I strongly second the idea of using real science as a test. Jeffreyssai wouldn't be satisfied with feeding his students -- even the beginners -- artificial puzzles all day. Artificial puzzles are shallow.

It wouldn't even have to be historical science. Science is still young enough that there's a lot of low-hanging fruit. I don't think we have a shortage of scientific questions which are genuinely unanswered, but can be recognized as answerable in a moderate amount of time by a beginner or intermediate student.

Just to mention in passing, when I read your particular example, my immediate thought was "right, I'd fail right away". Someone who sucks at math would probably find it very difficult to derive those solutions. Yet, I don't think that means they couldn't be rational. You'd have to take into account their personal skills and affinity in the scientific domain you're testing, and adjust for that.