Question 148
Consider a $3 \times 3$ chessboard. At the start, the digit $0$ is written in each of the $9$ cells. Then, at each step, the following operation is performed: one chooses two cells sharing a common side, then adds $1$ to the number written in these two cells, or subtracts $1$ from the number written in these two cells. Is it possible to obtain a configuration in which the number $2017$ is written in all $9$ cells?