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Algebra

Blazing goIITian

Joined:	20 May 2008
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15 Jun 2008 12:56:27 IST

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475

How many squares and rectangles are possible in a chess board( having 64 squares)?

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How many squares and rectangles are possible in a chess board( having 64 squares)?

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®µD®A

Blazing goIITian

Joined: 12 Apr 2008

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15 Jun 2008 13:01:52 IST

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1296 rectangles

Vivek Roy

Blazing goIITian

Joined: 20 May 2008

Posts: 332

15 Jun 2008 13:03:03 IST

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Yeah but how..............even i can refer a book and answer.

®µD®A

Blazing goIITian

Joined: 12 Apr 2008

Posts: 2717

15 Jun 2008 13:07:18 IST

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You can use the formula

No of rectangles=[{n(n+1)}/2]^2

®µD®A

Blazing goIITian

Joined: 12 Apr 2008

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15 Jun 2008 13:08:07 IST

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this is the formula for a n*n square.

SUNDEEP ALLAMRAJU

Blazing goIITian

Joined: 28 Feb 2008

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15 Jun 2008 13:12:50 IST

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To find no. of squares,we have,

No.of 1X1 squares=8X8

No.of 2X2 squares=7X7

.....

No.of 8X8 squares=1X1.

So,total no. of squares=1²+....+8²=(8)(9)(17)/6=(17)(12)=204.

®µD®A

Blazing goIITian

Joined: 12 Apr 2008

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15 Jun 2008 13:14:13 IST

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oh sorry didn't see that no. of squares. formula = {n(n+1)(2n+1)}/6=204
in a n*n square.

Priyesh

Blazing goIITian

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15 Jun 2008 13:14:27 IST

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total no. of rectangles (including squares) are

9C2 * 9C2 = 1296

sumeet

Cool goIITian

Joined: 19 May 2008

Posts: 47

4 Feb 2010 21:02:43 IST

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dude...the answer is 9C2 multiplied by 9C2.

first of all...you have to select any two lines forming a horizontal row on a chess board and then you have to select any two lines forming the vertical column on chess board and according to multiplication theorem multiply them

now for more clarification...

a square or a rectangle is formed when one pair of parallel lines intersects other pair of parallel lines.

In chess board as there are 9 vertical lines parallel to each other and 9 horizontal lines parallel to each other...forming 8 rows and 8 columns

in order to form a square or a rectangle ...you have to select any 2 of the vertical lines AND two of the horizontal lines

and according to multiplication theorem(wrt to the the word AND above)the answer is 9C2 * 9C2.

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