this post was submitted on 26 Jun 2024
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We've figured out optimal packing methods for any number of squares inside a big square. When a number is below and near a square number like 15, you just leave an empty box, but when it's far from the next square number, you'll be able to pack them more efficiently than just leaving empty squares around. Turns out this kind of stuff is hilariously hard to prove that it's the most efficient method.