Complex mathematical tasks such as problem solving are an ideal way to provide students opportunities to develop higher order mathematical processes such as representation, abstraction, and generalization. In this study, 9 freshmen in a ninth-grade accelerated algebra class were asked to solve five nonroutine combinatorial problems in their journals. The problems were assigned over the course of 3 months at increasing levels of complexity. The generality that characterized the solutions of the 5 problems was the pigeonhole (Dirichlet) principle. The 4 mathematically gifted students were successful in discovering and verbalizing the generality that characterized the solutions of the 5 problems, whereas the 5 nongifted students were unable to discover the hidden generality. This validates the hypothesis that there exists a relationship between mathematical giftedness, problem-solving ability, and the ability to generalize. This paper describes the problem-solving experiences of the mathematically gifted students and how they formulated abstractions and generalizations, with implications for acceleration and the need for differentiation in the secondary mathematics classroom.