Wednesday, November 13, 2019

20x20 Diagonal Square with Heptominoes

It turns out the heptominoes can do four congruent right-angled triangles, each with a single-square hole at the right angle:
Fig. 1: Four 19x19 triangles
I solved the first three quadrants of this by hand (the red, blue and green ones) then utterly despaired at the thought of having to do the fourth one. As a result of using my normal solving technique, I'd found myself left with a selection of mostly quite blocky, squarish pieces then realised that these pieces don't generally lend themselves well to building wiggly edges. For finishing off relatively square shapes like the last corner of a rectangle or something they're fine, but for this I wasn't sure. So I wrote it off as a bad job.
Then a few days later, I drew the pieces into FlatPoly2 just for the sheer hell of it and it found a solution in about a minute.

These four triangles can then be put together in various different ways, including this 19x19 (Edit: it's 20x20, I can't count) diagonal square:
Fig. 2: The holes don't quite match the symmetry of the outer perimeter but whatever.

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