I've seen a lot of people get into a flap over problems that they think are difficult but turn out not to be. I think this is probably the same thing. Hampered, of course, by the fact that I feel unable to explain the answer properly without giving the solution away which is bad etiquette.
Counting works the same, anyway, in every base. You just have more or fewer options to count. Don't even need to fuss too much about converting from one base to another. The question of what to put under the grid can become: "What is the next largest number containing only the thematically allowed digits?" You can answer that question in "normal" numbers if you like. There is no need to fuss about countng, or converting, or even checking the date.