Bolivian triangles can get messy sometimes
Source: Iberoamerican MO 2024 Day 1 P3
September 21, 2024
combinatoricscombinatorial geometry
Problem Statement
Let be a fixed point in the plane. We have red points, yellow points and green points in the plane, where there isn't any three colinear points and all points are distinct from . It is known that for any two colors, the convex hull of the points that are from any of those two colors contains (it maybe contain it in it's interior or in a side of it). We say that a red point, a yellow point and a green point make a bolivian triangle if said triangle contains in its interior or in one of its sides. Determine the greatest positive integer such that, no matter how such points are located, there is always at least bolivian triangles.