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Found problems: 1

2010 N.N. Mihăileanu Individual, 4
Tags: pigeonhole principle , discrete mathematics , square grid , locusts , combinatorics , modular arithmetic
A square grid is composed of $ n^2\equiv 1\pmod 4 $ unit cells that contained each a locust that jumped the same amount of cells in the direccion of columns or lines, without leaving the grid. Prove that, as a result of this, at least two locusts landed on the same cell. [i]Marius Cavachi[/i]