Latest m4maths Aptitude Question SOLUTION: calculate the total no of squares of any size on a chess board

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(#M40013414) M4MATHS question logical Keep an EYE

calculate the total no of squares of any size on a chess board

Asked In m4maths parmeet (11 years ago)

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Sourav  (11 years ago)

Let us consider for the left hand column,
for 1*1 square there are 8 squares, so 8 squares on the topmost row also,
thus number of squares= 8^2 = 64

for 2*2 squares there are 7 arrangements of squares on first column and also first row,thus no. of squares= 7^2 = 49

for 3*3 squares we will get no. of squares= 6^2 = 36
hence by this way we can say:

Size Of square Number of squares
--------------- -----------------
1 * 1 8^2 = 64
2 * 2 7^2 = 49
3 * 3 6^2 = 36
4 * 4 5^2 = 25
5 * 5 4^2 = 16
6 * 6 3^2 = 9
7 * 7 2^2 = 4
8 * 8 1^2 = 1
---------------
Total no. of squares = 204
We can also calculate this by using the formula= 1^2 +2^2 +3^2 +...+n^2
= n(n+1)(2n+1)/6 where n=8
= 204 (Ans)

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