles >> hard >> mentally disordered criminals
        
(Message started by: antkor on Dec 14^th, 2013, 3:14pm)

Title: mentally disordered criminals
Post by antkor on Dec 14^th, 2013, 3:14pm

The warden of a prison for mentally disordered criminals invited Sherlock Holmes and Dr. Watson to his prison to solve a difficult case.
He informs our two friends that his prison is inhabited only by mentally disordered criminals and doctors. But it seems that something wrong goes on. The criminals behave like doctors and vice versa. All inhabitants have invented and agreed upon following the rules below.
A. Some people have become ''masters'' of the remaining. Everyone has at least one ''master''.
B. Nobody becomes a person's master if he does not believe that this person trusts himself.
C. There is somebody that trusts all the criminals but trusts none of the doctors.
D. For any given person X exists a person Y that trusts only the ones that have a ''master'' that X trusts. (meaning that if a person Z has at least one master that X trusts, then Y trusts Z, otherwise if X trusts none of Z's ''masters'', then Y does not trust Z)
E. Each person either trusts or does not trust somebody else.
F. A non- mentally disordered person understands the trust relations of everyone else as they are, whereas a mentally disordered person understands the trust relations of everybody else in the opposite way.

Watson: So Sherlock this is indeed a strange case, ain't it? How are you gonna solve it?
Sherlock: Elementary my dear Watson. It is obvious that either a criminal is not really mentally disordered or that a doctor is mentally disordered himself!

How did Sherlock draw this conclusion?

Title: Re: mentally disordered criminals
Post by Grimbal on Dec 14^th, 2013, 4:55pm

C and E imply that there are either only criminals or only doctors.

Title: Re: mentally disordered criminals
Post by antkor on Dec 14^th, 2013, 7:02pm

on 12/14/13 at 16:55:27, Grimbal wrote:

C and E imply that there are either only criminals or only doctors.

Sorry, maybe i wrote it the wrong way. What E implies is that every person inside the prison either trusts somebody or does not trust him. And that goes on for every inhabitant of the prison. As far as I am concerned, E is there to eliminate neutral behavior towards others.

Title: Re: mentally disordered criminals
Post by antkor on Feb 13^th, 2014, 1:48am

anyone who wants to try this one before i give the solution?

Title: Re: mentally disordered criminals
Post by Dao007forever on Mar 2^nd, 2014, 8:15pm

A, B, C, E, and F seems to be enough.

Assume all doctors are mentally sound and all criminals are mentally disordered.

Take the member Z in (C). Z's master can't be a doctor, since Z doesn't trust doctors, and so, the doctors believe Z doesn't trust them. Z's master can't be a criminal either, since Z trust criminals, and so, the criminals believe Z doesn't trust them.

Title: Re: mentally disordered criminals
Post by antkor on Mar 7^th, 2014, 3:43am

I think you misunderstood instruction B. As I read it (and mean it), if I am A and you're B, in order for me to become your master (or anybody else's), I must think you trust yourself, not me necessarilly. Also, no instruction is given by chance, all of them are needed to solve the problem (because you ommit D).
on 03/02/14 at 20:15:21, Dao007forever wrote: