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
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