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From: jkenton@pinocchio.encore.com (Jeff Kenton)
Newsgroups: comp.databases,rec.puzzles
Subject: Re: SQL puzzle
Message-ID: <12518@encore.Encore.COM>
Date: 17 Aug 90 15:01:15 GMT
References: <125@guug.guug.de>
Sender: news@Encore.COM
Followup-To: comp.databases
Lines: 47

From article <125@guug.guug.de>, by greil@guug.guug.de (Anton Greil):
> 
> Can you solve the following puzzle by SQL?
> 
> "Here is an arithmetical problem which is belonging to the  great
> classics.   Two  natural  numbers were selected which are greater
> than 1 and less than 100. The sum of these two numbers  was  told
> Mr. S, the product of the numbers was told Mr. P.
> 
> Each of the two men doesn't know the number of the other.  Mr.  P
> rings up Mr. S:
> 
> P: I can't find the two numbers.
> S: I knew, that you would not succeed.
> P: Oh ... But now, I know them!
> S: In this case, I know them too."
> 


The two numbers are 3 and 14.  Solved by following the clues:

> P: I can't find the two numbers.

Therefore, the PRODUCT has at least 3 prime factors, all less than 50.

> S: I knew, that you would not succeed.

Therefore, all decompositions of the SUM into two numbers must produce
a product which satisfies the condition above.  This leaves 11, 17, 23,
27, 29, 35, 41, 47 and 51.

> P: Oh ... But now, I know them!

Therefore, of all the factorings of the PRODUCT into two numbers, in
only one case is the sum of those numbers in the list above.

> S: In this case, I know them too."

Therefore, of all decompositions of the SUM into two numbers exactly one
produces a product which, when factored into pairs of numbers, has only
one of those pairs whose sum is in the list above.  Only the sum 17
satisfies this last condition (with the pair 4 + 13).

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      jeff kenton  ---	temporarily at jkenton@pinocchio.encore.com	 
		   ---  always at (617) 894-4508  ---
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