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.

2. 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

Given a $n\times n$ big square.
$1^2+2^2+3^2+...+n^2 = \frac{n(n+1)(2n+1)}{6}$