You can make it harder by using 16x16, 25x25, 36x36 etc boards, and see how fast you can make it. There are lots of known patterns to allow for elimination of options http://www.sudokuwiki.org/Getting_Started, of different computation complexity relative to each other, and all faster than regular backtracking. So the goal is to find the order at which to apply them for maximum speed and minimal need to backtrack. You can also try to multithread and use GPU, or FPGA if you're nuts.

All that said, it's all still pretty mechanical. So if you're looking for something more inferential, then another game would be better.