How to Lay Out Tiles to Create Largest Circular Area

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SUMMARY

The optimal arrangement for covering the largest circular area with twenty-four 6" x 6" metal squares is not a square layout. Instead, the most effective configuration involves arranging the tiles in a circular pattern, as demonstrated in the referenced resource. This method maximizes coverage of the circular area while utilizing all available tiles. The discussion emphasizes the importance of strategic layout over simple geometric shapes.

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joncarlos
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A few months ago during college apps I came across the following question:

a man has twenty-four 6" x 6" metal squares. he wants to lay them out on his desk so that he can cover as large a circular area as possible. how should he arrange the tiles? (note that the tiles will not form a circle themselves, but must completely cover the circular area.)

im not very good at math, so i chose to answer another question instead of this one for the application, but i always wondered what the answer to this problem was. the only thing i can think of is that you should lay the tiles out in a square...what do you guys think?
 
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Did you get to use a computer and how much time did you have for it?

According to this link http://www2.stetson.edu/~efriedma/sqcovcir/"

making a square is not the best solution if you have 16 squares, and you can't make
a square with 24 tiles anyway.
 
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we had as much time as we needed. it was a part of a college application I did. So yes, we were allowed to use a computer.
 

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