Bicolor floor

On a white finite plane, Eddy paints some of the points black in an attempt to color every point black or white such that no two points 20 units apart are the same color. If two points are 20 units apart and they have the same color, he will change the color of one of them. Assuming the plane has length \(l\) and width \(w\) such that \(l,w > 10\sqrt{2}\), will Eddy ever finish painting this plane?

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