Problem

Source: Tuymaada 2015, Day 2, Problem 8, Senior League

Tags: combinatorics, geometry, parallelogram



There are $\frac{k(k+1)}{2}+1$ points on the planes, some are connected by disjoint segments ( also point can not lies on segment, that connects two other points). It is true, that plane is divided to some parallelograms and one infinite region. What maximum number of segments can be drawn ? A.Kupavski, A. Polyanski