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From: holmes@dalcs.UUCP (Ray Holmes)
Newsgroups: net.puzzle
Subject: Re: How did they do in the test
Message-ID: <1625@dalcs.UUCP>
Date: Sat, 8-Mar-86 12:48:15 EST
Article-I.D.: dalcs.1625
Posted: Sat Mar  8 12:48:15 1986
Date-Received: Sat, 8-Mar-86 19:03:51 EST
References: <> <6490@cca.UUCP> <1432@mhuxt.UUCP>
Organization: Dalhousie University, Halifax, N.S., Canada
Lines: 43

> > ] My old friend, Professor Flootersnoot at Arkham University, has three
> > ] prize students in his Creative Ontology class, Jones, Smith, and Wilson.
> > ] Recently he sent me a small puzzle about how they placed in a recent
> > ] exam.  The puzzle consisted of three statements:
> > ] 
> > ] (1)	No other employee of the Adelphi bookstore placed ahead of
> > ] 	Wilson.
> 
>    Note that this statement does *not* imply that more than one of
> Flootersnoot's prize students work for the Adelphi bookstore, as asserted
> by whoever posted the 'solution' to this problem.  
> -- 
> Jeff Sonntag
> ihnp4!mhuxt!js2j

	Not true see below. However the problem is flawed in another way:
Flootersnoot lied when he said that all three statements were necessairy to
determine the ordering of the three students.  Statement 2 is NOT necessairy.
Consider that we have only statements 1 and 3 and that they are necessairy.

Consider statement 1:
	If Wilson is the only one of the three that works at Adelphi then
this statement contains no information at all about the relative ordering
of the three students and is not necessairy (also there is not a unique
solution).  Thus Wilson plus one or both of the others works at Adelphi.

CASE 1: All three work at Adelphi.
	From #1, Wilson must be first, thus Jones and Smith must be second
	and third. #3 then inplies that Smith finished ahead of the youngest
	of the three. Thus the only possible ordering of the three is:

	Wilson 1st, Smith 2nd, and Jones 3rd.

CASE 2: Wilson and one other work at Adelphi's.
	Wilson must then be either first or second. If Wilson is second then
	#3 gives no additional information and is not necessairy (if fact
	both orderings are possible). Thus Wilson must be first. Now the
	reasoning of CASE 1 gives us the same ordering.

Hence, in any case, we get the correct ordering without ever considering
statement #2.

				Ray