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In the diagram above, there is a 6 dotted lattice. 

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How many squares in the plane have two or more vertices on dots in this grid? All dots are an equal distance from their nearest neighbors. 

 

 

 

--> Thank-you for taking a look at my question. 

 Mar 29, 2021
 #1
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How many have you counted?

 

Say the horizontal distance between the dots is 1 unit.

 

How many 1x1 squares will there be?

How many 2*2 squares will there be?

How many sqrt2 x sqrt2 squares will there be?

How many sqrt2/2  x  sqrt2/2  squares will there be?

How many  sqrt5  x  sqrt5  squares will there be?

 

Have I missed any?

 Apr 3, 2021
edited by Melody  Apr 3, 2021

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