Not a very Perlish answer, but perhaps helpful to a fellow Perl user in real life:
If this an actual real-life project in your backyard, I would just make a point of buying from a store that takes returns. Choose 5 or 6 sizes and buy approximately equal surface areas of each size to equal patio size + ~20%. Lay them out randomly following the rules. You'll spend less time, and get more exercise, working it out on your hands and knees in real time than you'll spend writing a progrma that produces a set of coordinates that almost noone can actually follow. Then, use the time you've saved to enjoy your new patio with your kids.
Like I said, not Perlish, but Perl-coders' real lives are more important than Perl itself. Call me crazy.
Forget that fear of gravity,
Get a little savagery in your life.
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