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