2014 HMIC #1
Source:
December 26, 2016
Problem Statement
Consider a regular -gon with , call a line acceptable if it passes through the interior of this -gon. Draw different acceptable lines, so that the -gon is divided into several smaller polygons.(a) Prove that there exists an , depending only on , such that any collection of acceptable lines results in one of the smaller polygons having or sides.(b) Find the smallest possible which guarantees that at least one of the smaller polygons will have or sides.