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# Counting & Probability Problem

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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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Page 7

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

Guest Jun 28, 2021
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Here

Guest Jun 28, 2021
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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
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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