Posted tagged ‘sum’

Product and Sum (unsolved)

March 15, 2008

(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.” 

What are the two numbers? Prove that your solution is unique.