MathDB
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 1000×10001000 \times 1000 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 2×1,1×2,1×32 \times 1, 1 \times 2, 1 \times 3, or 3×13 \times 1 rectangle. The player that cannot move loses. Prove that some three players can cooperate to make the fourth player lose.