Tuesday, December 22, 2020

Puzzle #272 - Filling Space (Aho Fillomino)

Aho is a puzzle genre so rare, that I actually couldn't find any rules page for it outside of puzz.link, nor could I find any examples but those in its database. It's a fun twist on Shikaku where regions with areas divisible by 3 must be L-shaped, while areas not divisible by 3 must be rectangular. I thought it could be fun to add the core restriction from Fillomino where regions of the same size may not share an edge.

So in summary: divide the grid into regions where each region contains exactly one circle. The area of the region dictates the shape it should take- an L* if it's divisible by 3, and a rectangle if it isn't. Regions of the same size may not share an edge.

*Unlike Sashigane, each end of the L may be any size. As an example, a 21 may be satisfied by cutting a 2x2 out of a 5x5 square, among many other possibilities.

puzz.link interface

The coolest step during construction ended up just barely not working, with a second possibility I had overlooked. Thankfully the rest of the logic ended up working out better than I intended, again due to a missed possibility that had a neat step to eliminate. See if you can guess what I'm referring to!

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