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From: luke@uicsgva.UUCP
Newsgroups: comp.ai.digest
Subject: Re: mr. s & mr. p
Message-ID: <1200004@uicsgva>
Date: Wed, 19-Aug-87 19:27:00 EDT
Article-I.D.: uicsgva.1200004
Posted: Wed Aug 19 19:27:00 1987
Date-Received: Tue, 25-Aug-87 00:47:58 EDT
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	     I definitely saw  this  problem  in  the  "Mathematical
	Games"  section of Scientific American some years ago.  I am
	not sure which issue it appeared in, but I am positive  that
	it came out between 1979 and 1982.  I am 90% certain that it
	can be found in the range of January 1980 to December  1981.
	My first guess would be the October 1980 issue.  The article
	says that the problem made its debut at  a  party  primarily
	attended by mathematicians. I don't remember all the details
	of the problem, but here is what I do remember:
	
	     Mr. P and Mr. S are experienced mathematicians. X and Y
	are  two different positive integers (For the benefit of the
	reader, it has been disclosed that both X  and  Y  are  less
	than  or  equal  to  20.   This constraint, however, is sup-
	posedly unnecessary.) The sum of X and Y has been  disclosed
	to  Mr.  S  and the product of X and Y has been disclosed to
	Mr. P.  Neither man knows the value of X or Y, nor are  they
	allowed  to  tell  the  other  what their sum or product is.
	They are allowed to talk to each other over the  phone,  and
	do  so  after  sufficient time to think about what the other
	has said.  The dialogue, as far as I remember is as follows:
	
Mr P to Mr S:   I can't tell from the product what X and Y are.
(later....)
Mr S to Mr P:   I can't tell what they are either.
(later....)
Mr P to Mr S:   I still can't tell what X and Y are.

   At this point, my memory fails me.  But this is the earliest point
   that I could feel comfortable with the following dialogue.  I'm
   pretty sure that these guys start knowing something within two more
   bounces.

Mr ?? to Mr ??:   Now I know what X and Y are.
(later)
Mr ?? to Mr ??:   In that case, I know what X and Y are too!

	According to Scientific American, the answer is 4 and 13.
	If anyone finds the article, I would also like to  know  the
	reference.

					- Luke Young
					  Computer Systems Group
					  University of Illinois


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