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There is a total of 70 squares of three sizes whose vertices are points on this rectangular $3\times n$ grid of points. What is the value of $n$?

 Jun 28, 2021
 #1
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http://www.stutzfamily.com/mrstutzblog/wp-content/uploads/2012/02/2009_Chapter_Solution_Set_2009_-_v2.pdf 

Page 7

 Jun 28, 2021
 #2
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when I click on the link the page says "404 ERROR"

Guest Jun 28, 2021
 #3
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Here

Guest Jun 28, 2021
 #4
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I also have had this problem for alcumus- it was a very challenging one ! I eventually solved it, so I can give you a hint:

Consider the possible ways to make a square. Find a pattern in each of every one of them. Add them up to form an equation, and the answer is your answer.

I will post a solution later

 Jun 28, 2021
 #5
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oops I know my mistake, I forgot to include the squares made from going diagonal between the dots!

Guest Jun 28, 2021

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