For example, going from lights all on to all off in theĬase, there are four possible solutions to the all-lights pattern, illustrated above. Multiple solutions are sometimes possible. Or less are solvable for every possible starting pattern. In the language of linear algebra, they are theįor instance, the solvable patterns of the -lattice are illustrated above. In general, the solvable patterns of the lattice are those which are obtained from the no-light The matrix of the above system of equations has maximal rank (it is a matrix with nonzero determinant), the game on a -lattice is always solvable. ,, and (corresponding to the red dots in the figure above). It has exactly one solution: (, , ), which means that the game is solved by pressing the
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