2013 ToT Spring Senior A p3 lattice triangle with 2 lattice points interior v2
Source:
March 5, 2020
geometrylattice pointsparallelcombinatorial geometry
Problem Statement
A point in the plane is called a node if both its coordinates are integers. Consider a triangle with vertices at nodes containing at least two nodes inside. Prove that there exists a pair of internal nodes such that a straight line connecting them either passes through a vertex or is parallel to side of the triangle.