Problem

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

Tags: combinatorics unsolved, combinatorics



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