MathDB
Simple 2n-gon

Source: Iran TST 2014, second exam, day 2 ,problem 3

January 1, 2015
combinatorics unsolvedcombinatorics

Problem Statement

Consider nn segments in the plane which no two intersect and between their 2n2n endpoints no three are collinear. Is the following statement true? Statement: There exists a simple 2n2n-gon such that it's vertices are the 2n2n endpoints of the segments and each segment is either completely inside the polygon or an edge of the polygon.