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Path: utzoo!linus!decvax!mcnc!duke!bek
From: bek@duke.UUCP (Barrett E. Koster)
Newsgroups: net.math
Subject: sum product puzzle
Message-ID: <4546@duke.UUCP>
Date: Tue, 24-Jul-84 15:17:53 EDT
Article-I.D.: duke.4546
Posted: Tue Jul 24 15:17:53 1984
Date-Received: Fri, 27-Jul-84 02:12:22 EDT
Organization: Duke University
Lines: 20

I have a puzzle (an old unsolved favorite of mine) which was
rumored to have been discussed recently here.  I don't mean
to restart the discussion, but my news log doesn't go back far
enough to find it, and I would like very much to see a solution.
(If the puzzle is not in fact old to this group, then you all
can just take a crack at it now.)
 
Person A thinks of two integers between (but not including) 1 and
100.  A hands the sum of the two numbers to a person we shall
call S, and the Product to a person we shall call P.  The following
conversation takes place:
S: I don't know what the numbers are.
P: I don't know what the numbers are, either.
S: I knew you didn't know.
P: Oh, well, in that case, I DO know what they are.
S: In that case, so do I.

The question is, what were the two numbers?

Barry Koster      duke!bek