I have several questions that I ask. Each one is structured as python class, with unit tests that are failing. Your job is to make the unit tests pass by fixing the missing implementation/bug. You can add any debugging code, and run the interpreter as many times as you like (I use coderbyte, which isn't great, but it has an editor and an interpreter).
but typically it starts with: you have a list of 10K strings, containing duplicates. produce a counts table (IE, string -> number of times that string occurred). What python data type or class does this efficiently? What is the underlying data structure? What is the time complexity of that data structure?
Next are a few questions about a python Node class used to build a tree, where I have either a bug that breaks a recursive indented print routine, or you need to detect a cycle (IE, is the tree you handed me really a graph?)
Finally, for senior engineers or people who are going to be working with low-level code, I have a bit-packing question using DNA sequences (A, T, G, C). I work for a biotech so it makes sense to have at least one question about DNA.
I've had to refine the questions over time based on what I've seen so that nothing is rushed, the important parts are obvious, and the interviewee doesn't feel like I'm asking them to find an approximate solution to an NP-hard problem in 30 minutes.