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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: <6490@cca.UUCP>
Date: Sun, 2-Mar-86 16:56:13 EST
Article-I.D.: cca.6490
Posted: Sun Mar  2 16:56:13 1986
Date-Received: Tue, 4-Mar-86 02:18:24 EST
References: <>
Reply-To: g-rh@cca.UUCP (Richard Harter)
Organization: Computer Corp. of America, Cambridge
Lines: 104
Summary: 

[------- The statement in this line is provably false ------]

	Here is the solution to the student placement puzzle.
I was a little disappointed that no one posted a solution.  This
is, in my opinion, the most elegant logic puzzle ever created.
Here is the puzzle restated:
  
] 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.
] 
] (2)	If I loathe pepperoni pizza, then the person who placed first
] 	has red hair.
] 
] (3)	If either Jones or Smith is second, then Smith finished ahead
] 	of the youngest of the three.
] 
] Being the sly old dog that he is, Flootersnoot ommitted the relevant
] data.  He was, however, kind enough to reassure me that the problem
] was well posed.  That is, given the relevant data, all three of the
] above statements are necessary and sufficient for determining the
] order in which the three students placed.  Knowing this, I was able
] to reconstruct the missing data and the order in which they placed.
] 
] In what order did the three students place?
] Who works at the Adelphi bookstore?
] Who has red hair?
] Who is the youngest of the three?
] Do I loathe pepperoni pizza?

(a) First consider statement two.  Since Professor Flootersnoot posed
the puzzle, the "I" of statement two is Flootersnoot.  If he does not
loathe pepperoni pizza then statement two contributes no information
and therefore is not needed.  Therefore:

   (1)	Flootersnoot loathes pepperoni pizza.
   (2)  The person who placed first has red hair.

Since the "I" in the question "Do I loathe peppperoni pizza?" refers
to me (Richard Harter) the answer to the question is "insufficient
information".  As a matter of record, I adore pepperoni pizza and
loathe anchovy pizza -- Flootersnoot is perverted.

(b) Now consider statement one.  The wording of the statement implies
that Wilson and at least one other student works at the Adelphi book
store.  If both worked there then statements one and three together
would be sufficient to determine the order of placement and statement
two would not be needed.  Hence:

   (3)	Either Jones or Smith, but not both, works at the Adelphi
	bookstore.  This implies that Wilson did not finish last.

(c) Now consider statement three.  If Smith is the youngest of the
three then statement three can be true only is Wilson is second.
Since the other worker at the Adelphi finishes after Wilson statements
one and three (together with the data) would uniquely specify the
order of placement.  Hence:

   (4)	Smith is not the youngest of the three.

(d) Now consider statement two.  If all three have red hair then the
statement contributes no information.  Hence at least one of the three
does not have red hair.  If only Wilson has red hair then statement
one is not needed.  If Wilson does not have red hair then Wilson is
not first and, hence, from statement one and (3) must be second.
It follows that statements one and two alone would be sufficient
to determine the order.  Hence:

   (5)	Wilson and one other person has red hair.

(e) Now consider statements one and two together with what we know
so far.  Wilson and one other person, call him X, have red hair.
There is a person, call him Y, who does not work at the Adelphi
bookstore.  From one, either Wilson or Y is first.  From two,
either Wilson or X is first.  If X and Y are the same person then
statement two is not needed.  Hence X and Y are different people.
It follows that neither X nor Y can be first, i.e. Wilson finished
first.  From statement three we conclude that:

   (6) Wilson finished first, Smith finished second, and Jones third.
   (7) Jones is the youngest of the three.

(f) Finally, who has red hair?  A careful check of the possible
cases shows that the given information in the puzzle is insufficient
to determine uniquely who has red hair.  However we can state that:


   (8)	Either Jones but not Smith has red hair and works at the
	Adelphi bookstore or Smith but not Jones has red hair and
	works at the Adelphi bookstore.

[Note: This problem was given in "Problems Omnibus" by Hubert Philips
(Caliban), an English puzzle writer, ARCO publications, London, 1960.
The current presentation is a rewording of "Caliban's Will" by
H. M. Newman.  The solution given there has an error which is equivalent
to asserting that Jones has red hair.]

Now that's what I call a real puzzle.

	Richard Harter, SMDS Inc.