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Math Help - How many rectangles in a 10 x 10 checkerboard?

  1. #1
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    how many rectangles in a chess board

    how many rectangles in a chess board, I think it is 3025 but the teacher said no
    Last edited by MathGuru; December 10th 2005 at 03:23 PM.
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  2. #2
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    What was your logic that gave you that number?
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  3. #3
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    First, I created a checkerboard on paper and wrote in each square the number of rectangles that would use that square as a bottom right corner such as this:

    1 2 3 4 5 6 7 8 9 10
    2 4 6 8 10 12 14 16 18 20
    3 6 9 12
    4 8 12 16
    5 10 15 20 25
    6
    7
    8
    9
    10

    until I had the whole grid finished. Then I added them all up.

    Also, I found an equation on the internet that is supposed find the number of rectangles in a checkerboard. (also this isncludes squares)

    The formula is :

    [n(n+1)/2]^2

    therefore:

    [10(10+1)/2]^2
    =[10(11)/2]^2
    =[110/2]^2
    =55^2
    =3025


    Please, if you could help, it's really important.
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  4. #4
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    Quote Originally Posted by danielle_54321
    First, I created a checkerboard on paper and wrote in each square the number of rectangles that would use that square as a bottom right corner such as this:

    1 2 3 4 5 6 7 8 9 10
    2 4 6 8 10 12 14 16 18 20
    3 6 9 12
    4 8 12 16
    5 10 15 20 25
    6
    7
    8
    9
    10

    until I had the whole grid finished. Then I added them all up.

    Also, I found an equation on the internet that is supposed find the number of rectangles in a checkerboard. (also this isncludes squares)

    The formula is :

    [n(n+1)/2]^2

    therefore:

    [10(10+1)/2]^2
    =[10(11)/2]^2
    =[110/2]^2
    =55^2
    =3025


    Please, if you could help, it's really important.
    My solution agrees with what you have found, also a Google
    search seems to confirm that this is the correct answer to
    the problem as stated.

    Perhaps the actual wording of the problem set by your
    teacher was slightly different from what you have given?

    RonL
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