JZ>Doesn't Pete's first remark eliminate a lot of things, like products of two primes and squares of primes? --Joshua Yes, but S's remark means that he already knew that P's factorization was ambiguous, by virtue of trying every possible A and B summing to his A+B. Gareth's example is a bit confusing since the problem statement precluded values = 1, but my argument doesn't rely on that. Am I still alone on this matter?? Is this one of the early warning signs of senile dementia? --rwg Gareth McCaughan <gareth.mccaughan@pobox.com> wrote: On Monday 17 March 2008, Bill Gosper wrote:
There are two integers, A and B, which are greater than 1 and less than 101. Neither Sam nor Pete knows what they are, but Sam knows their sum, and Pete knows their product. The following conversation takes place.
Pete: ``I don't know what the numbers are.'' Sam: ``I knew that you did not know what the numbers are.'' Pete: ``Now I know what the numbers are.'' Sam: ``Then, so do I.''
What are the values of A and B?
I'm confused. Pete's first remark tells Sam nothing. Why can't this be shortened:
Sumit: You don't know them. Pradeep: I do now! Sumit: Likewise! ? --rwg
If the numbers were 1 and 2, Petronella would know that their product is 2 and would therefore know what they are. Similarly for 1 and p, for any p. Therefore, after Petronella's first statement, Sidney knows that the product of the numbers is not prime. -- g --------------------------------- Never miss a thing. Make Yahoo your homepage.