Australian AMC 2018 - Senior Question 29

For $n\ge3$, a pattern can be made by overlapping $n$ circles, each of circumference 1 unit, so that each circle passes through a central point and the resulting pattern has order-$n$ rotational symmetry.

For instance, the diagram shows the pattern where $n=7$.

If the total length of visible arcs is 60 units, what is $n$?