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

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In how many ways can a square be identified in a chess board (figure a  [#permalink]

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New post 02 Mar 2019, 00:08
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Difficulty:

  75% (hard)

Question Stats:

29% (01:34) correct 71% (01:15) wrong based on 34 sessions

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In how many ways can a square be identified in a chess board (8x8 squares) (figure attached)?

A) 64
B) 65
C) 204
D) 205
E) 408

http://www.GMATinsight.com

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chess.jpg
chess.jpg [ 44.46 KiB | Viewed 458 times ]


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Re: In how many ways can a square be identified in a chess board (figure a  [#permalink]

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New post 02 Mar 2019, 03:58
2
GMATinsight wrote:
In how many ways can a square be identified in a chess board (8x8 squares) (figure attached)?

A) 64
B) 65
C) 204
D) 205
E) 408

http://www.GMATinsight.com


total no of squares which can be formed in a 8x8 chess board :
no of 1*1 squares ; 8*8 = 64,
2*2 squares= 7*7 , 3*3 squares = 6*6;36, 4*4 squares=5*5
5*5 squares = 4*4
6*6 squares = 3*3
7*7 squares =2*2
8*8 squares = 1*1
total
1^2+2^2+3^2+....+8^2
1+4+9+16+25+36+49+64
IMO C ; 204
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Re: In how many ways can a square be identified in a chess board (figure a  [#permalink]

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New post 07 Mar 2019, 16:57
1
Archit3110 wrote:
GMATinsight wrote:
In how many ways can a square be identified in a chess board (8x8 squares) (figure attached)?

A) 64
B) 65
C) 204
D) 205
E) 408

http://www.GMATinsight.com


total no of squares which can be formed in a 8x8 chess board :
no of 1*1 squares ; 8*8 = 64,
2*2 squares= 7*7 , 3*3 squares = 6*6;36, 4*4 squares=5*5
5*5 squares = 4*4
6*6 squares = 3*3
7*7 squares =2*2
8*8 squares = 1*1
total
1^2+2^2+3^2+....+8^2
1+4+9+16+25+36+49+64
IMO C ; 204


Hello Archit3110 !

Could you please explain to me how do you get to 2*2 = 7*7 and 3*3 = 6*6?

I'm having trouble to see those squares.

Kind regards!
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Re: In how many ways can a square be identified in a chess board (figure a  [#permalink]

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New post 08 Mar 2019, 01:19
jfranciscocuencag wrote:
Archit3110 wrote:
GMATinsight wrote:
In how many ways can a square be identified in a chess board (8x8 squares) (figure attached)?

A) 64
B) 65
C) 204
D) 205
E) 408

http://www.GMATinsight.com


total no of squares which can be formed in a 8x8 chess board :
no of 1*1 squares ; 8*8 = 64,
2*2 squares= 7*7 , 3*3 squares = 6*6;36, 4*4 squares=5*5
5*5 squares = 4*4
6*6 squares = 3*3
7*7 squares =2*2
8*8 squares = 1*1
total
1^2+2^2+3^2+....+8^2
1+4+9+16+25+36+49+64
IMO C ; 204


Hello Archit3110 !

Could you please explain to me how do you get to 2*2 = 7*7 and 3*3 = 6*6?

I'm having trouble to see those squares.

Kind regards!


likewise, for me I see 16 squares that are 2x2 rather than 49,
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In how many ways can a square be identified in a chess board (figure a  [#permalink]

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New post Updated on: 08 Mar 2019, 02:13
1
Ish1996 & jfranciscocuencag

Solution attached

I solved question by visualising squares...

hope this helps

solution in two parts... :)

kind apologizes for my bad handwriting .. hope you are able to understand whats written..
Attachments

File comment: File 1
IMG_20190308_143223988.jpg
IMG_20190308_143223988.jpg [ 3.95 MiB | Viewed 195 times ]


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Originally posted by Archit3110 on 08 Mar 2019, 02:06.
Last edited by Archit3110 on 08 Mar 2019, 02:13, edited 3 times in total.
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In how many ways can a square be identified in a chess board (figure a  [#permalink]

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New post 08 Mar 2019, 02:08
1
Ish1996 & jfranciscocuencag

part 2 ...
hope this helps... :)
Attachments

File comment: File 2
IMG_20190308_143228986.jpg
IMG_20190308_143228986.jpg [ 3.51 MiB | Viewed 185 times ]


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In how many ways can a square be identified in a chess board (figure a   [#permalink] 08 Mar 2019, 02:08
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