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

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• June 10th 2007, 06:55 PM
jhonwashington
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.
• June 10th 2007, 07:53 PM
ThePerfectHacker
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.
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The problem generalizes.
Given a $n\times n$ big square.
Then the total number of square is:
$1^2+2^2+3^2+...+n^2 = \frac{n(n+1)(2n+1)}{6}$