number of aquares.. HELP!!!!!!

JEE Mains 2015 Coaching › Algebra questions › number of aquares.. HELP!!!!!!

A square of n units by n units is divided into n² squares of 1 sq. unit each. find the number of ways in which 4 points ( out of (n+1)² points) be selected so that they form the vertices of a square.

i was able to count the number of squares whose sides are horizontal and those whose sides are at 45Â° to horizaontal. please tell me how to count squares of this type..

(they dont appear to be squares but they are if diagram is accurate)
also suggest any alternate method as i find this method cumbersome

#Mathematics #Algebra

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4 Answers

1

Samarth Kashyap ·2009-05-15 19:59:48

somebody please try.

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Samarth Kashyap ·2009-05-17 02:37:22

[7][7][7][7][7][7][7]

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9

Celestine preetham ·2009-05-17 06:49:38

method :

Observe that each square of side r can have exactly r-1 diff squares inscribed inside it .

So evidently in the region occupied by a rXr sqr , r sqrs are present .

we know no of rXr regions = (n+1-r)²

so ans is

Î£(n+1-r)² .r which can be calculated

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Samarth Kashyap ·2009-05-17 07:27:14

thanks a lot[1][1][1]

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