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.geeksforgeeks.org/count-number-of-squares-in-a-rectangle/
Lekshmana Perumal Murugan 