[math-fun] Cute Puzzle: What Are The Two Numbers?

The puzzle is from the Winter 2000 issue of The Bent of Tau Beta Pi: www.tbp.org/pages/Publications/Bent/BTs/W00.pdf There are two integers, A and B, which are integers 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? — Don Holden ----- The solution is here: www.tbp.org/pages/Publications/Bent/BTs/Sp00.pdf