Week 8

There is a long tradition of Math contests.  In the US, many States have local exams.  Nationwide,
perhaps the most respected HS contests are the AMC contests.  At the collegiate level, the Putnam Exam has been a tradition more than 80 years old.

Another source of contest is not timed.  Problems are posed in various mathematics journals, and solutions to those problems are eventually published.  One example of problems can be found in the Math Magazine intended for undergraduates.