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In how many ways can a square be identified in a chess board

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In how many ways can a square be identified in a chess board

by GMATinsight » Fri Mar 01, 2019 10:56 pm

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In how many ways can a square be identified in a chess board (figure attached)?

A) 64
B) 65
C) 204
D) 205
E) 408
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Re: In how many ways can a square be identified in a chess board

by youcanyouwill » Wed May 27, 2020 10:37 pm
The number of squares present in square matrix of size

N*N =N*N+(N-1)*(N-1)+(N-2)*(N-2)+.....+1*1.

For a Chess Board , the size is of:

8*8=8*8+7*7+6*6+5*5+4*4+3*3+2*2+1*1=64+49+36+25+16+9+4+1=204.

This can be done in a simple way

The above formula computes to sum of the squares of N natural numbers:

N(N+1)(2N+1)/6
But can you beat A.I at chess unblocked in level 10?
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