Rokkakari

A combination of the japanese words rokkakkei (hexagon) and akari (light).

Akari

The latter is also the name for a pen and paper logic puzzle introduced by the japanese publisher Nikoli. It consists of a square grid that has to be entirely lit up by placing lamps into it, which will light up their corresponding column and row. Some cells of the grid may be walls that will block off the light and furthermore can constrain the number of lamps allowed to be placed directly adjacent to them (indicated by a number written in that cell). Also more importantly two lamps cannot light up each other.

Regular Tilings of the Plane

There are a lot of ways to subdivide a two dimensional surface, but only a few tilings are left when restricted to only one type of polygon:

• Triangular (isometric graph paper, etc.)
• Square (chess, akari, standard graph paper, etc.)
• Hexagonal (honeycombs, graphene's atom structure, etc.)

Due to their geometry pentagons and any polygon with more than 6 vertecies cannot subdivide the plane by themselves.

Hexagonal Akari

As I got interested in the akari puzzle and discovered a lot of interesting patterns arising from the interaction of the lamps on the board, I wondered how the akari rules would translate to a hexagonal grid and what kind of similar or different patterns would arise from that. I looked for anything on hexagonal akari online, but the only thing I found was this single example puzzle. It was not interactive however and so I tried to solve it the old fashioned way on pen and paper (or rather by digitally drawing onto a screenshot...), but found it to be a lot trickier than the interactive regular akari I had been solving for a while then. At some point I got frustrated and built an interactive (and to my knowledge the first) version of hexagonal akari in the better part of a month running on JavaScript and a lot of clumsy SVG. But hey, it worked :D

Now: Rokkakari

Because of my intrest in this puzzle and in an ongoing effort to learn Rust this is a project to write a library to support hexagonal akari logic. I also plan to write a frontend for this puzzle, maybe some WebAssembly compiled from Rust to interact with my previous SVG mess, a Flutter app or a text based program for starters. I'll see how this goes...

Thanks

Thanks to Mark and Simon from Cracking the Cryptic for introducing me to akari puzzles (and knight sudoku).

Thanks to Angela and Otto from janko.at for hosting so many puzzles including interactive akari, which really developed my interest in the puzzle.

Thanks to Palmer Mebane for uploading an hexagonal akari to that same site, which helped me to wrap my mind around them and inspired me to keep working on the puzzle.