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From: ags@pucc-k (Seaman)
Newsgroups: net.puzzle
Subject: Re: The solution to the S and P puzzle
Message-ID: <119@pucc-k>
Date: Wed, 23-Nov-83 09:58:39 EST
Article-I.D.: pucc-k.119
Posted: Wed Nov 23 09:58:39 1983
Date-Received: Sat, 26-Nov-83 06:25:38 EST
References: <576@alberta.UUCP>
Organization: Purdue University Computing Center
Lines: 18

Sorry, but you blew it.  You said that 23 was one of the possible sums that
S might have, such that P could not determine the sum.  As you already
pointed out, one of the possible products corresponding to 23 is 76.

If I am P, and I see that the product is 76, and if I also know that the
sum is less than 40, then I can immediately conclude that the sum is 23.
How?  Because the only admissible factorization of 76 is 4 * 19, and
4 + 19 = 23.   Note that 2 * 38 = 76 is NOT an admissible factorization
in your version of the puzzle, since the sum is not less than 40.

Therefore, when S announces that P does not know the sum, you can conclude
(since S does not make mistakes) that his sum is NOT 23.  The rest of the
analysis is exactly as I posted earlier, and every word of it is correct.
The only possible sums are 11 and 17, and there is no way for S to
determine the product.

				Dave Seaman
				..!pur-ee!pucc-k!ags