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Abstract: Tiger Electronics has sold two forms of the Lights Out Puzzle, a square board and a cube. We show how to use linear algebra over GF(2) to solve both puzzles. We show how to identify solvable and unsolvable patterns, how to find all possible solutions, and therefore how to find the minimum length solution. We determine the number of solvable patterns, both with and without symmetry. We determine the length of the longest possible minimum solution over all solvable patterns. We debunk the numerical data on the commerical package.
