(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:

P: “I don’t know them.”

S: “I knew that already.”

P: “Then I now know the two numbers.”

S: “Then I now know them, too.”

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.

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