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delete 2 numbers from 1/2016 - 2/2016 and replace them with 3ab - 2a - 2b + 2

Source: 2016 Latvia BW TST P1

December 17, 2022

combinatorics

Problem Statement

2016

numbers written on the board:

\frac{1}{2016}, \frac{2}{2016}, \frac{3}{2016}, ..., \frac{2016}{2016}

. In one move, it is allowed to choose any two numbers

a

and

b

written on the board, delete them, and write the number

3ab - 2a - 2b + 2

instead. Determine what number will remain written on the board after

2015

moves.