Expected Light

Bob has a circular land of radius R. He has built a circular building of radius r (r < R) at the center of his land. Bob wants to place n light sources on his land outside the building. He wants to place them such that expected number of lights can be seen from a random point on the land outside the building is maximized. A light source can be seen from a point if line segment connecting the point and light source doesn’t intersect with the building. For simplicity, suppose the building has infinite height. Find maximum possible expected number of lights can be seen from a random point outside the building (of course in his land) if light sources are placed optimally.


This is a companion discussion topic for the original entry at https://toph.co/p/expected-light