Turns out the algorithm is related to zero forcing sets. A fun concept. I found some nice slides on it. math.nsysu.edu.tw/~chlin/Publi

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For a \(n\times n\) grid, the lights out game can be considered as solving a linear system over \(n^2\) variables in mod \(2\). It takes \(O(n^6)\) time. Surprisingly, there is a \(O(n^3)\) time algorithm. chaoxuprime.com/posts/2019-01-

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