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Online now Злобный Ящур
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#877
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Uranium235
we are looking for the boundary between two differently colored areas
Considering that the coloring can be anything, there might not be any boundaries at all. :D For example, how about this coloring: all points with both coordinates being rational are green, and the rest are magenta. :D

Added 2 minutes later
Uranium235
If there are no color matches on a circle of radius x from (1) with (1), then there are 2 points of the same color on the circle itself, and a chord can be constructed between them, equal in length to the radius.
And this seems to be what we need!

Ничто не возникает из ничего и ничто не пропадает бесследно.
Если где-то чего-то убудет, то в другом месте добавится.
(Закон сохранения).

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