Circles on a Square
Geometry
Level
3
How many unit circles would it take to completely cover a square of side length 3?
8
4
2
6
5
7
3
9
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1 solution
It clearly cannot be done with four circles: If four circles cover all the vertices, then they will not cover the center, since the center is at a distance of 2 3 > 2 from the vertices. It is easy(and fun!) to cover the square with five circles, though, with a bit of wiggle room.