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Black and white squares

Posted on: April 22nd, 2013 by
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Consider an n x n chessboard, where each square is arbitrarily chosen to be either black or white. Your goal is to make all squares in the chessboard white. At each step, you are allowed to "switch" a square, but each switch will toggle not only the particular square being switched, but also the 4 squares that are adjacent to it: Two vertically up and down and two horizontally up and down the square being switched. Show how you can make the entire chessboard white.
(NOTE: At corners only 4/3 squares are toggled, while at the center all 5 squares are toggled.)

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