MathDB
My (almost) first combgeo

Source: Ukrainian Mathematical Olympiad 2024. Day 2, Problem 11.7

March 20, 2024
combinatorial geometrycombinatorics

Problem Statement

You are given 20242024 yellow and 20242024 blue points on the plane, and no three of the points are on the same line. We call a pair of nonnegative integers (a,b)(a, b) good if there exists a half-plane with exactly aa yellow and bb 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