Problem

Source: Iran TST1 Day 2 P6

Tags: combinatorics, triangulation, Iranian TST, Morteza Saghafiyan



$n$ positive numbers are given. Is it always possible to find a convex polygon with $n+3$ edges and a triangulation of it so that the length of the diameters used in the triangulation are the given $n$ numbers? Proposed by Morteza Saghafian