Prove, that if a given rectangle can be covered by 100 circles each of r=2, then it can
be covered by 400 circles each of r=1.

(In reply to

Possible solution by broll)

Broll:

I don't get your last post at all. The area of the rectangle is necessarily less than the total area of the circles, because the circles cover the rectangle. So if "efficiency" x is less than 1, then the area of the rectangle = 400pi * x.

And the area of the r=1 circles is the same as the area of the r=2 circles, so if they cover the rectangle, they also do so with "efficiency" x