Post #2672394
2026-01-22 18:36 UTC
This, for example, is what I have in mind: two solutions for n=6 which use different sets of rectangles.
(Someone already noted btw that I accidentally showed this right example upthread as an n=7 specimen. Whoops! Should have double-checked my late-night diagramming before posting.)
One uses two 1x2s and four 2x4s to make a 6x6 square; the other uses three 1x2s, one 2x4, one 3x6, and one 4x8 to make an 8x8 square. Qualitatively different species!
Replies (1)
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@joshmillard@mastodon.social 2026-01-22 18:38
Reiterating: the actual numeric values don't matter -- I am descrbing those two n=6 solutions above as filling a 6x6 and an 8x8 square respectively, but that's just for notational convenience: I'd rather describe the smallest rectangle as 1x2 in both cases than as 1/6x1/3 in one case and 1/8x1/4 in the other. It's all just proportions and we're breaking toward readability here.