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From: rmd@ccieng5.UUCP (James Walter Reid)
Newsgroups: net.puzzle
Subject: numbers game
Message-ID: <497@ccieng5.UUCP>
Date: Thu, 12-Jul-84 17:16:30 EDT
Article-I.D.: ccieng5.497
Posted: Thu Jul 12 17:16:30 1984
Date-Received: Sat, 14-Jul-84 01:08:34 EDT
Organization: CCI Central Engineering, Rochester, NY
Lines: 23


<   for the line demon >

This interesting puzzle was posed to me in India.  It took quite some
time to solve it.  Here it is:

Some one gives the product and sum of two integers between 2 and 100
(both inclusive), one each, to two mathematicians MP and MS.
MP knows only the product and MS knows only the sum.
You do not know the two numbers, the sum or the product.
A conversation ensues between the mathematicians which you overhear:

MP mutters:    I do not know the two numbers.

MS counters:   I know that you know the two numbers.

MP chirups:   Is that so?  Well, in that case I know the two numbers.

In closing MS adds:  Now even I know the two numbers.

Both the mathematicians walk of in different directions.  Given the above
conversation, can you guess the two numbers?  Try and PROVE your answer and
its uniqueness if it is unique.