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George is playing on the \(5\times 5\) “Lights Out" board and says that since each light can be on or off, and there are \(25\) lights on the board, the number possible light patterns that can be achieved by playing the game is \(2^{25}\). It turns out that the number is much smaller, it is \(2^{23}\). Can you explain why? You may take it as a fact that these three are the only quiet plans of the \(5\times 5\) board:
