math problem?

Question

helppp! how many squares are there in a 8 by 8 checkerboard? hint: NOt 64!

Answer 1

There are 64 that are 1 × 1.

There are 49 that are 2 × 2.

There are 36 that are 3 × 3

There are 25 that are 4 × 4

There are 16 that are 5 × 5

There are 9 that are 6 × 6

There are 4that are 7 × 7

And finally,

There is 1 that is 8 × 8.

So that makes 204 squares

Answer 2

if you look at smaller cases, i.e., a 3 x 3 board or a 4 x 4 board, you will notice a pattern. Obviously, the number of 1 x 1 squares on an 8 x 8 board is 64. For 2 x 2 squares, you have 49 (7^2) possibilities. You can convince yourself of this by noticing that one end of any 2 x 2 square, say the top left end, must be contained in a 7 x 7 square which does not contain the bottom row or right column of the 8 x 8 board. Furthermore, the # of 3 x 3 squares in the 8 x 8 board is 6^2, which is 36. Summing 1^2 + 2^2 + 3^2 + ... + 8^2 gives 204 as your final answer.

Answer 3

Let's start with an easier question: how many 8 x 8 squares are there?

ans.: 1

Okay, here's a marginally harder question: how many 7 x 7 squares?

Well, there's one "in the bottom left corner" (it excludes the top row and the right-most column) one in the bottom right, one in the top left, and one ni the top right. There are 2 choices for the row to be excluded, and 2 choices for the column. So the answer is 4.

For 6 x 6 squares, there are 3 horizontal choices and 3 vertical, so that's 9 6 x 6 squares. We can go all the way to 1x1 squares where we have 8 x 8 = 64 choices.

So, in total, there are
1 + 4 + 9 + 16 + 25 + 36 + 49 + 64 = 204 squares.

Answer 4

1 by 1 : 1
2 by 2 : 5
3 by 3 : 14
4 by 4: 30
5 by 5: 55
6 by 6: 91
7 by 7: 140
8 by 8: 204
9 by 9: 285

just add the squares of the next one
the following one for a 10 by 10 would be
285 + 10^2 = 385

Answer 5

8^2 + 7^2 + 6^2 + .... + 2^2 + 1^2

64+49+36+25+16+9+4+1

204 is my guess.

You can draw 8^2 1x1 squares
and 7^2 2x2 squares... and so on.

Answer 6

its gotta be 64???!!! right???? 8X8=64 or i could be 1 because you don't say how big the squares are

Answer 7

Im guessing 78 but i think there's more