With arbitrary generation rules they are surely not. This is a counter example on 4x4: | 1 | 1 | 1 | 1 | | 1 | 3 | 3 | 3 | | 1 | 3 | 2 | 2 | | 1 | 3 |

With arbitrary generation rules they are surely not. This is a counter example on 4x4: | 1 | 1 | 1 | 1 | | 1 | 3 | 3 | 3 | | 1 | 3 | 2 | 2 | | 1 | 3 | 2 | G | Or | 2 | 2 | 2 | 2 | | 2 | 2 | 2 | 1 | | 2 | 2 | 2 | 2 | | 2 | 1 | 2 | G | This seems to be able to be understood as a reachability graph problem of some sort perhaps. Edit: formatting