Authors: Ryohei Miyadera, Shunsuke Nakamura and Ryo Hanafusa
In this article chocolate games that are variants of the game of nim are studied. The traditional chocolate game was presented as a rectangle shaped figure, and in this article the authors present new chocolate games. These new chocolate games have interesting mathematical structures, since the coordinates of states of the game satisfy inequalities. The authors are the first researchers to study chocolate games conditioned by inequalities. As to the coordinates of the states, see Example 1.2 of this article. The authors proved some formulas of L-states (losing states) for these new games, and made a new function that is more efficient than Grundy Number.
Keywords: chocolate game, combinatorial games, computer algebra system, Grundy Number, losing state, nim.