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Thread: Chess board?

  1. #1
    Expert Member
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    Jun 2006
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    410

    Chess board?

    Let me ask you a very familiar question,

    How many squares are there on a chessboard? How many rectangles?


  2. #2
    Contributing Member
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    Sep 2006
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    962

    Re: Chess board?

    Number of squares in a chessboard:

    1^2 + 2^2 + 3^2 + 4^2 + 5^2 + 6^2 + 7^2 + 8^2 = 204.

    Formula N = (n(n+1)(2n+1))/6

    Number of rectangles in a chessboard:

    There are 9 vertical lines and 9 horizontal lines. To form a rectangle
    you must choose 2 of the 9 vertical lines, and 2 of the 9 horizontal
    lines. Each of these can be done in 9C2 ways = 36 ways. So the number
    of rectangles is given by 36^2 = 1296.

    Formula N = (n(n+1)/2)^2

    --------------------
    suresh


  3. #3
    Contributing Member
    Join Date
    Aug 2007
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    59

    Re: Chess board?

    Number of squares in a chessboard:

    1^2 + 2^2 + 3^2 + 4^2 + 5^2 + 6^2 + 7^2 + 8^2 = 204.

    Formula N = (n(n+1)(2n+1))/6

    mmm suresh are u sure thats 204 squares in chess board!!!


  4. #4
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    Sep 2006
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    962

    Re: Chess board?

    If you have a doubt then work it out manually (first work it out 3x3 and 4x4) and let me know if it is correct or not.

    ----------------------
    suresh


  5. #5
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    Aug 2007
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    59

    Re: Chess board?

    ya suresh i go it now!!!


  6. #6
    Junior Member
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    Jan 2008
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    1

    Re: Chess board?

    squares-204


  7. #7
    Expert Member
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    Jun 2006
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    410

    Re: Chess board?

    Right approach from Suresh. Hats off man


  8. #8
    Banned
    Join Date
    Oct 2009
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    6

    Re: Chess board?

    no yaar.........chess board has 205 squares....coz chess board itself is also a square


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