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        riddles >> hard >> New Puzzle: P and S
        
(Message started by: Garzahd on Dec 10^th, 2002, 5:17pm)

Title: New Puzzle: P and S
Post by Garzahd on Dec 10^th, 2002, 5:17pm

Two mathematicians, Mr. P and Mr. S, are trying to identify two integers. Both know that the integers are greater than one and less than 100. P knows their product and S knows their sum.

They have a little conversation:

P: I don't know what the two numbers are.
S: I knew that you didn't know. But I don't know either.
P: In that case, I do know what the numbers are.
S: In that case, then so do I.

What are the two numbers?

Afterpuzzle: If you've solved this one, search Google with the terms "product sum ___" where the blank is the number P knows and go to the first hit.

Title: Re: New Puzzle: P and S
Post by James Fingas on Dec 11^th, 2002, 10:58am

Garzahd,

I figured out one solution, but it depends upon whether or not you are including the number 1. If both integers are greater than 1, then the solution is different than if both integers are greater than or equal to 1.

I notice that the website you are referring to is now ranked second on Google, and I also notice that they include 1.

Title: Re: New Puzzle: P and S
Post by Garzahd on Dec 11^th, 2002, 3:26pm

The puzzle requires that both numbers be strictly greater than 1.

My intended website for the afterpuzzle was (hidden and missing an initial w)
ww.mathematik.uni-bielefeld.de/~sillke/PUZZLES/logic_sum_product
which has since dropped to #3 on google (Damn them for being clever.)

Title: Re: New Puzzle: P and S
Post by SWF on Dec 11^th, 2002, 7:39pm

I am not sure which web site you mean, but when I type in the answer, it looks like the site you mean is 4th on Google now.

Title: Re: New Puzzle: P and S
Post by James Fingas on Dec 12^th, 2002, 8:44am

SWF,

That's probably because we typed in different queries.

Title: Re: New Puzzle: P and S
Post by NickH on Jan 3^rd, 2003, 2:55am

I present a solution (http://www.qbyte.org/puzzles/p003s.html) to a very similar problem on my math puzzle site.

Nick