Some Assorted Solutions

Polyform-related shenanigans have been on the back burner somewhat recently, mainly because I'm in the process of moving house and don't have table space right now to spread out even a full set of hexominoes, let alone a larger set. So this post is going to be a collection of solutions I found several weeks ago but didn't write about at the time for whatever reason.

First up, continuing with the last post's theme of long skinny rectangles we've got the heptominoes in a 9x85 rectangle with nine holes. I think I found this with the intention of including it in that post, but then I found the 5 high rectangle which was way more interesting and in the interest of not making that post a mile long I took this one out.

In February some time I put together another variant of the well-known side 20 diamond found originally by David Bird - same outer shape, different hole configuration. Nothing particularly groundbreaking to look at, but the solving process was interesting. The jagged outer edges use up pretty much every piece with any stairstep-type edges, leaving a glut of pieces with 2-cell protrusions for the middle. Which is less than ideal.

And finally, I found a few more fun things with the hexominoes, in what I call the 15x15-15 challenge because I'm terrible with names like that. The idea is, make a 15x15 square with 15 holes using the hexominoes. The challenge is to make the 15 holes look nice, given that they can't retain the symmetry of the outer square. There's some examples here (from back in 2019) and a few more just below, from back in March.

A silicon ship looking configuration.

Side note: For whatever reason the word 'quincunx' makes me giggle like an idiot.

Oh yeah. One last thing that I almost didn't include since it's a shameful chapter indeed in the history of polyominoes. I had attempted a heptomino construction with the crenelated edges similar to that top hexomino one. And I made the classic mistake of doing the math for it late one night when I was too tired to be trusted with simple tasks like adding a few numbers up. This was the result:

Yep. For whatever reason I'd thought that each edge had one more protrusion than it did which threw my area calculation off by 4. And because it was late and I was just itching to get my solve on, I didn't even think to double-check everything. I just never learn...