Question 136
A square $n \times n$ is divided into $n^2$ cells. In total $n^2$ tokens are placed at some cell. During every round, a player can move one token from cell $A$ to cell $B$, and one token from cell $A$ to cell $C$, provided that cell $A$ contained at least two tokens, $B$ and $C$ are symmetric with respect to $A$, and finally $B$ and $C$ are adjacent to $A$. Is it possible that after a few such rounds every cell on the board contains exactly one token, in case:
a) $n = 2016$;
b) $n = 2017$?
a) $n = 2016$;
b) $n = 2017$?