Post #2672397
2026-01-22 18:47 UTC
So here's one thing on my mind: these solutions can be thought of in part as a transition from a single rectangle to a set of sub-rectangles. Here's a couple that have shown up in the specimens so far:
1. a four-way split of a single 2x4 rectangle into four 1x2 rectangles, like we did to get the original n=5 solution from the n=2 solution
2. a five-way split of a 4x8 into a 3x6, a 2x4, and three 1x2, like in the bottom of one of the n=6 solutions
Replies (1)
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@joshmillard@mastodon.social 2026-01-22 18:53
So maybe part of what we're doing is building up a vocabulary of valid transformations from a starting rectangle to distinct sets of multiple sub-rectangles. And then we could find some of the solutions for any given n by looking at various kinds of transformations that add some number m rectangles to a smaller solution of size n-m. i.e. if we know an n=2 solution, and we know there's a +3 transformation, that gives us an n=5 specimen. (Which is sort of where we started!)