ELMO SL 2011 A1

Let $n$ be a positive integer. There are $n$ soldiers stationed on the $n$ t h root of unity in the complex plane. Each round, you pick a point, and all the soldiers shoot in a straight line towards that point; if their shot hits another soldier, the hit soldier dies and no longer shoots during the next round. What is the minimum number of rounds, in terms of $n$, required to eliminate all the soldiers?

David Yang.