Post #2672386
2026-01-22 17:51 UTC
So, quick summary of what the video covers: there is *no* solution for n=1 (can't fill a square with one rectangle half its size), and also none for n=3 or n=4. (Try it!)
So after n=2 our next solution is for n=5: take one of the rectangles and divide it into four smaller rectangles, voila!
For n=6, we also have a solution: wrap four larger rectangles around a core of two smaller rectangles, voila!
Replies (1)
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@joshmillard@mastodon.social 2026-01-22 17:56
Well, what about larger values of n? The video makes a beautiful point: both the n=5 and n=6 solutions can be repeated indefinitely. e.g. you can get from 2 to 5 by subdividing one rectangle into four, essentially adding three new rectangles. You can then do the same thing again to any of those 5 rectangles to get to 8: split up the remaining large one, or split up one of the new smaller ones. And you always do that, so for any solution n, you've got n+3, n+6, ad inf.