How many squares can you get with a 64 square grid?

Answer 1

I'll assume the 64 square grid is 8 by 8, like a chess board. There are a few ways to interpret this; the solution below is for squares whose sides match sides on the grid. If you allow squares whose sides are slanted, there are many more.

Count the squares by their size. There are 64 1x1 squares. For 2x2, there are 7 along the top, 7 down the side, so 49 total. For 3x3, there are 6 along the top, 6 down the side, so 36 of those. You see the pattern: 25 4x4, 16 5x5, 9 6x6, 4 7x7, and the 1 single 8x8. That makes 64 + 49 + 36 + 25 + 16 + 9 + 4 + 1 = 204 total.

Answer 2

Quite a few. You have the 8x8 biggie and 64 single width squares. But you can make 2x2s and 3x3s up through 7x7s. I believe the sequence is that there will be 7^2 2x2s, 6^2 3x3s, etc.
Then you can add up all the squares.

Answer 3

assuming that it's 64 square tiles, then yes, you can construct an 8 by 8 square from 64 tiles.