Sudoku puzzles of different sizes (e.g., 4 x 4) and difficulties (number of initial assignments) can be used in addition to the standard 3 x 3 puzzles.
The order in which the legal domain values are attempted can be modified to see how that affects the search.
Since it is possible for there to be more than one variable with the same MRV value, rather than greedily using the first such variable found, some thought can be put into discriminating between them.
The MRV heuristic can be augmented by the Least Constraining Value (LCV) heuristic, which attempts to choose the optimal order in which to try the values available after the MRV heuristic has been applied.
Arc consistency can be added to provide forward checking capability.
The assignment can also be viewed as a graph coloring problem. With this approach, the constraint would be that no two adjacent cells may have the same value.