(Seen in a presentation by Rineke Verbrugge, in NVTI Theory day, 2007)
Of two unknown integers, each between 2 and 99 inclusive, a person P is told the product and a person S is told the sum. When asked whether they know the two numbers, the following dialog ensues:
S: “I knew that already.”
P: “Then I now know the two numbers.”
S: “Then I now know them, too.”
What are the two numbers? Prove that your solution is unique.