Some squares: How many squares are in this grid of squares?

[Spambot]

How many squares are in this square?

I counted:
25 1x1 squares
16 2x2 squares
9 3x3 squares
4 4x4 squares
and 1 5x5 square

Am I correct and does this way work for different sizes of squares e.g. A 4x4 square would have 1² + 2² + 3² + 4² number of squares?

 

[Dr.Peterson]

How many squares are in this square?

I counted:
25 1x1 squares
16 2x2 squares
9 3x3 squares
4 4x4 squares
and 1 5x5 square

Am I correct and does this way work for different sizes of squares e.g. A 4x4 square would have 1² + 2² + 3² + 4² number of squares?

Assuming each little box is square (they don't look like that on the actual page), your answer is correct. There are 5^2 places that can be the upper left corner of a 1x1 square, 4^2 places for a 2x2 square, and so on. The rule generalizes to any size.