I enjoy this comic (my favorite is the Laplace's Demon comic that manages to sneak Boltzmann brains into the story).

I wonder why they haven't challenged her to solve and justify the solution to some sort of scientific puzzle, like Blackbody Radiation or the equation of state for a white dwarf for a degenerate fermi gas or something.

Unless the answer is so universally known (blackbody radiation may have been a poor choice), she would have to use the type of reasoning they're looking for to solve it, and then it doesn't matter what she is, as it demonstrates that she's sentient and capable of reasoning in the way needed.

(Tl;dr: Employ some sort of existential entrance exam?)