Intelligent Tutoring Systems have made great strides in recent years. Many of these gains have been achieved for well-defined problems. However, solving ill-defined problems is important because it can enhance the cognitive, metacognitive and argumentation skills of a student. In this paper, we demonstrate how to apply the constraint-based modelling approach to describe the solution space of ill-defined problems in logic programming. This technology has been integrated into a web-based ITS (INCOM) and has been evaluated with student solutions from past examinations.