MathDB
2014 HMIC #1

Source:

December 26, 2016

Problem Statement

Consider a regular nn-gon with n>3n>3, call a line acceptable if it passes through the interior of this nn-gon. Draw mm different acceptable lines, so that the nn-gon is divided into several smaller polygons.
(a) Prove that there exists an mm, depending only on nn, such that any collection of mm acceptable lines results in one of the smaller polygons having 33 or 44 sides.
(b) Find the smallest possible mm which guarantees that at least one of the smaller polygons will have 33 or 44 sides.