One of my favorite interviews was like this. The interviewer started by asking me some of the basic logic problems. I had heard most of these many years before. He actually appreciated it when I stopped him mid-question and finished the question for him. He asked another one, I finished the question for him. He saw that I had a math degree and asked about a particular problem involving infinity that he had heard about, and I gave him the summary of a half-hour talk I had given on the topic. Finally he sat down and he told me about a startup he had worked on when he was young and we talked through the technical problems. He stumped me most of the time but we both agreed that it was a very enjoyable interview. Funny thing is, that was also the only interview I had ever been on where I didn't get the job. Probably because I didn't where a tie to the interview and this particular company is apparently known for requiring ties.