Chessboard riddle

On the right, you see a paper with a chessboard print on it. We want to cut the chessboard paper into pieces (over the lines!) such that each piece has twice as much squares of one color than of the other color (i.e. twice as much black squares as white squares or twice as much white squares as black squares).

Is it possible to do this? Give a proof!

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SherlockHolmes Expert Asked on 19th September 2018 in Aptitude Question.
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  • 1 Answer(s)

    No, it is not possible to cut the chessboard paper into pieces such that each piece has twice as much squares of one color than of the other color.

    If it would be possible, then every piece would have a number of squares divisible by 3 (because if a piece has n squares of one color and 2×n squares of the other color, it has 3×n squares in total).
    The total number of squares of all pieces would then also be divisible by 3.
    This is, however, impossible since the total number of squares on the chessboard is 64, which is not divisible by 3.

    SaintlyZero Guru Answered on 19th September 2018.
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