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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.

Slični zadaci

#NaslovOznakeRj.KvalitetaTežina
1808IMO Shortlist 1991 problem 101
1967IMO Shortlist 1997 problem 111
1969IMO Shortlist 1997 problem 132
1973IMO Shortlist 1997 problem 175
1975IMO Shortlist 1997 problem 192
1982IMO Shortlist 1997 problem 260