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SMO 2010 senior q2

Source: SMO 2010 senior , date: sat, 25 jun 2010

March 31, 2018
algebra

Problem Statement

The numbers 11,12,...,12010\frac{1}{1}, \frac{1}{2}, ... , \frac{1}{2010} are written on a blackboard. A student chooses any two of the numbers, say xx, yy, erases them and then writes down x+y+xyx + y + xy. He continues to do this until only one number is left on the blackboard. What is this number?
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