[math-fun] What are the values of A and B?
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 --------------------------------- Be a better friend, newshound, and know-it-all with Yahoo! Mobile. Try it now.
I think the idea is that at the start it is mutual knowledge that S knows the sum and P knows the product. So P's first statement means ``the product can be factored into integers between 1 and 100 in more than one way'' On Sun, Mar 16, 2008 at 7:49 PM, Bill Gosper <rwmgosper@yahoo.com> wrote:
Neither Sam nor Pete knows what they are, but Sam knows their sum, and Pete knows their product. The following conversation takes place.
There are two integers, A and B, which are greater than 1 and less than
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
________________________________ Be a better friend, newshound, and know-it-all with Yahoo! Mobile. Try it now.
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
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.
On Tue, 18 Mar 2008, Bill Gosper wrote:
Am I still alone on this matter?? Is this one of the early warning signs of senile dementia?
No, I don't think anybody contradicted the notion that Pete's first statement adds no information.
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
participants (4)
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Bill Gosper -
Gareth McCaughan -
Jason -
Peter Norvig