This article describes the first results gained from a problem solving test that was administered to grade 4 students in the Netherlands. The students involved are all high achievers in mathematics. The analysis of the student responses gives cause for concern. The often-heard belief that teachers do not need to worry about the better students is clearly in need of revision. It turned out that when high achievers in mathematics are challenged to take on non-typical problems, their abilities are more limited than expected. The study revealed that the students wrote down hardly anything on their scrap paper to solve certain problems. Also it was found that they were not very persistent in their looking for a solution. In this paper we illustrate these first findings by discussing the results of one of the test problems.