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.
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