**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.

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MathyGoo13 Mar 29, 2021

#1**+1 **

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?

Melody Apr 3, 2021