Heptominoes Miscellany

A few more heptominoes type things I've done recently, since lots of small posts is easier than one big post. Again, nothing particularly groundbreaking here.

Here's a 11x71 with 25 holes arranged in a central grille:

I solved the middle bit first seeing as it put the most restriction on pieces that could be used. Then built the left side (using up a handful of nice useful 2x2-blocky pieces in the process), then the right hand side. I don't know whether it's possible to do a 23x35 with a grid of 49 internal holes. The maths says yes but the pieces themselves might not allow it.

And here's an 11x69 rectangle with 3 holes.

I think I'm getting the hang of rectangles now; the biggest challenge here seemed to be finding a surface long enough to construct it on. Next time I think I'm going to have to try my hand at putting together some more involved figures, and confront my fear of building things with diagonal edges. (I mean, it can't be that hard can it? Look at how many heptominoes have got those wiggly zig-zag edges anyway.)

Congruent Rectangles with Heptominoes - Part 2

Part 1 is here. It's dead disappointing, mind, there's only one set of rectangles and it's the 4x 10x19s. But in that post I mentioned a couple of other possibilities for sets of rectangles that use the entire set of heptominoes between them. Here are some (coincidentally none of these are the ones mentioned in the above post...)

First there's this set of three 15x17s using 36 pieces each which I found ages ago, but didn't feel like it deserved an entire blog post to itself at the time

Fig. 1: Three 15x17 rectangles. You can almost tell by the pieces used in each which order I built them in.

In the first post or Part 1 or whatever we're calling it, I had somehow overlooked the fact that 108 divides by 6, and that a set of 6 rectangles should therefore be possible. The minimum number of holes that works is 12 (I think), 2 per rectangle, and that gives each an area of 128 cells which can be done as 8x16 (I can't rule out 4x32, but at the same time I'm utterly terrified of the prospect of trying to fit heptominoes into a 4-cell-wide anything.)

Fig. 2: Six 8x16 rectangles.

There wasn't really any pleasing ways of distributing the holes, this is about as good as it gets. Also, just look at those four hideous stretched-F-pentomino-looking pieces clustered in the middle of the top-right rectangle. I had accidentally forgotten to use those up sooner, and wound up stuck with them at the very end. That last rectangle (top-right, the one with all the supposedly easy to work with pieces) was partially a computer search job too. I think it was getting late and I needed the table space for something else so I had to speed up the solving process somehow.

Still not touching the nine 5x17s with centered holes though. It's gonna take one hell of a rainy day to drive me to attempt that.