TITLE: Packing squares into a circle
QUESTION [8 upvotes]: I need determine the maximum number of squares  of the given size that can be packed into a circle of the given radius. Squares can  be rotated. I'm not sure how complex this problem is and i can find little about it on the other sites.

REPLY [15 votes]: This is a hard case-by-case problem.  This beautiful page shows the records for the smallest circle packed with $n$ unit squares for $n$ from 1 to 35.  You can see that there's nothing obvious about most of the solutions.  Of course, as you pack more and more squares into a circle, there's less and less to be gained by finding a clever arrangement.