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.
exasperation@lemmy.dbzer0.com 2 months 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.