100-part broken lines, odd no of self-intersections points
Source: St. Petetsburg 2016 10.6
May 1, 2019
combinatoricscombinatorial geometryoddpolygonclo
Problem Statement
The circle contains a closed -part broken line, such that no three segments pass through one point. All its corners are obtuse, and their sum in degrees is divided by . Prove that this broken line has an odd number of self-intersection points.