Post #2672387
2026-01-22 17:56 UTC
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.
Replies (1)
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@joshmillard@mastodon.social 2026-01-22 17:59
The same is true for the n=6 solution, which adds four new rectangles to the n=2 solution (by, for example, wrapping four larger rectangles around the original two). And you can keep doing that for any square: do the "wrap-around" technique to add four more rectangles. n=10 is just n=6 with another layer! So for any solution n, we also have n+4, n+8, ... ad inf.