I tried really, really hard to not need that 6 to make everything resolve uniquely in the way I wanted it to... Ultimately it was necessary, no matter what I changed to try to use 5s instead.
Hexagonal Fillomino is quite tough to construct, as everything has so many possible options for where to expand. I ended up with a somewhat subtle break-in here, and then I just made the rest of the puzzle flow around. This was still worth 15 points, however, as tracking connections to see where things are forced is somewhat time consuming.
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