Post #2672367
2026-03-10 15:33 UTC
Boy this is a nice potent nerdsnipe. So, scratching around with it, a couple observations so far:
1. This is done with Tetris pieces (aka square tetrominoes), but it's not done with *all* the Tetris pieces -- some are never gonna fit in any finite 2xn tiling (let alone the 2x2n here): T and S/Z pieces are out of play. That leaves us with only O, I, and L/J pieces to work with.
(We're also omitting the tall/skinny rotations of I and L/J because we only have two blocks of height.)
Replies (1)
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@joshmillard@mastodon.social 2026-03-10 15:38
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.