Tuesday, April 30, 2019

Heptominoes Part Deux

At the end of Part One, I mentioned trying for a 11x69 rectangle construction. Sadly, the table in my room isn't quite long enough to accommodate a heptomino construction 69 squares wide without having to rearrange things, so I settled for the next best thing: a 20x38 rectangle with four holes. Symmetrically-placed holes, I might add.

After about 45 minutes (either this was a fluke or I'm getting better) I found the following solution - or at least I thought I had:


Notice anything unusual?

That's right, I somehow managed to centre the four holes incorrectly. They're all one square up from where they should be, giving the total rectangle only one axis of symmetry instead of two. And I only noticed this right at the very end when it came to drawing up a neat copy of the solution.

In my defence, the table's perspective made it looks completely fine as I was solving. That, and I clearly couldn't be bothered to count to 17.

Actually, just for the hell of it, here's a bonus heptomino construction from a few weeks back.

The 108 heptominoes (and 3 monominoes) in a 23x33 parallelogram. You've gotta call the holes 'monominoes', it makes it sound more like they're intentional.
Those wiggly edges are an absolute nightmare. You can see on the left hand side where I started, I use up all the shapes with zig-zag edges and by the time I got to the right-hand side I was just desperately trying any vaguely wiggly piece I could get my hands on.
There'll be a parallelogram with base 23 and height 33 out there, but that would mean having to build even more wiggly edges again, so I'll pass on that one for now.

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