Math

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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 -

    a web search turns up several well-explained solutions

  • Math -

    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.

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