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Packing squares, again


Best Answer harey, 13 October 2013 - 06:55 PM

Spoiler for I think I can do better

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#1 bonanova

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Posted 12 October 2013 - 10:28 AM

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


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The greatest challenge to any thinker is stating the problem in a way that will allow a solution.
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#2 dgreening

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Posted 13 October 2013 - 06:22 PM

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

 

 

# # #

# # -

- - -

 

or 

 

# # #

# - -

# - -

 

 

or 

 

# - #

- # -

# - #

 

or ...


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#3 harey

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Posted 13 October 2013 - 06:55 PM   Best Answer

Spoiler for I think I can do better


Edited by harey, 13 October 2013 - 06:55 PM.

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