论文标题
以前玩家的公正三维巧克力棒游戏的位置
Previous Player's Positions of Impartial Three-Dimensional Chocolate-Bar Games
论文作者
论文摘要
在这项研究中，我们研究了三维巧克力棒游戏，这是Chomp游戏的变体。三维巧克力棒是一个三维的立方体，其中棒的某些部分中存在一个苦涩的立方盒。两名玩家轮流沿着凹槽水平或垂直切割条。设法离开对手的球员是赢家。我们考虑了这款游戏的p位，其中P位置是游戏的位置，只要他们在每个阶段都正确地打球，就可以迫使以前的玩家（将在下一个球员比赛之后玩的球员）赢得胜利。当且仅当P-1，Q-1，R-1的Bitxor分别是巧克力棒的长度，高度和宽度时，我们就会提供足够的情况。
In this study, we investigate three-dimensional chocolate bar games, which are variants of the game of Chomp. A three-dimensional chocolate bar is a three-dimensional array of cubes in which a bitter cubic box is present in some part of the bar. Two players take turns and cut the bar horizontally or vertically along the grooves. The player who manages to leave the opponent with a single bitter block is the winner. We consider the P-positions of this game, where the P-positions are positions of the game from which the previous player (the player who will play after the next player) can force a win, as long as they play correctly at every stage. We present sufficient conditions for the case when the position {p,q,r} is a P-position if and only if the bitxor of p-1, q-1, r-1, where p, q and r are the length, height, and width of the chocolate bar, respectively.
