Latest TCS Aptitude Question SOLUTION: how many total no. of square in chess board...?

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(#M40029740) TCS question Square Keep an EYE

how many total no. of square in chess board...?

Asked In TCS ARUN GUPTA (11 years ago)

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RAKESH  (11 years ago)

no. of square of size 1*1=8*8=8^2
no. of square of size 2*2=7*7=7^2
no. of square of size 3*3=6*6=6^2
........
similarly
no of square of size 8*8=1*1
so total no. of square=
1^2+2^2+3^2+...+8^2=8(8+1)(2*8+1)/6=204

Is this solution Helpfull? Yes (37) | No   

Md.Sultan Khichi  (11 years ago)

n(n+1)(2n+1)/6
where n= no rows or clm
so 8(8+1)(16+1)/6=204

Is this solution Helpfull? Yes (13) | No (1)  

ARUN GUPTA  (11 years ago)

1^2+2^2+....+8^2 = 204

Is this solution Helpfull? Yes (4) | No   

Abhishek Kumar  (11 years ago)

answer should be 204 -:)

Is this solution Helpfull? Yes (4) | No (1)  

Syed Zohair Abbas  (11 years ago)

Consider the lefthand vertical edge of a square of size 1 x 1.
This edge can be in any one of 8 positions. Similarly, the top
edge can occupy any one of 8 positions for a 1 x 1 square.
So the total number of 1 x 1 squares = 8 x 8 = 64.

For a 2 x 2 square the lefthand edge can occupy 7 positions and
the top edge 7 positions, giving 7 x 7 = 49 squares of size 2 x 2.
Continuing in this way we get squares of size 3 x 3, 4 x 4 and so on.
the answer turns to be 204

Is this solution Helpfull? Yes (3) | No   

Shashidhar C  (11 years ago)

for num of squares formula is summation of n^2 where n is num of rows or columns
for num of rectangles formula is summation of n^3 where n is num of rows or colomns

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SANU CHANDRA  (11 years ago)

1^2+2^2+3^2+4^2+5^2+6^2+7^2+8^2
use this formula
n(n+1)(2n+1)/6 where n=8
=8(8+1)(2*8+1)/6=204

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Sarthak Chakraborty  (11 years ago)

no of squares = 1^2 + 2^2 +...+8^2 = 204

Is this solution Helpfull? Yes (3) | No (1)  

Suman Saurabh  (11 years ago)

toal no. of square=1^2+2^+.....+8^2=204

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DIVYA KUKRETI  (11 years ago)

ANS 204
simple formula:
number of squares in s square of side n*n=1^2+2^2+...+n^2
now, chess board is a square of side 8*8
so, no of squares=1^2+2^2+....+8^2=204

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Lakshmi Kundu  (11 years ago)

In ques it is not said that repetition is allowed or not.
1: If repetition is alowed--given solution is true.
2: if not...then the answer will be: 8^2+4^2+2^2+2^2+1+1+1+1=92

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amaresh  (11 years ago)

answer is 204

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Guru Pranav  (11 years ago)

204 !!!!

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soham ghosh  (11 years ago)

here is an way to find it-
let n=no of side horizontally
x=no of side vertically
so the no of squares will be=(n*x)+(n-1*x-1)+(n-2*x-2)+ .....
If n>x then stop when n=1
If x>n then stop when x=1
but here n=x so,
(8*8)+(7*7)+(6*6)+(5*5)+(4*4)+(3*3)+(2*2)+(1*1)=204

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