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On weight-one solvable configurations of the Lights Out puzzle. (English) Zbl 1414.05193

Summary: We show that the center-one configuration is always solvable in the Lights Out puzzle on a square grid with odd vertices.

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
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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
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