1997 IMO Problems/Problem 4

Problem

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 $n$ .

Solution

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

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