We describe a preliminary study exploring how computer science students solve a problem in an attempt to understand differences between the successful and the unsuccessful problem solver. Students followed a verbal protocol as they solved a data structures problem, and we analyzed the transcripts of these problem-solving sessions, classifying the statements students made using the revised Bloom's taxonomy. Based on our analysis in this case study, we conclude that the successful problem solver seems to move more frequently from one type of cognitive process to another than the unsuccessful problem solver. For the particular data structure problem the students attempted to solve, we observed that all problem solvers, successful or unsuccessful, tend to follow patterns in their problem-solving process.