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Math Help - please help! find the # of squares in the figure.

  1. #1
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    please help! find the # of squares in the figure.

    Hello everybody.

    Could you please go to this page aurora.wells.edu/~acs/math105/lectures/pexam1.rtf and help me to solve question number 18, I can't understand that question, in class we have a similar exercise, the professor provide us with a figure which apparently seemed to have 9 squares, I mean just by counting them, but the professor told us it had 14 squares, in the exercise of the page that I just posted I Genuinely would say that that figure has 25 squares, but I know that it would be wrong because that's exactly what happened with the exercise in the classroom.
    thank you.
    Attached Thumbnails Attached Thumbnails please help! find the # of squares in the figure.-picture8.gif  
    Last edited by ThePerfectHacker; June 10th 2007 at 06:55 PM.
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  2. #2
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    We will do this problem in parts.

    1)How many 1x1 squares? The answer is 5^2 = 25

    2)How many 2x2 squares? The answer is 4^2 = 16

    3)How many 3x3 squares? The answer is 3^2 = 9

    4)How many 4x4 squares? The answer is 2^2 = 4

    5)How many 5x5 squares? The answer is 1^2 = 1

    Add those up to get your answer.
    ---
    The problem generalizes.
    Given a n\times n big square.
    Then the total number of square is:
    1^2+2^2+3^2+...+n^2 = \frac{n(n+1)(2n+1)}{6}
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