• exasperation@lemmy.dbzer0.com
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      3 days ago

      And the solutions we have for 5 or 10 appear elegant: perfect 45° angles, symmetry in the packed arrangement.

      5 and 10 are interesting because they are one larger than a square number (2^2 and 3^2 respectively). So one might naively assume that the same category of solution could fit 4^2 + 1, where you just take the extra square and try to fit it in a vertical gap and a horizontal gap of exactly the right size to fit a square rotated 45°.

      But no, 17 is 4^2 + 1 and this ugly abomination is proven to be more efficient.