Identifying mathematically gifted students is an important objective in mathematics education. To describe skills typical of these students, researchers pose problems in several mathematical domains whose solutions require using different mathematical capacities, such as visualization, generalization, proof, creativity, etc. This paper presents an analysis of the solutions to two problems by 75 students (aged 11-14), as part of the selection test for a workshop to stimulate mathematical talent. These problems require the use of the capacity for mathematical generalization of solution methods. We define a set of descriptors of such capacity, use them to analyze students' solutions, and evaluate how well students with high capacity for generalization can be distinguished from average students. The results indicate that the two problems are suitable for identifying potential mathematically gifted students and several descriptors have high discriminatory power to identify students with high or low capacity for generalization.