In this study, the group of finite cyclic lamplighter states is reinterpreted as the novel lamplighter puzzle. The rules of the puzzle are outlined and related back to properties of the lamplighter group with specific interest placed upon the discussion of which puzzle instances are solvable. The paper shows that, through the use of algebra, many puzzle instances can be identified as solvable without the use of an exhaustive search algorithm. Solvability depends upon the creation of irregular generating sets for subgroups of the finite cyclic lamplighter group and the cosets formed by these subgroups. Further possible generalizations of the lamplighter puzzle are also discussed in closing.

中文翻译：

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新型点灯者谜题的代数可解性

在这项研究中，有限循环点灯状态组被重新解释为新的点灯谜题。拼图的规则被概述并与点灯组的属性相关联，特别感兴趣的是讨论哪些拼图实例是可解决的。该论文表明，通过使用代数，许多谜题实例可以被识别为可解的，而无需使用穷举搜索算法。可解性取决于为有限循环点灯者群的子群和由这些子群形成的陪集的不规则生成集的创建。最后还讨论了点灯者谜题的进一步可能的概括。