论文标题
点和聚合物
Dots-and-Polygons
论文作者
论文摘要
点和盒子是一项受欢迎的儿童游戏，其获胜策略已由Berlekamp，Conway，Guy等人研究。在本文中，我们考虑了两种变体，即点和三角形和点和聚合物，它们都使用了与点和盒子相同的晶格游戏板结构。这些变化的性质以及该晶格结构使自己适用于Pick的定理来计算所要求的区域。与点和盒中研究的几种策略用于分析这些新变体。
Dots-and-Boxes is a popular children's game whose winning strategies have been studied by Berlekamp, Conway, Guy, and others. In this article we consider two variations, Dots-and-Triangles and Dots-and-Polygons, both of which utilize the same lattice game board structure as Dots-and-Boxes. The nature of these variations along with this lattice structure lends itself to applying Pick's theorem to calculate claimed area. Several strategies similar to those studied in Dots-and-Boxes are used to analyze these new variations.
