A mathematical problem that involves conceptual challenges, may offer students opportunities to show and develop their conceptual understanding. However, to meet specific conceptual learning goals, a deliberate design of the problem is important. In the study, a single problem is used in different versions to investigate what conceptual understanding of the concept perimeter is visualized in students’ solutions. The result shows that the chosen problem offers reasonable conceptual challenges and thus is suitable for visualizing and possibly developing students’ conceptions. Three conceptual aspects are identified and suggested to be used to support further discussions on task design: properties and definitions of concepts, the use of non-typical examples, and the relations between processes and concepts.