MathDB

The numbers

\frac{1}{1}, \frac{1}{2}, \cdots , \frac{1}{2012}

are written on the blackboard. Aïcha chooses any two numbers from the blackboard, say

x

and

y

, erases them and she writes instead the number

x + y + xy

. She continues to do this until only one number is left on the board. What are the possible values of the final number?

Problem Statement