I had made two valiant attempts at solving this shape before I owned a set of physical octominoes, and failed hard both times. In March 2020, armed with my nice new acrylic octominoes, I had another crack at itand managed. Third time lucky, eh?
Getting that central 13-hole configuration to work was surprisingly tricky - they're too close together to just treat as individual holes, sling a holey octomino around some of them and be done with it.
This construction by David Bird does something similar, there's probably only a handful of ways of accommodating those holes in that shape.
Then throughout the rest of the solve I had in the back of my mind a little nagging concern that maybe some issue like parity would render this solution impossible anyway. The octominoes as a full set have no glaring issues the way the tetrominoes and hexominoes do, but the 363 non-holey ones are imbalanced when checkerboard-coloured. And since I'd used the 6 holey pieces first I was in effect left with this imbalanced set. I assumed (well, hoped) that since the construction's dimensions were odd x odd this might negate the issue; I use this as a rule of thumb for hexomino constructions because it usually means that the overall structure is sufficiently unbalanced and therefore solvable.
Whether this makes any sense mathematically I have no idea.
Total solve time was approximately 5 hours spread over a few days. Total time drawing up the digitised image of the solution probably took another hour on top of that, come to think of it.
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Lewis Patterson. Last updated 08/05/21.
