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This thesis describes algorithms for determining if a grid of switches can be turned into all-off state from any initial configuration by various methods of activation operation (push). Among these push methods, besides the regular "+" push, "+" push with no center, "X" push, "X" push with no center, and a "V"-typed unbalanced push are studied. The research methods used in this work are mainly linear algebra and algorithm analysis. Results obtained include that the grid m x n is completely solvable with push "+" no center, if and only if co-prime (m+1, n+1).