Combinatorics · Latin squares · Constructions · Modular arithmetic · Diagonals
Problem 1, 2017
In every cell of a table with \(2017\) rows and \(2017\) columns one of the numbers \(1, 2, 3, \dots, 2017\) is written. Is it possible to do this so that in every row, in every column and along every diagonal each of these numbers occurs at most once?
(Diagonals of all lengths count: the two diagonals with \(2017\) cells, the four with \(2016\) cells, the four with \(2015\) cells, and so on down to the four with \(2\) cells and the four with \(1\) cell.)
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Serbian National Competition (Drzavno takmicenje) 2017, high school grade I, category A, problem 1. Organized by the Mathematical Society of Serbia (DMS). Source