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.
Problem
Source: Iran TST 2014, second exam, day 2 ,problem 3
Tags: combinatorics unsolved, combinatorics
Isogonics
04.05.2015 04:24
Please show why the answer is yes...
Cristiano-Ezio
12.07.2019 10:20
why no solutions here, even offical solution?
MeGustaElArroz23
04.04.2023 20:07
Answer is no (unless there's a typo or smth, if you allow ALL SEGMENTS TO BE OUTSIDE the polygon the answer may be different, i believe that may be the typo?) Counterexample: