Create (fallback) SATSolver Solutionfinder #2
Description
(Thanks to Oliver for sending me the problematic puzzle per email)
The puzzle #16230509 can't currently be fully solved by the HexSolver algorithm.
Either the current algo must be (drastically) improved or we add a second (slower) fallback step that uses some kin dof off-the-shelf SAT solver to also find these really hard solution steps
Explanation (from Oliver) how to argue the next solution step:
Start by assuming the blue-circled hex is blue. It's in the radius of the blue 4. This means all four blue cells in that radius are accounted for, even if we don't know exactly where they are, since the black 4 to the upper-right must have two blue cells inside the radius. That means a lot of cells are forced into being either black or blue respectively, as shown by the dots on each cell. This eventually leads to a contradiction between the two red-circled conditions which can't be satisfied simultaneously. Therefore, we reject the assumption and the initial blue-circled hex must in fact be black.
The current algo is definitely not able to do such complex logic and needs to be improved.