Happy new year! Going to kick off 2021 with a lazy low effort post.
In an older post I found two hexomino rectangles which had twelve holes, each in the shape of a different pentomino. Or it could be thought of as a combined pentomino/hexomino rectangle with the added condition that none of the pentominoes touch each other or the edge of the rectangle.
The topic was brought up on the 'Puzzle Fun' Facebook group, and the gauntlet was thrown down - was the same thing possible for heptominoes with hexomino-shaped holes? I had a go and found the following:
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| Fig. 1: 22x44. Separating the hexominoes and heptominoes out when dismantling the finished construction was not a fun job. |
There's two monomino holes in there, one has to be there to placate the harbour heptomino, the second is there because otherwise the combined area (7*108 + 6*35 + 1 = 967) would be a prime number. And the hexominoes are at a higher concentration in the bottom half of the rectangle. I wasn't sure how much space I had when I started off constructing this so I packed them in really tightly at first, then when I got about three-quarters of the way through I realised I had like 4 hexominoes left so they're a tad sparser up there.
the inevitable next step will be the octomino/heptomino equivalent of this. I'm putting off starting it but I'd give it a month tops before I cave and begin trying to solve it.
