(They could arguably also be 'noniamonds' but I've never seen anyone call 'em that.)


You know that feeling you get the instant it hits you you've bitten off more than you can chew? I may have got just a little bit of that feeling when I first tipped out the set of enneiamonds onto my desk:

The actual pieces themselves are smaller than I'd anticipated, due to me scaling down the SVG files I'd made then forgetting before I sent them off to be cut out. But they still work properly, now with the added bonus that they don't hog my entire tabletop when I'm mid-solution.

They're a lot like heptominoes, if you were to take everything I hate about heptominoes and turn it up to 11. There's a similar number of pieces (160 vs. 108), including one with a hole, but their complexity seems to be upped just a tiny little bit - I think it could be the mixture of 60 and 120 degree angles which pushes the difficulty a step beyond. And there's a very small selection of easy looking shapes (see the top left of the photo where I've tried to pick them out). It's less than the amount of nice heptominoes, but enough that it promises an endgame that feels a little less like the random trial-and-error ordeal of heptiamonds.

The total area of the enneiamonds is 1440 triangles, which is 4 less than 38²=1444 which means a triangle with side length 38 and four holes is (in theory) possible. A hole at each corner and a fourth hole dead centre; I decided not to think too hard about possible parity constraints and jumped right in.

There's a 'difficult zone' with polyiamonds. For small sets (hexiamonds and below) there are fewer pieces so usually you can solve puzzles with them fairly quickly. And for much larger sets the amount and variety of pieces is so great that no matter what kind of jagged mess you've got yourself into mid-solution, there's always a piece (maybe several) which will fit perfectly. And there's a good handful of the aforementioned chunky pieces that make the very end easier. Between these two extremes lies the heptiamonds and octiamonds - as mentioned in the previous post these seem unreasonably hard. And I was fearing that the enneiamonds would be the same.

I'm tempted to say that the enneiamonds fall just beyond the far side of the 'difficult zone'. But I can't really since I didn't actually finish solving the triangle manually. I got as far as the last 8 or so pieces then threw in the towel after half an hour or so of trying various possibilities. I resorted to inputting the remainder into a solver (Peter Esser's trisolve) and backtracking one piece at a time until I found a solvable state. From there I could have returned to the puzzle with the knowledge that it was at least doable but I was pushed for time, and I knew the sense of achievement would no longer be there.

The colours look nice, but they still don't allow you to see the borders between pieces very well.

Centering the hole in the middle was tricky too. With polyominoes it's easier; the grid on the green cutting mat is to the same scale as the pieces so I can just stick a monomino wherever the holes are going to be. But with this it was tougher - solve up to the rough place where the holey piece is going to go, then count rows in all three directions and shift the piece around until they're equal.

Had I not been on my lunch break (and conscious of how long I was spending playing around with these) there's a chance - yeah, a low one admittedly - that I could have solved the entire thing by hand. But for now, it's a respectable enough first attempt at solving something with this set. And I learnt some valuable lessons: mainly that some of the pieces I was holding onto weren't as cooperative as I'd previously hoped. There were a few long skinny pieces with fairly smooth edges that I'd kept back and these turned out to be a total ball-ache and part of the reason I gave up when I did.

Here it is, drawn out so you can see the individual pieces:

I tried drawing it in Inkscape instead of MS Paint this time, which was much faster but caused all these little variations in line thickness. Some day I'm going to have to learn how to properly use image editing software.

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Lewis Patterson. Last updated 15/04/21.

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