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SKMO 2023 P6

Source:

April 4, 2023
combinatorics

Problem Statement

Let nn be a positive integer such that n≥3n \geq 3. Consider a grid with size n×nn \times n where each square can be white or black, in the beginning they are all white. In every step we can change the colors of cells forming a shape like below https://imgtr.ee/images/2023/04/04/k0i9m.png or any of its rotations. Determine all nn such that the whole grid can be black after a finite number of steps.
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