Minevich (2012) Symmetric Matrices over \(F_2\) and the Lights Out Problem Anderson (2006) Turning Lights Out with Linear Algebra In this article the optimal solution in terms of the number of moves for LightsOut is derived using linear algebra and a demo is implemented in JavaScript.Ī given light configuration can be represented as a matrix \(\mathcal\).
The goal is to turn all lights out, starting with a random pattern of lights, although we will see that not every pattern has a solution.Ī related problem consists of finding a solution when all lights are initially turned on, which is known as the "all-ones problem" and is possible for any square lattice, as shown by Sutner (1989).
Additionally, all four horizontally and vertically adjacent lights - forming a cross - get inverted as well when a single light gets pressed. Each of these lights can either be on or off and its state can be inverted with a button related to that light. In the original version, 25 lights are arranged in a 5 by 5 lattice. LightsOut is an electronic single player game manufactured by Tiger Toys in 1995. LightsOut Solution using Linear Algebra July 30th, 2018.
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