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Packing squares, again

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What is the area of the smallest square that holds five unit squares without overlap?

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Posted · Report post

I think the smallest square would be a 3 x 3.

If we start with the most compact area to contain 4 unit squares, it would be a 2 x 2 square. The addition of another unit square will force it to add at least one row or column - thus forcing you to a 2x3 configuration. To meet the criteria of the problem, we must expand that to a 3 x 3

There are multiple configurations [many are just reflections of others

# # #

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or

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or

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or ...

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Posted (edited) · Report post

Place four unit squares into the corners of the resulting square and the 5th one into the middle after a 45 degree rotation.



The diagonal of the new square:
d=sqrt(2)+1+sqrt(2)

giving the surface 4.5+2*sqrt(2) (about 7.33).
Edited by harey
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