Hayata, Yuki; Yamagishi, Masakazu On weight-one solvable configurations of the Lights Out puzzle. (English) Zbl 1414.05193 Involve 12, No. 4, 713-720 (2019). Summary: We show that the center-one configuration is always solvable in the Lights Out puzzle on a square grid with odd vertices. Cited in 1 Document MSC: 05C57 Games on graphs (graph-theoretic aspects) 05C38 Paths and cycles 05C76 Graph operations (line graphs, products, etc.) 94B05 Linear codes (general theory) 91A46 Combinatorial games 94B60 Other types of codes 91A43 Games involving graphs Keywords:Lights Out; path graph; Cartesian product; linear code PDFBibTeX XMLCite \textit{Y. Hayata} and \textit{M. Yamagishi}, Involve 12, No. 4, 713--720 (2019; Zbl 1414.05193) Full Text: DOI References: [1] 10.1007/978-3-642-40273-9_13 · Zbl 1395.91075 · doi:10.1007/978-3-642-40273-9_13 [2] ; Goldwasser, Congr. Numer., 126, 99 (1997) [3] 10.1080/10586458.2010.10390633 · Zbl 1292.11134 · doi:10.1080/10586458.2010.10390633 [4] ; MacWilliams, The theory of error-correcting codes. North-Holland Math. Library, 16 (1977) · Zbl 0369.94008 [5] 10.1007/BF03023823 · Zbl 0770.68094 · doi:10.1007/BF03023823 [6] 10.1016/S0304-3975(97)00242-9 · Zbl 0947.68540 · doi:10.1016/S0304-3975(97)00242-9 [7] 10.1016/j.laa.2015.03.004 · Zbl 1314.05121 · doi:10.1016/j.laa.2015.03.004 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.