Post #2672373
2026-03-12 17:05 UTC
Coming back to this to look at some patterns and make a couple more notes.
First off: for odd n, there's never going to be a solution that uses ONLY L or ONLY I shapes. Which makes sense: for a 2x2n rectangle for odd n, you'd need to arrange n-1 I's or L's into most of the space (and the only way we know how to do that is 2x4 blocks) and then fit one extra one into...a 2x2 space. Oops! So for odd n, those specimens just will never exist.
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@joshmillard@mastodon.social 2026-03-12 17:09
The other interesting thing is where totally new specimens show up -- that is, solutions that aren't a combination of two smaller solutions. The answer seems to be "literally only in the I+L row", and only and exactly one for each successive value of n >= 3. I've highlighted all brand-new specimens in green. n=1 introduces the O as a 2x2 solution n=2 has two I's and two L's respectively as new 2x4 solutions n=3 has a new L+L+I 2x6 solution n=4 has a new L+L+I+I n=5 has a new L+L+I+I+I...