Post #2672400
2026-01-22 19:00 UTC
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.
Replies (1)
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@joshmillard@mastodon.social 2026-01-22 19:05
More specifically, that transformation works if we treat the source square as 6x6 if we want the new rectangles to have nice integer values for their side lengths. But it's all just proportional. We can do a similar idea with more rectangles that have a different proportion: for this example consider the square 7x7, and we see a collection of new 1x2 and 2x4 rectangles creating a DIFFERENT frame.