The phone interview went very quickly. He was very nice and asked about my specific talents, things I enjoy doing, and projects I’d worked on–especially those I listed on my resume. He asked about the ray tracer I wrote in college, since he had an interest in that. He also asked some general questions about the stuff I do for work. Then he got into the technical question. It was an interesting problem, and I asked follow-up questions, talked out loud, wrote things down in front of me (and told him what I was writing and why). I immediately thought of the naive solution–always a good place to start. He was interested in the asymptotic complexity. I knew there were better ways of doing it, so I started thinking of optimizations to the algorithm, trying to come up with ways of caching information, reusing previously-computed values, etc. He gave me some gentle prodding, and I think I understood immediately where he was going. I answered the question fairly well, I though.