论文标题
数学链接游戏的数学基础
A Mathematical Foundation for the Numberlink Game
论文作者
论文摘要
NumberLink是一款益智游戏，在该游戏中，玩家将获得带有自然数字（$ n $）的节点的网格，并要求与相邻节点创建$ n $连接。连接只能用顶部，底部，左和右邻居进行，并且一个相邻节点之间的连接不能超过两个连接。在本文中，我们通过图给出了难题的数学表述，并给出了这种表述的直接后果。这项工作的主要结果是一种算法，该算法可深入了解这些难题及其解决方案的特征。最后，我们给出了一些空旷的问题和进一步的方向。
Numberlink is a puzzle game in which players are given a grid with nodes marked with a natural number, $n$, and asked to create $n$ connections with neighboring nodes. Connections can only be made with top, bottom, left and right neighbors, and one cannot have more than two connections between any neighboring nodes. In this paper, we give a mathematical formulation of the puzzles via graphs and give some immediate consequences of this formulation. The main result of this work is an algorithm which provides insight into characteristics of these puzzles and their solutions. Finally, we give a few open questions and further directions.
