Posted by **Ell** on Thursday, October 27, 2011 at 5:06pm.

How many total squares are there on a standard 8 by 8 checkerboard?

(It is more than 64)!

Make sure to show all your work and explain your reasoning.

Explain how you can determine the number of

total squares for any N by N board.

Bonus: How many total rectangles?

Thanks!

- Math -
**Steve**, Thursday, October 27, 2011 at 5:28pm
a web search turns up several well-explained solutions

- Math -
**MathMate**, Thursday, October 27, 2011 at 5:30pm
Number of 1x1 squares = 64.

Number of 2x2 squares:

7 rows x 7 columns = 49

Number of 3x3 squares:

6 rows x 6 columns = 36

....

Number of 8x8 squares:

1 row x 1 col. = 1

So the total number of squares

=1²+2²+3²+...+8²

=n(n+1)(2*n+1)/6

where n=8.

## Answer This Question

## Related Questions

- Math - Okay so I have to find how many total squares are in an 8 by 8 ...
- counting - how many squares are in an 8x8 checkerboard? (the answer is not 64 ...
- Math - a standard checkerboard with 8 blocks to a side contains 204 squares of ...
- math quadratic functions - Alice cuts a ribbon of length 40cm into two pieces ...
- math - how many differnt squares are in each figure ? count the small squares ...
- math - suppose you covered your desktop with small squares.Then you cover your ...
- Statistics Please Help - Hi Ms. Sue I was wondering if you could give me some ...
- math HELP!! - Adam colored two parts of a 4 × 4 grid. He colored 1_ 2 of the ...
- math - a quilter wants to use as many of his 65 small fabric squares as possible...
- MATH - Carolyn and Kim are selling lemonade this summer. It costs $0.10...

More Related Questions