Saturday, May 18, 2019

More Heptomino Constructions

I've been playing with the heptominoes a hell of a lot recently. Actually, thinking about it, it's not really surprising that these pieces have the same kind of addictive properties as Tetris does, given that they are pretty much just Tetris pieces on steroids.
First big success was about a week ago. I'd spent most of my day at work distracted, thinking about what other shapes I could try and knock out with the heptominoes (rectangles were getting a tad old at this point). I can't quite remember how I came to the conclusion that a 29x29 rectangle with a missing central 9x9 gap and 4 extra holes (to allow the harbour heptomino to fit) seemed doable, but I did. Of course, actually doing it was another matter entirely.

Basically, the long and short of it is by the time I've been at work all day then got back in in the evening, my mind's not exactly firing on all cylinders. So (this is becoming a common theme) after having placed about 60 pieces and thinking I was well on my way, I noticed I'd made one of the 'walls' of the square ring too narrow, off-centering the central hole. And it just ain't a central hole if it's off-centered, is it, so I had to tear huge chunks of construction up and start again, not quite from scratch but not far off.

Fig. 2 - The 29x29 square with symmetrical square holes.
Finally got it though! Took about two hours of my life I'll never get back, but there it is.

Spurred on by the above success, I decided later in the week to revisit the other construction I'd made-but-not-quite a little while back: the 20x38 from here.

Fig. 1 - New, improved 20x38 rectangle, with the four holes placed in the centre this time...
This was a lesson in taking care which order you use the pieces in. The usual technique is to leave the chunky blocky bits until the end (see the bottom-left corner of this one, where all the easier pieces are hanging out). But equally important is getting rid of the more awkward pieces earlier on, so you're not stuck trying to place them in the frustrating repeated-backtracking stages that is the endgame of a construction like this.
Look at the 'Z'-shaped piece and the cross bit touching it, about halfway up the left hand edge of this one. These pieces are nightmares, and being stuck having to place them twenty times each as I went full trial-and-error completing the last 5% of the puzzle was something I wouldn't wish on anybody.

Then today I managed to do this:

Fig. 3 - Three 11x23 rectangles with central holes.
This was more of a personal milestone for me than anything. I remember my first introduction to heptominoes was seeing the construction on the Kadon Enterprises website, three 11x23s with centrally-placed holes. That and Michael Keller's 51x58 octominoes further down the page just absolutely floored me when I was like 9 or however old I was, struggling to make rectangles with my little set of pentominoes hacked out of the back of a Weetabix box. These solutions seemed like superhuman achievements to me back then, so it's just a nice feeling having found my own alternate solution to this one - I mean, I'm still nowhere near the level of that octomino rectangle, or some of the even crazier solutions, but I'm getting there. Slowly.

Of course now I'm itching to have a go at something with octominoes... The only thing really stopping me is the fact that I don't have a physical set of 'em handy. The thought of tackling something like an octomino construction as a purely pencil-and-paper thing just terrifies me.

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