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Puzzle—Shedding Light on Higher Dimensions

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  • Martin J. Chlond

    () (Lancashire Business School, University of Central Lancashire, Preston PR1 2HE, United Kingdom)

Abstract

Lights Out puzzles have been a popular computer pastime since the eighties. They consist of a grid of cells with each cell in one of two states, lit or unlit. When a cell is clicked, then that cell and its immediate neighbors toggle between lit and unlit. The objective is to identify the set of cells that must be clicked such that the entire grid is lit. Many variations on this theme devised by Jaap Scherphuis are at www.jaapsch.net/puzzles/lights.htm and one particularly interesting twist is at www.jaapsch.net/puzzles/java/lograph/lographapp.htm . This page implements, in the form of a Java applet, a set of tools to allow the creating, editing and playing of Lights Out puzzles on graphs. The nodes of the graph represent cells, and edges join any two cells that are considered neighbours. I show how to formulate Lights Out puzzles as integer programs and produce solutions using GLPK and Minisat. These are, respectively, open source software programs to solve Integer Programs and Satisfiability problems and are available within the GUSEK environment which may be downloaded from http://gusek.sourceforge.net/gusek.htm.

Suggested Citation

  • Martin J. Chlond, 2015. "Puzzle—Shedding Light on Higher Dimensions," INFORMS Transactions on Education, INFORMS, vol. 15(2), pages 197-199, January.
  • Handle: RePEc:inm:orited:v:15:y:2015:i:2:p:197-199
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    File URL: http://dx.doi.org/10.1287/ited.2014.0135
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    Keywords

    puzzles; lights out; integer programming;

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