You've reminded me of another useful skill:
Working with incomplete specifications.
I found that most requests were not meant literally, were ambiguous at the outset, or were given in some technical jargon [other than programming]. The ability to refine and negotiate the problem statement will finish projects (sooner), and be more satisfying for everyone.
So consider writing up your toy interview problems incompletely, with some inconsistencies and red herrings, just like in real life.
Quantum Mechanics: The dreams stuff is made of