At the last place I worked our interview was split into 3 sections; Technical, Personality, and Critical Thinking (mirroring your three questions). While it wa

At the last place I worked our interview was split into 3 sections; Technical, Personality, and Critical Thinking (mirroring your three questions). While it wasn't a programming job, it was a support job with a wide array of third-party and in-house software, written in a variety of languages. Because of the size and mobility, they preferred resourceful generalists over hiring people who were extremely specialized. When I was interviewing, the whole goal of any puzzles wasn't to find the answer, but insight into their process of assessing the situation and seeing how reasonable their through process was. If they were familiar with the puzzle, it was obvious because there wasn't any thought process before answering--which isn't a problem, just move onto the next question.