Question 4
An $n \times n$ matrix whose entries come from the set $S = \{1, 2, \dots , 2n - 1\}$ is called a *silver* matrix if, for each $i = 1, 2, \dots , n$, the $i$-th row and the $i$-th column together contain all elements of $S$. Show that:
(a) there is no silver matrix for $n = 1997$;
(b) silver matrices exist for infinitely many values of $n$.
(a) there is no silver matrix for $n = 1997$;
(b) silver matrices exist for infinitely many values of $n$.