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Nine squares, each one either black or white, are arranged in a 3X3 grid. Figure shows one possible arrangement. When touched, each square changes its own state and the states of some of its neighbors (black --->white and white---> black). State changes for the nine squares puzzle how the state changes work. (Touching the square whose number is circled causes the states of the squares marked * to change.) The object of the game is to turn all nine squares black. (a) If the initial configuration is the one shown in Figure, show that the game can be won and describe a winning sequence of moves. (b) Prove that the game can always be won, no matter what the initial configuration.
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