Mathematically promising students are defined as those who have the potential to become the leaders and problem solvers of the future. The purpose of this research is to reveal what problem solving abilities mathematically promising students show in solving non-routine problems and type of profiles they present in the classroom and during problem solving. The students participating in this study were chosen on the basis of mathematics contest scores. Accordingly, four students from an urban private school, taking the first, ninth, tenth, and fourteenth place on the contest formed the sample of the study. The data were collected through non-routine problem solving activities, administered to the participating students after school hours at their school. After examining the students' responses to the questions, students were interviewed on those same questions. The results suggest that mathematically promising students were very determined, spent a long time in thinking, reflecting and planning. They attempted to solve the challenging problems multiple times, and looked for alternate ways if the one they tried did not work. They found an authentic solution when they do not know or remember the general algorithm. (Contains 2 figures.)