There are 49 of the smallest squares.
However, any grid forms "squares" that consist of more than one of the smallest squares.
For example, there are four different 6x6 squares that each include 36 of the small squares, nine different 5x5 squares, sixteen 4x4 squares, twenty-five 3 x 3 squares, and thirty-six different squares that contain 4 of the small squares. One could therefore discern 140 distinct "squares."
The number can be calculated from the formula
[(n)(n+1)(2n+1)] / 6
where n is the grid size.
100
There are 5 squares in a 2 by 2 grid if the large square enclosing all four smaller squares is included in the count.
If they are 1 x 1 squares there would be 144 in a 12 x 12 grid.
608
30
4 squares in a 2 by 2 grid 9 squares in a 3 by 3 grid 16 squares in a 4 by 4 grid 25 squares in a 5 by 5 grid 36 squares in a 6 by 6 grid 49 squares in a 7by 7 grid 64 squares in a 8 by 8 grid 81 squares in a 9 by 9 grid 100 squares in a 10 by 10 grid
7 x 7 = 49
12 squares.
5
25
100
There are 5 squares in a 2 by 2 grid if the large square enclosing all four smaller squares is included in the count.
If they are 1 x 1 squares there would be 144 in a 12 x 12 grid.
608
30
400
2 x 2 = 4 squares