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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