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The joint focus of TSG-46 on mathematics competitions and other challenging activities is devised in recognition of the fact that all students benefit from studying mathematics through challenging activities but some students do not like to compete. This group gathered mathematicians, teachers, mathematics educators and mathematics education researchers and served as a stage for presentations and discussions related to the following themes: (i) Organizational formats for challenging students mathematically, (ii) Research on students’ experiences with mathematically challenging activities, (iii) Characterizing and theorizing mathematical challenge, and (iv) Competition problems as impetus for mathematical research and discoveries.