Better challenge: generate these puzzles in a way to have a unique solution.
n=1 is trivial, and n=2 it small enough to enumerate with 3^4 = 81 solutions, but many of them being degenerate (no solutions), but already n=3 is pretty bad with ~20.000 possible puzzles. I do not see an obvious path to compose solutions either and make use of some kind of structural induction.
| 2 | 3 | 3 | 3 |
| 3 | 3 | 3 | 3 |
| 3 | 3 | 3 | 1 |
| 3 | 3 | 3 | G |