三角钉纸牌无限
Triangular Peg Solitaire Unlimited
摘要：
三角桩接龙是一个著名的单人游戏或益智。当一个桩连续捕获多个桩时，这称为扫描。我们研究游戏是否可以戏剧性地结束，一个钉子把所有剩下的钉子都扫出棋盘。对于边6和边8的三角形棋盘（分别有21和36个洞），几何上最长的扫掠可以作为游戏中的最后一步。在较大的三角形板上，我们演示了如何构造以任意长的扫描结束的解决方案。我们还考虑了寻找最小化移动总数的解决方案的问题（其中移动是同一个挂钩的一个或多个连续跳跃）。
英文摘要：
Triangular peg solitaire is a well-known one-person game or puzzle. When one peg captures many pegs consecutively, this is called a sweep. We investigate whether the game can end in a dramatic fashion, with one peg sweeping all remaining pegs off the board. For triangular boards of side 6 and 8 (with 21 and 36 holes, respectively) the geometrically longest sweep can occur as the final move in a game. On larger triangular boards, we demonstrate how to construct solutions that finish with arbitrarily long sweeps. We also consider the problem of finding solutions that minimize the total number of moves (where a move is one or more consecutive jumps by the same peg).
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
