MathDB

Polygon and set of points inside, triangulation

Source: Romanian TST 1 2008, Problem 4

May 1, 2008

analytic geometryinductioncombinatorics proposedcombinatorics

Problem Statement

Prove that there exists a set

S

of n \minus{} 2 points inside a convex polygon

P

with

n

sides, such that any triangle determined by

3

vertices of

P

contains exactly one point from

S

inside or on the boundaries.