John and Mary select a natural number each and tell that to Bill. Bill wrote their sum and product in two papers hid one paper and showed the other to John and Mary. John looked at the number (which was 2002 ) and declared he couldn't determine Mary's number. Knowing this Mary also said she couldn't determine John's number as well. What was Mary's Number?
Problem
Source: Tournament of Towns, Fall 2002, Junior O Level, P2
Tags: number theory proposed, number theory