河内塔Two Player Tower of Hanoi
Two-Player Tower of Hanoi
摘要：
汉诺塔博弈是娱乐数学中的经典难题（Lucas 1883），在纯数学中也有很好的记录。在这两个领域之间的边界，我们发现的最小数量的移动，这是$2^n-1$，转移塔的$n$磁盘的特征。但也有其他变化的游戏，例如涉及实数权重的移动磁盘。这引起了类似类型的问题，但最终得分寻求优化。我们研究扩展的一个球员设置为两个球员，调用经典的获胜条件组合博弈论，如球员谁移动最后获胜，或最高分获胜。这里我们在三个堆上解决这两个获胜条件。
英文摘要：
The Tower of Hanoi game is a classical puzzle in recreational mathematics (Lucas 1883) which also has a strong record in pure mathematics. In a borderland between these two areas we find the characterization of the minimal number of moves, which is $2^n-1$, to transfer a tower of $n$ disks. But there are also other variations to the game, involving for example real number weights on the moves of the disks. This gives rise to a similar type of problem, but where the final score seeks to be optimized. We study extensions of the one-player setting to two players, invoking classical winning conditions in combinatorial game theory such as the player who moves last wins, or the highest score wins. Here we solve both these winning conditions on three heaps.
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。
