Latest Miscellaneous Company Exam Aptitude Question SOLUTION: how many squares and rectangle has in chase board ??prove your answer...

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(#M40029718) MISCELLANEOUS COMPAN Logical Reasoning question Keep an EYE

how many squares and rectangle has in chase board ??prove your answer...

Asked In Miscellaneous Company Exam krishna yadav (10 years ago)

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RAKESH  (10 years ago)

a chess board has 9 vertical & 9 horizontal lines
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+3^3+...+8^2=8(8+1)(2*8+1)/6=204

a chess board has 9*9 lines
to form a rectangle
we have to choose 2 of the 9 vertical lines and 2 of the 9 horizontal lines
as square is also a rectangle
so no. of rectangles=9C2*9C2=36*36=1296

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

vishal rathore  (10 years ago)

for sqre u do , 1^2+2^2+3^2.....+8^2 , that is 17*12 squares
for recatangles u do 1^3+2^3+3^3+....+8^3, that is 36*36 rectangles =1296

Is this solution Helpfull? Yes (2) | No   

murthy  (10 years ago)

No'of squares equal to 'the sum of the squares of the first n natural numbers i.e
n(n+1)(2n+1)/6.
so here n=8 because it has 8 horizontal and 8 vertical lines.
now ANS= 8(9)(17)/6=204.

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sumit anand  (10 years ago)

No. of square= sigma of x*x = n*(n+1)*(2n+1)/6=204

No. of rectangle = sigma of x*x*x =[n*(n+1)/2]*[n*(n+1)/2] =1296

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RAJRATAN  (10 years ago)

[n(n+1)/2]^2-----for total rectangle = 1296

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RAJRATAN  (10 years ago)

[RAJRATAN]
[n(n+1)/2]^2-----for total rectangle = 1296
[n*(n+1)(2n+1)]/6-----for square = 204

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sravani  (9 years ago)

no.of squares = n(n+1)(2n+1) /6=204
no.of rectangles=(n+1)c2 * (n+1)c2=1296
as n=8.....

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