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Sample problem: Let S be a subset of {1, 2, ..., 500} such that no two distinct elements of S have a product that is a perfect square. Find, with proof, the maximum possible number of elements in S.

Math Online

USA Mathematical Talent Search (USAMTS)

USAMTS is a free, proof-based online math competition for US middle and high school students. Students have a month or more to work on problems. Registration is open year-round.

USA Mathematical Talent Search Free

Science Civics & History Online

eCYBERMISSION

A free, virtual STEM competition for middle school students (grades 6-9) to identify and solve community problems using science or engineering. Teams work online to submit projects for state, regional, and national awards.

📅 Feb 24, 2027 Free