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avatar+2720 

How many different rectangles with sides parallel to the grid can be formed by connecting four of the dots in a 4*4 square array of dots, as in the figure below?

 

https://latex.artofproblemsolving.com/a/4/a/a4a59568ea933ddf215ba70b428ac6b8615d7cb2.png
(Two rectangles are different if they do not share all four vertices.)

tertre  Feb 12, 2018
 #1
avatar+86939 
+1

i believe there is a "formula" for this

 

We have a pattern of   3 x 3  "boxes"

 

The possible rectangles  =  [ 3(4) / 2] * [ 3(4)/2]   = [ 6 ] * [ 6 ]   =   36

 

 

cool cool cool

CPhill  Feb 12, 2018
 #2
avatar+2720 
+1

I see now! Thanks for the explanation, CPhill!smiley

tertre  Feb 12, 2018

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