Question 62
The numbers
$$
\frac{1}{2016}, \frac{2}{2016}, \frac{3}{2016}, \dots, \frac{2015}{2016}
$$
are written on a blackboard. With each move, one may erase any two numbers $a$ and $b$ and replace them with
$$
3ab - 2a - 2b + 2.
$$
What will be the single remaining number after 2014 moves?
$$
\frac{1}{2016}, \frac{2}{2016}, \frac{3}{2016}, \dots, \frac{2015}{2016}
$$
are written on a blackboard. With each move, one may erase any two numbers $a$ and $b$ and replace them with
$$
3ab - 2a - 2b + 2.
$$
What will be the single remaining number after 2014 moves?