My (almost) first combgeo
Source: Ukrainian Mathematical Olympiad 2024. Day 2, Problem 11.7
March 20, 2024
combinatorial geometrycombinatorics
Problem Statement
You are given yellow and blue points on the plane, and no three of the points are on the same line. We call a pair of nonnegative integers good if there exists a half-plane with exactly yellow and blue points. Find the smallest possible number of good pairs. The points that lie on the line that is the boundary of the half-plane are considered to be outside the half-plane. Proposed by Anton Trygub