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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 (11 years ago)

Unsolved Read Solution (7)

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Read Solution (7) :

RAKESH  (11 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  (11 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  (11 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  (11 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  (11 years ago)

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

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RAJRATAN  (11 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  (10 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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