Question 20
For a positive integer $n$ assume that $n$ numbers have been chosen from the table
$$
\begin{array}{cccc}
0 & 1 & \cdots & n-1 \\
n & n+1 & \cdots & 2n-1 \\
\vdots & \vdots & \ddots & \vdots \\
(n-1)n & (n-1)n+1 & \cdots & n^2-1
\end{array}
$$
with no two of them from the same row or the same column. What is the maximal product of these $n$ numbers?
$$
\begin{array}{cccc}
0 & 1 & \cdots & n-1 \\
n & n+1 & \cdots & 2n-1 \\
\vdots & \vdots & \ddots & \vdots \\
(n-1)n & (n-1)n+1 & \cdots & n^2-1
\end{array}
$$
with no two of them from the same row or the same column. What is the maximal product of these $n$ numbers?