Problem solving and collaborative communication are among the key 21st century skills educators want students to develop. This paper presents results from a study of the collaborative work patterns of 133 participants from a university level course designed to develop transferable problem-solving skills. Most of the class time in this course was spent on actually solving puzzles, with minimal direct instruction; students were allowed to work either independently or in small groups of two or more, as they preferred, and to move back and forth between these two modalities as they wished. A distinctive student-driven pattern blending collaborative and independent endeavour was observed, consistently over four course offerings in four years. We discuss a number of factors which appear to be related to this variable pattern of independent and collaborative enterprise, including the thinking and learning styles of the individuals, the preference of the individuals, the types of problems being worked on, and the stage in a given problem at which students were working. We also consider implications of these factors for the teaching of problem solving, arguing that the development of collaborative problem solving abilities is an important metacognitive skill.