IMO Shortlist 1997 problem 4


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2. travnja 2012.
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An n \times n matrix whose entries come from the set S = \{1, 2, \ldots , 2n - 1\} is called a silver matrix if, for each i = 1, 2, \ldots , 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.
Izvor: Međunarodna matematička olimpijada, shortlist 1997