The problem is taken from my course on randomized algorithms :
There is a circle made of wire. n birds (assume n>2) occupy uniformly random position over it (visualize each bird occupying a point on the circumference of the circle). This will lead to partitioning of circle into n segments. We follow the following rule for painting these segments. A segment is painted if it is smaller than at least one of its neighboring segments. What is the expected fraction of the circle which gets painted?
I am not able to frame it mathematically. Any hints?