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Encircle yourself with the circles? That would be finite and if you're thin enough, might even be minimal? Certainly easier to find the configuration than the actual solution.

(ok ok, it looks like the blockers are point-size, so this wouldn't work of couse)

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Not finite. Not even countably finite.

Or even countably infinite :) One could argue that all finite sets are countable since it's not too hard to find a surjection from the naturals to a given finite set.

(Intended to be mildly humorous.)

Oops, that's what I meant, not even countably in-finite

I wrote the top of my comment before realising that the points were points and bot circles with a radius.

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