+126 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.
+126 Thanks but the answer is not 14. But then why not 16 then? Could you please explain
+129847 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 !!!
+126 No : the answer wa possible areas are 1,2,4,5, and 9 . So sum of all possible areas was 21
