Saturday, April 6, 2019

Solving Strategy (or a lack of it)

I wish there was more out there on technique when it comes to constructions with polyforms. (Don't get me wrong, I wish there was just more out there in general to do with polyforms, but this topic especially.) It's like, "such-and-such created an x-by-y rectangle using the set of z-ominoes" but there's never anything written about the process of creating it, how they did it.

The only bit of wisdom I've picked up (I have no idea where I originally got it from, but looking at all the well-known big constructions out there I'd imagine it's pretty common knowledge) is the idea of saving the big blocky rectangular 'more co-operative' shapes until the end. And using up the awkward wiggly pieces as soon as possible.
But aside from that, I have no idea. I'm pretty much chucking pieces down and crossing my fingers at this point. And of course, all bets are off when it comes to pentominoes. Since there's so few of them and none are particularly pleasant to work with (apart from the P maybe?) With hexominoes or heptominoes you can generally get the first 4/5ths of the shape done without too much pain, it's only in the end-game where the going gets tough. With pentominoes though, it's all endgame. Or at least that's how I justify it to myself when it takes me ages to do a 6x10 rectangle.

This 23x33 heptomino construction from November last year is as good as I'm able to do so far (aside from running computer searches, but where's the fun in that?)

Fig. 1 - 23x33 heptomino construction (in a fab rhubarb-and-custard colour scheme)
Yeah, the holes aren't arranged symmetrically, and it's riddled with crossroads (4 'ominoes meeting at a point) and other such un-aesthetically-pleasing things, but hey. It's a start!

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