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MathNet 2010 — Part 01 Question 90

Math Olympiad Vault · MathNet 2010 — Part 01

Question 90

All cells of a $7 \times 7$ table are painted black and white. Per move it is allowed to choose any $n \times n$ square, $1 \lt n \lt 7$ (with the sides coinciding with the sides of the cells) and to change the color of all its cells (from black to white and vice versa).
Is it possible to get the table with all white cells from the table with the arbitrary number of black cells?