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From: lhl@lanl.ARPA
Newsgroups: net.puzzle
Subject: Re: Who is the thief?
Message-ID: <23874@lanl.ARPA>
Date: Fri, 29-Mar-85 10:24:44 EST
Article-I.D.: lanl.23874
Posted: Fri Mar 29 10:24:44 1985
Date-Received: Tue, 2-Apr-85 00:18:50 EST
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Organization: Los Alamos National Laboratory
Lines: 50

> 
> 
> Get out your graph paper and try this one:
> 
> One of the six students A, B, C, D, E, F stole a book from the library
> last Monday night.  Each student is questioned about whom they saw
> at the library, and all tell the truth except the thief (it is possible
> one student saw another without in turn being observed, but we assume
> that one must have seen the other if both were there at the same time).
> A saw B and E; B saw A and F; C saw D and F; D saw A and F; 
> E saw B and C; and F saw C and E.  Who is the thief?
> 
> 
> This is taken from APPLIED COMBINATORICS by Alan Tucker (page 215).
> I highly recommend this text for anyone interested in combinatorics.
> 
> 
> Have Fun,
> 
> Tom Hill

  Since our mailer doesn't recognize the return address, and there
has been no answer posted, I'll broadcast mine.

  Suppose A and F were not in the library at the same time.  Then
a) if B and D are truthful, they were both there in the interval;
but neither saw the other.
b) if B only lied, then D and E were there in the interval.
c) if D only lied, then B and E were there in the interval.

  By contradiction, A and F were there at the same time, and one of
them is lying.
If it is F, then A and C were both present in the interval between
D and E, but neither saw the other.

  Therefore A is the liar.

  The sequence could have been as follows:

A, B, E, and F arrive in any order (A sees F).

B leaves.

C arrives (A sees C).

E leaves.

D arrives.

A, C, D, and F leave in any order but perhaps A last, with book.