We try very hard to NOT ask questions that have only one correct answer, and my team only interviews/hires senior people. So my approach to interviewing might be different than someone who's interviewing a fresh grad.
I treat all questions as conversational. The direction the question goes depends on where I (or other prior interviewers) think more evidence is needed.
For example: merge sort is an answer that satisfies the conditions of the problem. Given that, I would decide if I need more evidence about your ability to code, if so I'd ask you to implement merge sort; I might want more evidence on how you explain things, so I would pretend that I didn't know what merge sort was and ask you to give me a description of it.
I treat all questions as conversational. The direction the question goes depends on where I (or other prior interviewers) think more evidence is needed.
For example: merge sort is an answer that satisfies the conditions of the problem. Given that, I would decide if I need more evidence about your ability to code, if so I'd ask you to implement merge sort; I might want more evidence on how you explain things, so I would pretend that I didn't know what merge sort was and ask you to give me a description of it.