Question 77
In an $n \times n$ board, the numbers $0$ through $n^2 - 1$ are written so that the number in row $i$ and column $j$ is equal to
$$
(i-1) + n(j-1) \text{ where } 1 \le i, j \le n.
$$
Suppose we select $n$ different cells of the board, where no two cells are in the same row or column. Find the maximum possible product of the numbers in the $n$ cells.
$$
(i-1) + n(j-1) \text{ where } 1 \le i, j \le n.
$$
Suppose we select $n$ different cells of the board, where no two cells are in the same row or column. Find the maximum possible product of the numbers in the $n$ cells.