How many number of squares in below 8 x 8 chessboard??

64….???????

No it have *204 squares*.

How to find out easily.

*if we have n x n square like chess board, we find number of square easily using sum of squares up to n*

for e.g 8 x 8 square 1^2 + 2^2+…. 8^2 = 204 using formula *(n(n+1)(2n+1))/6*

ok if it have different row and column size then for e.g m x n then

If m x n size and m<=n then using below you can get, if its m > n then just swap it…

**Total number of squares = (m x (m+1) x (2m+1)/6 ) + ( (n-m) x m x (m+1)/2 )**

*Ref:*

*http://www.academia.edu/3626433/The_Total_Number_of_Squares_and_Rectangles_are_there_in_Rectangle_Square_Boards*

*http://www.geeksforgeeks.org/count-number-of-squares-in-a-rectangle/*

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## About Lekshmana Perumal M

Proud be an Indian, passion to teaching & learn, love mathematics, enjoy with family & friends, job to code. Care about child education, Indian culture