Tromping Games: Tiling with Trominoes

Abstract

AbstractThe game of Domineering is a combinatorial game that has been solved for several boards, including the standard 8 × 8 board. We create new partizan – and some impartial – combinatorial games by using trominoes instead of and along with dominoes. We analyze these Tromping games for some small boards providing a dictionary of values. Further, we prove properties that permit expressing some connected boards as sums of smaller subboards. We also show who can win in Tromping for some boards of the form