game with 2x1, 1x 2, 1x3, 3x1 rectangles in a 1000x1000 board
Source: Tuymaada Olympiad 2019 juniors p8
July 22, 2019
geometryrectanglegamegame strategycombinatoricscombinatorial geometry
Problem Statement
Andy, Bess, Charley and Dick play on a board. They make moves in turn: Andy first, then Bess, then Charley and finally Dick, after that Andy moves again and so on. At each move a player must paint several unpainted squares forming , or rectangle. The player that cannot move loses. Prove that some three players can cooperate to make the fourth player lose.