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Coloring chess square

Source: St Petersburg Olympiad 2010, Grade 10, P7

September 14, 2017
combinatoricsgeometryrectangleChessboardinvariant

Problem Statement

200×200200 \times 200 square is colored in chess order. In one move we can take every 2×32 \times 3 rectangle and change color of all its cells. Can we make all cells of square in same color ?
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