Question 4
(IRN) IMO4. An $n\times n$ matrix with entries from $\{1,2,\ldots,2n-1\}$ is called a coveralls matrix if for each $i$ the union of the $i$th row and the $i$th column contains $2n-1$ distinct entries. Show that:
(a) There exist no coveralls matrices for $n=1997$.
(b) Coveralls matrices exist for infinitely many values of $n$.
(a) There exist no coveralls matrices for $n=1997$.
(b) Coveralls matrices exist for infinitely many values of $n$.