1997 IMO Problems/Problem 4


An $n \times n$ matrix whose entries come from the set $S={1,2,...,2n-1}$ is called a $\textit{silver}$ matrix if, for each $i=1,2,...,n$, the $i$th row and the $i$th column together contain all elements of $S$. Show that

(a) there is no $\textit{silver}$ matrix for $n=1997$;

(b) $\textit{silver}$ matrices exist for infinitely many values of $n$.


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See Also

1997 IMO (Problems) • Resources
Preceded by
Problem 3
1 2 3 4 5 6 Followed by
Problem 5
All IMO Problems and Solutions