There's not a technical term for shapes like this, is there?
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| Fig. 1: With heptominoes. |
Those toothed edges are just as difficult as they look. They start out easy enough - the bottom edge was done first using pieces that it makes sense to put there, the 'H' shape and various other U-pentomino-derived pieces that fit perfectly. But alas there aren't enough of those shapes to go all the way around. And by the time I got to the middle of the top edge desperation had kicked in and I was using any piece I could to try and complete the perimeter. The straight line heptomino for example. And even one or two of the pieces with a 2x2 block which I generally try to hold onto until near the end.
Once the perimeter is done it doesn't get any easier. See, now I'm left with a very irregular cavity to fill, and if we want the central hole to be, well, central that forces the position of the harbour heptomino too. So you're left to squeeze an already awkward batch of pieces into a shape that really wasn't designed to accomodate them, just like last time.
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As I was solving the above I wondered whether this sort of shape would be any easier with octominoes. On paper it felt like it should be - sure, an octomino rectangle would have a longer perimeter but the amount of pieces which would fit nicely into that perimeter would increase too. And the ratio of perimeter to area ought to mean that once the perimeter was completed we'd still have a large variety of pieces for the middle.
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| Fig. 2: The octominoes. Yeah, the corners are a slightly different style - I'd miscounted the number of teeth needed and offsetting them by one like this was a lucky save. |
Turns out it isn't really that much easier after all. Maybe a tiiiny bit easier because of pieces like that 'E' shape in the top edge, but the perimeter got way longer and the number of nice pieces just hadn't increased enough to counterbalance it. Admittedly once I'd cleared that first hurdle, completing the rest of the solution was no worse than any other octomino solve I'd done in the past, so maybe I was partially right. Total time, maybe about 4 hours or so, spread out over one afternoon and evening. I don't know, I don't time these things. I just occasionally glance at the clock and realise I've wasted a whole afternoon and I should have had dinner an hour ago. But hey, there are worse ways to waste time.
