Question 91
We consider an $n \times n$ chessboard, where $n$ is an even positive integer. On the board we put all numbers $1,2,3, \dots, n^2$, one at each square. Let $S_1$ be the sum of the numbers lying at the white squares and let $S_2$ be the sum of the numbers lying on the blank squares. Find all the numbers $n$ for which it is possible an arrangement such that:
$$
\frac{S_1}{S_2} = \frac{39}{64}.
$$
$$
\frac{S_1}{S_2} = \frac{39}{64}.
$$