Post #2672368
2026-03-10 15:38 UTC
Now, L/J can be thought of as the same piece mirrored across one axis; we can't actually just treat it as the same at all times (more on that) but for organizational simplicity let's call it L. O, I, L are our three piece types.
From there we can say that every possible tiling of a 2x2n rectangle is going to be made up of one of these seven subsets of O, I, and L:
{O}, {I}, {L}, {O,I}, {O,L}, {I,L}, {O,I,L}
So that might be as good a way as any to organize our specimens.
Replies (1)
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@joshmillard@mastodon.social 2026-03-10 15:44
The first couple of values of n are very trivial: n = 1 (so 2x2n = 2x2) the only solution is a single O. n = 2 (so 2x4) has four solutions: a pair of O's, a pair of I's, and two different orientations of a pair of L's. But me being me, I want to avoid repetitions across mirror/rotational symmetry, so I'm going to decide that second pair-of-L's isn't interestingly different from the first one. I'm only going to count that once. So really we have three n=2 solutions, controlling for symmetry.