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From: g-rh@cca.UUCP (Richard Harter)
Newsgroups: net.puzzle
Subject: Re: How did they do in the test
Message-ID: <6610@cca.UUCP>
Date: Sun, 9-Mar-86 04:18:15 EST
Article-I.D.: cca.6610
Posted: Sun Mar  9 04:18:15 1986
Date-Received: Sat, 15-Mar-86 20:52:20 EST
References: <> <6490@cca.UUCP> <1432@mhuxt.UUCP> <>
Reply-To: g-rh@cca.UUCP (Richard Harter)
Organization: Computer Corp. of America, Cambridge
Lines: 103
Summary: 

In article <> holmes@dalcs.UUCP (Ray Holmes) writes:
>
> ....... [Sonntag's comments deleted] .....
>
>	Not true see below. However the problem is flawed in another way:
>Flootersnoot lied when he said that all three statements were necessary to
>determine the ordering of the three students.  Statement 2 is NOT necessary.
>Consider that we have only statements 1 and 3 and that they are necessary.
>
>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 necessary (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 necessary (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.
>
	Sorry, this is another logical trap, albeit a good deal more
subtle.  You are correct that case 1 is ruled out.  Now the possible
data cases are:

A:	Wilson and Smith work at the Adelphi book store.
	Wilson and Smith have red hair.
	Jones is the youngest of the three.

B:	Wilson and Jones work at the Adelphi book store.
	Wilson and Jones have red hair.
	Jones is the youngest of the three.

Cases A and B are isomorphic, so we will consider case A only.  The
following table gives the only orderings consistent with each statement,
considered singly:

(1)	Wilson, Smith, Jones
	Wilson, Jones, Smith
	Jones, Wilson, Smith

(2)	Wilson, Smith, Jones
	Wilson, Jones, Smith
	Smith, Wilson, Jones
	Smith, Jones, Wilson

(3)	Wilson, Smith, Jones
	Smith, Wilson, Jones
	Jones, Wilson, Smith

Now consider, any two statements, taken as pairs.  The following table
gives the orderings consistent with each pair of statements:

(1,2)	Wilson, Smith, Jones
	Wilson, Jones, Smith

(1,3)	Wilson, Smith, Jones
	Jones, Wilson, Smith

(2,3)	Wilson, Smith, Jones
	Smith, Wilson, Jones

That is, no pair of statements is sufficient to determine the order;
all three statements are necessary.  Where, then, is the fallacy in
your argument?   You say:

"Wilson must then be either first or second. If Wilson is second then
#3 gives no additional information and is not necessary (if fact both
orderings are possible). Thus Wilson must be first. Now the reasoning
of CASE 1 gives us the same ordering."

Now it is true that if Wilson were known to be second then #3 would
be unnecessary.  However it is not known (from #1) whether Wilson is
first or second.  Given statement 1, #3 contributes the information
that the order (Wilson, Jones, Smith) is not admissable.  Your error
lies in insisting that statement 3 must give information about each
possible placement of Wilson.  However all that is required of 3 is
that it eliminate some of the possible orders implied by #1.

What you are saying is equivalent to this:

Premise 1:	If I had the datum, 'Wilson is second', then statement
		three is not needed.

Premise 2:	Statement three is needed.

Conclusion:	Wilson is not second.

However the correct conclusion is that you do not have the datum,
'Wilson is second', which is, in fact, the case.  I hope this clarifies
the matter.  Tricky little bugger, ain't it.

	Richard Harter, SMDS Inc.