Bicolor square

In a square of side length $$10 \sqrt{2}$$, Eddy paints some of the points black in the following way:

• He starts out with the square entirely white.
• If he finds 2 points that are 20 units apart which have the same color, he will change the color of one of them to the the other color.
• He continues until there are no 2 points that are 20 units apart which have the same color.

How many black points will there be?

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