MathDB

5

Part of 1990 Mexico National Olympiad

Problems(1)

19 lattice points with no 3 collinear, always exist 3 with lattice centroid

Source: Mexican Mathematical Olympiad 1990 OMM P5

7/29/2018
Given 1919 points in the plane with integer coordinates, no three collinear, show that we can always find three points whose centroid has integer coordinates.
combinatorial geometrylattice pointsCentroidgeometry