Math
posted by Ell .
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!

a web search turns up several wellexplained solutions

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.
Respond to this Question
Similar Questions

counting
how many squares are in an 8x8 checkerboard? 
Math
Okay so I have to find how many total squares are in an 8 by 8 checkerboard. I have a roman letter thing that kinda looks like a capitol 'e' but without the middel line. On the bottom I have N=1 on the side of it i have N^2 and 8 on … 
math
a quilter wants to use as many of his 65 small fabric squares as possible to make one large square quilt . A how many small squares can the quilter use ? 
math
how many differnt squares are in each figure ? 
math HELP!!
Adam colored two parts of a 4 × 4 grid. He colored 1_ 2 of the squares red and 1_ 4 of the squares blue. How many of the squares are not colored? 
MATH
Carolyn and Kim are selling lemonade this summer. It costs $0.10 to make each cup of lemonade. They are going to sell each cup of lemonade for $0.25. a. What is the total cost to make 55 cups of lemonade? 
Math
a standard checkerboard with 8 blocks to a side contains 204 squares of various sizes. in how many such squares are there an equal number of red blocks and black blocks? 
math
suppose you covered your desktop with small squares.Then you cover your desktop with large squares.Would you use more small squares or large squares? 
Statistics Please Help
Hi Ms. Sue I was wondering if you could give me some advise in doing explain and unexplain variation and leastsquares regression line. I know how to compute the numbers, but I am having a problem with: say there is 3.0270, 30.0463 … 
math quadratic functions
Alice cuts a ribbon of length 40cm into two pieces to form two squares as shown in th figure (there was no figure, but from my assumption the two squares are probably different ). Let xcm be the length of a side of one of the two squares …