Post #2672376
2026-03-12 17:28 UTC
The implication of the uniqueness of this one specimen is that *every other solution* for n >=3 is simply the concatenation of two or more previous solutions for smaller values of n. Which makes sense: other than this one configuration that constantly overlaps its layers of I shapes, every other solution ends in a nice flat wall on both sides. They can be mashed together arbitrarily to create a longer solution made up of distinct unrelated parts.
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@joshmillard@mastodon.social 2026-03-12 17:30
And once we're talking concatenation it starts to feel interesting and tingly to remember that this all started with an observation about the Fibonacci sequence, which is all ABOUT concatenating smaller values. People capable of crunchy analysis can tackle the actual formal combinatorics here, I know better than to try and put myself and others through that. But it's neat!