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Math Help - Ten by Ten grid

  1. #1
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    Ten by Ten grid

    How many squares can be made from a grid of ten by ten dots (ignore diagonal squares)?
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  2. #2
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    Quote Originally Posted by Aquafina View Post
    How many squares can be made from a grid of ten by ten dots (ignore diagonal squares)?
    Here is a strong hint to get you started.

    if we draw the vertical sides of the square and extend them all the way to the top and bottom of the grid, how many choices are there for the lines? Just as many ways as there are to choose 2 objects out of 10.
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    Quote Originally Posted by awkward View Post
    Here is a strong hint to get you started.

    if we draw the vertical sides of the square and extend them all the way to the top and bottom of the grid, how many choices are there for the lines? Just as many ways as there are to choose 2 objects out of 10.
    Hi, what I did was that if there are 10x10 dots, then we can make:

    9x9 (1x1 squares), 8x8 (2x2 squares), 7x7 (3x3 squares),....., 1x1 (9x9 squares)

    So in total, we can make: 1^2 + 2^2 + .... + 9^2 = 315

    is this correct?
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    Quote Originally Posted by Aquafina View Post
    Hi, what I did was that if there are 10x10 dots, then we can make:

    9x9 (1x1 squares), 8x8 (2x2 squares), 7x7 (3x3 squares),....., 1x1 (9x9 squares)

    So in total, we can make: 1^2 + 2^2 + .... + 9^2 = 315

    is this correct?
    Hi Aquafina,

    Your method is correct, but I think you better check your arithmetic.

    (The "hint" I gave wasn't very helpful in this case. I had a different but very similar problem in mind-- sorry, I didn't mean to mislead.)
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