Number of square???

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

FOIV6Q7GOHMB1SO

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
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