Variations on a class of 2 person games are studied. The games, called Sprouts and Brussels Sprouts, originated with Conway and Paterson and discussed in Scientific American’s mathematics column by Gardner. Sprouts’ complexity is similar to that of chess. Brussels Sprouts always ends in the same number of moves, i.e., it is a deterministic game. Though valued primarily as recreational mathematics - the distinction between recreational mathematics and mathematics not being that sharp anyway - the games are also useful as practical exercises in introductory graph theory and computer programming courses.
The payoff in all of the games considered is that the last mover wins - referred to as the normal version. There is also the corresponding misère versions where the last mover loses. In this paper, the authors introduce two coloured versions of the Brussels Sprouts game. In contrast to the original game of Conway, the two new colored versions are amenable to analysis mathematically without the aid of computers, in large families of cases.