On Conway’s Brussels Sprouts

Abstract

John Horton Conway stood out from many famous mathematicians for his love of games and puzzles. Among others, he is known for inventing the two-player topological games called Sprouts and Brussels Sprouts. These games start with n spots (n crosses resp.), have simple rules, last for finitely many moves, and the player who makes the last move wins. In the misère versions, the player who makes the last move loses. In this paper, we make Brussels Sprouts colored, preserving the aesthetic interest and balance of the game. In contrast to the original Sprouts, Colored Brussels Sprouts allows mathematical analysis without computer programming and has winning strategies for a large family of the number of spots.