New Chocolate Games Variants of the Game of Nim

Abstract

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.