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The following two 5x5 Lights-Out puzzles are not solvable. Is there a way to find out why, without trying to solve them?
[1, 0, 0, 1, 0]
[1, 1, 1, 1, 0]
[1, 1, 1, 0, 0]
[0, 0, 1, 0, 0]
[1, 1, 1, 1, 1]
[1, 1, 1, 0, 1]
[1, 0, 0, 1, 0]
[0, 1, 0, 1, 0]
[0, 1, 0, 1, 1]
[0, 1, 1, 1, 1]
(These are just ...