Problems for students with a high mathematical potential can be far more complex and challenging than problems normally used in regular classrooms. The problems we developed for mathematically gifted students offer the possibility of acquiring and using heuristics (so called patterns of actions) which are useful in problem solving processes. Because these kinds of capablities are valuable for all students, we ask whether it is possible to work on the problems in regular classrooms. In this paper two studies are presented, which examine to what extent students in regular classrooms are capable of working on problems designed for mathematically gifted students. The results show that the problems used in the support programme can also be successfully applied in regular classroom teaching and that students working on them experience high motivation. However, students of our support programme achieved better results regarding generalization and proving. In addition, they needed less time to solve the problems.