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The grid below contains 16 points whoce x and y coordinates are in the set of {0,1,2,3}. A square with all four vertices are among these 16 point has an area A. What is the sum of all possible A.

 

 Jan 31, 2021
 #1
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A = 1 + 4 + 9 = 14.

 Jan 31, 2021
 #2
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Thanks but the answer is not 14. But then why not 16 then? Could you please explain

 Jan 31, 2021
edited by geoNewbie21  Jan 31, 2021
 #3
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The guest  has  correct number of  squares, but  not the correct area sum

 

 

We will  have   9   1 x 1    squares    ....area  = 9

We will  have  4     2 x 2     squares ......area =  4 squares each with an area of  4 = 16

W will have  1   3 x 3     square........area =   9

 

 

The sum of these possible  A's    is     16 +  18 =   34

 

 ( I believe  this is correct....)

 

BTW....there is a formula  for finding the  number of squares in a n x n  grid like this

 

It    is   

 

  n ( n + 1) (2n + 1) / 6

 

Check

 

3 ( 4) ( 7)   /  6     =    84  / 6    =   14   !!!

 

cool cool cool 

 Jan 31, 2021
edited by CPhill  Jan 31, 2021
 #4
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No : the answer wa possible areas are 1,2,4,5, and 9 . So sum of all possible areas was 21

 Jan 31, 2021

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