Why do we need $k \geq n$ in Dijkstra's token ring self-stabilizing system?
Here is how to solve this for your particular $n$ and $k$. Your system has $k^n = 81$ possible states. You can describe the evolution of the system as a directed graph: there is an edge $s_1 \to s_2$ if state $s_1$ evolves in one step to state $s_2$. Some states are legal, some are illegal. You want to find an illegal state $s$ from which no legal state is reachable. This is a question that can be solved using a graph traversal algorithm such as DFS.

Once you find such a state, you can try to generalize the construction to other values of $n$ and $k$. Other simulations (with other values of $n$ and $k$) could be helpful here.