It's an awful photo, but here's the gist of it. Imagine a 7x9 pentomino rectangle (with a little 3-cell hole) inside a 13x21 hexomino rectangle, inside a heptomino rectangle I can't remember the dimensions of and can't be arsed to count, all surrounded by the octominoes (plus 8 holes) in a whopping 47x85 rectangle. And that's what I spent an entire afternoon doing. Well, two sittings with a break for dinner in the middle.
It would maybe have been a bit nicer if I'd started with a central monomino and worked my way up through all polyomino sizes, a la Karl Wilk's Polyominium, but there didn't seem to be a way of doing it that yielded such nice symmetrical layers like this. It's difficult to wrap a pentomino rectangle around a hole big enough for just the tetrominoes, let alone anything else.
In fact, when I had the original idea that became this, it was born out of the fact I'd built a hexomino pattern that just happened to be able to fit the 7x9 rectangle inside.
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| A sort of precursor solution found way back. |
Fun fact about the 7x9 pentomino solution: when the triomino hole is vertical there are 360 possible solutions, whereas with the horizontal hole there are a mere 150 (excluding rotations, reflections and all that jazz.)
Here's the full solution drawn up so you can actually see where one piece ends and another begins:
And there's a little voice inside me saying "What about a layer of nonominoes?" but realistically I'm not going to be able to do that without a physical set of them and that ain't gonna be cheap. Besides, there's not a flat surface in my house big enough to hold all those pieces.
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