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From: al@mot.UUCP (Al Filipski)
Newsgroups: net.puzzle
Subject: metapuzzle
Message-ID: <139@mot.UUCP>
Date: Fri, 12-Apr-85 23:26:53 EST
Article-I.D.: mot.139
Posted: Fri Apr 12 23:26:53 1985
Date-Received: Thu, 18-Apr-85 04:28:12 EST
Organization: Motorola Microsystems, Phoenix AZ
Lines: 33


Can someone help me reconstruct this puzzle? I have never seen it 
in print; the fellow I heard it from (a couple of years ago) 
cannot remember it exactly either, but thinks it might have come 
from some magazine for mathematics teachers.  (In a sense this is 
a second order puzzle or metapuzzle, since the puzzle is to reconstruct 
the puzzle)

It goes something like this:  It involves two logicians and a third 
party.  The third party chooses two integers (I don't remember if the 
range of the integers was restricted) and tells the first
logician the sum of the numbers and the second logician the product
of the numbers. Say the logicians' names are Athol and Elba.  Then
the following conversation ensues:

	Athol: I can't tell what the numbers are.
	Elba: I can't tell what the numbers are.
	Athol: Now I know what the numbers are.
	Elba: Now I know what the numbers are.

From this it is possible to deduce the two numbers.
I don't remember which of the above logicians was the one that knew 
the sum. (No remarks about my not knowing my Athol from my Elba).
Does anyone know the source or correct version of the above or any
similar puzzle?

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Alan Filipski, UNIX group, Motorola Microsystems, Tempe, AZ U.S.A
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