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1/2 n^2 colors in a nx n board

Source: 1981 Hungary - Kürschák Competition p2

October 10, 2022
combinatoricsColoring

Problem Statement

Let n>2n > 2 be an even number. The squares of an n×nn\times n chessboard are coloured with 12n2\frac12 n^2 colours in such a way that every colour is used for colouring exactly two of the squares. Prove that one can place nn rooks on squares of nn different colours such that no two of the rooks can take each other.
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