P is told the product of two integers chosen from [2, 99] and S is told the sum. The following dialogue ensues:

(1) P says, "I do not know the two integers."

(2) S replies, "I knew that already."

(3) P exclaims, "Ah! I now know the two numbers.",

(4) S smugly replies, "Now I know them too."

What are the two numbers?

Do not remember.

Article by E W Dijkstra and myriad variations of this puzzle.