Post #2672399
2026-01-22 18:56 UTC
I think this by itself is NOT enough to find all specimens -- there are solutions that don't proceed solely from subdividing existing rectangles -- but it feels like a fun space to explore.
There's other kinds of transformations we can document as well; one is the basis of all this, transforming a square into a set of rectangles, and all our solutions for n are new members of that family.
But there's other things to look at to, like...
Replies (1)
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@joshmillard@mastodon.social 2026-01-22 19:00
What about this little move? Take an nxn square, and add some 2x4 and 1x2 rectangles to it to get a new n+2xn+2 square! I'm using an abstract square here rather than any other solution; we can do this with *any* known full solution of n, we're just looking at what gets added: a frame around two sides, which add five new rectangles.