USA Mathematical Talent Search Winners
Unlike most competitions, participants of the USA Mathematical Talent Search (USAMTS) are allowed an entire month to complete the math test. This contest for middle and high school students has four rounds from October to March, and each round contains five problems. Students can download the problem set on the USAMTS Web site at least four weeks before the solutions are due, and a justification for each problem is mandatory. While resources such as calculators and books are permitted, students can't ask for live help (USAMTS uses the honor system). Problem sets are graded by mathematicians and sent back with comments to the contestants, in order to encourage growth and understanding. The American Mathematics Competitors, the organization that runs the American Invitational Mathematics Examination (AIME), sets a qualification score each year for participants who score well on the first three rounds. Those who qualify are given a bid to the AIME and therefore the chance to be a part of the USA Mathematical Olympiad team. Past awards include certificates, books, software and partial scholarships to the Canada/USA Mathcamp.
You can register for the competition on the USAMTS Web site and take a look at past years' problems and hints for writing solutions.