Post #2672396
2026-01-22 18:41 UTC
So how many ways ARE there to solve n=6 with distinct sets of rectangles? Are these two it, or are there more? How about 7? 8? And how can we prove that we've exhausted all the possibilities?
I cannot emphasize how much I do not know the answer to any of those questions. We are done with the "saying things I've already satisfied myself about" part of the discussion, now it's just mucking around and seeing what we notice.
So!
Replies (1)
-
@joshmillard@mastodon.social 2026-01-22 18:47
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