Paint half the square so unpainted still a square
Create diagonals in every small square and paint just the outside triangle of every small square. This way half of the large square is painted and there is still a square rotated by 45 degrees in the center that is unpainted.
Create diagonals in every small square and paint just the outside triangle of every small square. This way half of the large square is painted and there is still a square rotated by 45 degrees in the center that is unpainted.
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