Firstly, I am glad to say that I have passed the evaluation. But that does not mean that my project is over, the Gnome Sudoku game is not yet something that I would call complete.
So, since my last update, I have been working on learning, and implementing in Vala some of the logic techniques that can be used to solve sudokus. The best resource I have found so far for this is Sudopedia. I plan to display opportunities to apply the technique in a help section, as well as highlighting the relevant cells on mouseover.
I also decided to change the way possibilities for a cell are displayed to the user. You can see this, and the previously described feature in the following screenshot.