How can we do it?

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We all know that a chess board has 64 squares This can be completely covered by 32 cardboard rectangles, each cardboard covering just 2 squares. Supposing we remove 2 squares of the chess board at diagonally opposite corners, can we cover the modified board with 31 rectangles? If it can be done, how can we do it? And if it cannot be done, prove it impossible.

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    No It cannot be done. Each rectangle covers one white square and one black square, because on a chess board the white and black squares are always adjacent…..The two squares which we remove from the chess board are of the same colour, and so the remaining board has two more boxes of one colour than the other. And after the rectangles have covered 60 boxes, there will be left two squares of the same colour…… Obviously the remaining rectangle cannot cover these two squares.

    pnikam Expert Answered on 22nd August 2015.
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    It can not be done.
    When we remove 2 squares of the chess board at diagonally opposite corners they have the same color so there is a difference between the blacks and white colors now and  since each carboard is covering 2 squares that are made of black and white we cant cover two whites or two blacks squares

    Moshe Expert Answered on 12th January 2023.
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