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A graph theoretic solution to the 8 × 8 light’s out problem

Author:

Edward M. Kiunisala

Subject Area:

Physical Sciences and Engineering

Abstract:

This paper is concerned with a mathematical solution to the 8 × 8 Lights Out Problem, a modification of an originally 5 × 5 electronic one-person puzzle game played on a rectangular lattice of lamps which can be turned on and off. A move consists of flipping a "switch" inside one of the squares, thereby toggling the on/off state of this and all four vertically and horizontally adjacent squares. Starting from a randomly chosen light pattern, the aim is to turn all the lamps off. The researcher describes the mechanics of the game and the solution to it from two different perspectives, (the first as a curious puzzle fan, and the second as a mathematician), with the end intention of presenting a result of entertaining mathematical research and to share it with anyone who is interested in it.

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