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Infinite chessboard - TT 2009 Junior-A6

Source:

September 3, 2010
modular arithmetic

Problem Statement

On an in finite chessboard are placed 2009 n×n2009 \ n \times n cardboard pieces such that each of them covers exactly n2n^2 cells of the chessboard. Prove that the number of cells of the chessboard which are covered by odd numbers of cardboard pieces is at least n2.n^2.
(9 points)
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