We describe and axiomatize finite solitaire puzzles and zero sum sequential games graph theoretically. Zermelo's theorem telling that there is a win for one of the players or a draw follows from the definitions. The god number is a geometric quantity that quantifies the number of moves necessary to solve the puzzle. In the solitaire case, the god number is the minimal distance from the initial state $v$ to the solution space $A$. If $v$ and $A$ are not specified, the god number is the graph diameter. God number computations are related to combinatorial sorting problems and is a NP-complete problem in general even when restricted to concrete sliding problems. In the two-player case, the god number is a minimax critical value: it minimizes the maximal game event length over the set of all strategies. A strategy is a sub-graph of the game graph that contains the initial vertex. The definition is done so that a ``mate in k" chess problem has god number k. As for examples: in the solitaire case, we look at group games like Rubik type problems, transposition games related to sorting, at sliding puzzles like the 15 puzzle or rainbow ball, or the tower of Hanoi. For two-player games, we illustrate the story using examples of small chess games, a small card game or tic-tac-toe type problems.

翻译：本文从图论角度描述并公理化有限单人谜题与零和序贯博弈。策梅洛定理（即博弈中必有一方获胜或平局）可由定义直接导出。上帝数是一个几何量，用于量化解决谜题所需的最少步数。在单人谜题情形下，上帝数是初始状态$v$到解空间$A$的最小距离。若未指定$v$与$A$，则上帝数即为图直径。上帝数计算与组合排序问题相关，即使限制于具体滑块问题，通常也属于NP完全问题。在双人博弈情形下，上帝数是一个极小极大临界值：它在所有策略集合上最小化最大博弈事件长度。策略是包含初始顶点的博弈图子图。该定义使得“k步将杀”的象棋问题的上帝数为k。在单人谜题方面，我们考察群类游戏（如鲁比克型问题）、与排序相关的置换游戏、滑块谜题（如15 puzzle或彩虹球）以及汉诺塔。在双人博弈方面，我们通过小型象棋博弈、小型纸牌游戏或井字棋类问题等实例进行说明。