What will be the total number of squares in a chessboard ?
2305
The number of squares with side 8x8 = 1
Let us consider a mxm square at the upper left corner.
Each time we move the square towards right we get a new square.
Each time we move the square downwards we get a new square.
Since there are 8-m options while going towards left as well as down.
No. of mxm squares = (8-m)*(8-m) = (8-m)2
\dpi{200} \sum_{i=0}^{8} (8-m)^{2} = \sum_{i=0}^{8}m^{2} = \frac{8(8+1)(2\cdot 8+1)}{6}
Answer-204
105712+22+32....+82 which is 204.
Suvajit Sinha Thanks for adding the sum for squared numbers upto 8 . But actually i asked for the number of squares in the chessboard
Soumyabrata Mondal @suvajit, 204 is the total number of squares in a chessboard...:PSuvajit Sinha @Soumyabrata , i know its 204 :) and that is also using
n(n+1)(2n+1)/8 , but the deduction and the explanation with details is necessary :PSuvajit Sinha Sorry , instead of n(n+1)(2n+1)/8 it would be n(n+1)(2n+1)/6 . A typo error :P
Hardik Sheth @ketan..we obviously know that n(n+1)(2n+1)/6 is wat u told...you of course dnt knw hw people want you to give d ans!!!
996no.of squares = n(n+1)(2n+1)/6
In our case, with n = 8, this formula gives 8 x 9 x 17/6 = 204.