Relay-Version: version B 2.10 5/3/83; site utzoo.UUCP
Path: utzoo!dciem!ntt
From: ntt@dciem.UUCP
Newsgroups: net.math
Subject: Re: SPOILER (solution) for the Sum/Product problem parse date string
Message-ID: <258@dciem.UUCP>
Date: Thu, 28-Jul-83 11:09:42 EDT
Article-I.D.: dciem.258
Posted: Thu Jul 28 11:09:42 1983
Date-Received: Thu, 28-Jul-83 16:10:47 EDT
References: uwvax.937
Lines: 34

Repeating the problem statement again:

--------------------------------------------

   I have picked two integers between 3 and 100 (inclusive),
   and given their sum to Sally and their product to Paul,
   both very clever mathematicians.

   After suitable time for thought, Sally says to Paul:
   "It is impossible for you to figure out my sum."

   After more time for thought, Paul replies:
   "I have figured out your sum."

   After still more thought, Sally says:
   "I have figured out your product."

   What are the two numbers?

--------------------------------------------

This was printed in Martin Gardner's Mathematical Games in the December 1979
Sci.Am., but with the upper bound changed to 20.  A solution was given in the
same column as 4 and 13.  In March 1980, MG printed a correction to the effect
that since the two mathematicians use the upper bound in their computations,
the solution is not independent of it; 4 and 13, he said, is correct for an
upper bound of 100, which is how the problem was originally proposed, while
there is no solution for an upper bound of 20.  In May 1980 he gave solutions
for various other upper bounds.
   According to the March column, the problem was originally proposed by one
David J. Sproule in Mathematics Magazine, March 1976 (vol 49 #2), page 96,
and a correct solution printed there, November 1977 (vol 50 #5), page 268.

                                       Mark Brader, NTT Systems Inc.