The kind of question I had in mind would be along the lines of "say you have a tree, how could you find the nearest common ancestor of two nodes in that tree?". I actually got this question during an interview recently, and I felt it was of a suitable difficulty where I could figure out a solution without any specific knowledge other than what a tree is (which most developers should know).
I'm sure I'm still young and naive, but my line of thinking is that a question like that is good for having a person show their thought process when figuring out a problem they haven't seen before. Design questions are a bit different because they tend to just require a rehash of a codebase you've worked with before.