MathDB
Classical invariant combo

Source: Serbia IMO TST 2024, P1

May 18, 2024
combinatorics

Problem Statement

Three coins are placed at the origin of a Cartesian coordinate system. On one move one removes a coin placed at some position (x,y)(x, y) and places three new coins at (x+1,y)(x+1, y), (x,y+1)(x, y+1) and (x+1,y+1)(x+1, y+1). Prove that after finitely many moves, there will exist two coins placed at the same point.