MathDB

6

Part of 2020 Iranian Combinatorics Olympiad

Problems(1)

Triangular Grid Polynomial with Sides in Grid

Source: Iranian Combinatorics Olympiad 2020 P6

4/26/2020
Consider a triangular grid of equilateral triangles with unit sides. Assume that P\mathcal{P} is a non-self-intersecting polygon with perimeter 1399 and sides from the grid. Prove that P\mathcal{P} has either an internal or an external 120-degree angle.
Proposed by Seyed Hessam Firouzi
combinatorics