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Math Help - Number of rectangles on a checkerboard

  1. #1
    Member oldguynewstudent's Avatar
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    Number of rectangles on a checkerboard

    How many different rectangles are hiding in a 4 X 7 checkerboard?

    Hint: Any rectangle is uniquely specified by the two horizontal and two vertical grid lines that enclose it.

    For a two by three checkerboard, I drew 18 different rectangles which seem to correspond to

    \left({4\atop 2}\right) * \left({3\atop 2}\right)

    So I think the answer to the original problem would be

    \left({8\atop 2}\right) * \left({5\atop 2}\right)

    Is this correct reasoning?
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  3. #3
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    Re: Number of rectangles on a checkerboard

    ans. will be 280 rectangles.
    Last edited by sumittripathi15; October 27th 2012 at 08:30 PM.
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