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(#M40007797) 3I-INFOTECH Numerical Ability question Number Keep an EYE

Q. How many squares are there in a 10X10 matrix.

Asked In 3i-Infotech Romoni (13 years ago)

Unsolved Read Solution (6)

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Vignesh  (13 years ago)

385 squares of different sizes

1×1 squares: 10x10 = 100
2×2 squares: 9x9 = 81
3x3 squares: 8x8 = 64
.
.
.
10×10 squares: = 1

Total number of squares = 10^2 + 9^2+ 8^2 +...+1^2 = 385

Is this solution Helpfull? Yes (2) | No (1)  

Pargat Pal Singh  (13 years ago)

Total no of squares = 1^2+2^2+..+10^2= 385

Is this solution Helpfull? Yes (2) | No (1)  

Manavalan K R  (13 years ago)

385 squares of different sizes

1×1 squares: 10x10 = 100
2×2 squares: 9x9 = 81
3x3 squares: 8x8 = 64
.
.
.
10×10 squares: = 1

Total number of squares = 10^2 + 9^2+ 8^2 +...+1^2 = 385

Is this solution Helpfull? Yes | No (1)  

selva krishnan  (13 years ago)

Answer is 385.

Lets try to derive the General Pattern,

1) n=1
Matrix has only one number eg. 4.
So, no. of squares for n = 1 is 1.
2) n=2
Matrix has four numbers.
eg. 1 2
2 4
no. of 1x1 squares = 4.
no. of 2x2 squares = 1.
So, Total no. of Squares when n=2 is 5.
3) n=3
consider a 3x3 matrix of nine numbers.
eg. 1 2 3
2 4 6
3 6 9
no. of 1x1 squares = 9
no. of 2x2 squares = 4
no. of 3x3 squares = 1
so, Total no. of squares for n=3 is 14
Now, we compare the Results
For n=1 ans is 1(1^2)
for n=2 ans is 5(1^2+2^2)
for n=3 ans is 14(1^2 + 2^2 + 3^2)
........................
for n ans is the sum of 1^2 + 2^2 + 3^2 + ......+ n^2.
ie sum of the squares of natural number = n(n+1)(2n+1)/6;

Hence for n=10, we get no. of squares = 385

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niru  (13 years ago)

total 385
1*1
2*2
.
.
.
.
.10*10
so total them we get 385

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mayank  (11 years ago)

for n*n matrix total no of square is given by 1^2+2^2+......+n^2
in this case it is 1^2+2^2+......+10^2

so by formula ie: [n*(n+1)*(2n+1)]/6

=> [10*11*21]/6

=> 385

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NOTE: in n*n matrix total no of square are given by => [n*(n+1)*(2n+1)]/6

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