United States of America Mathematical Olympiad (USAMO)
The USAMO and USAJMO are proof-based problems. In each of the two 4.5-hour sessions contestants are given three problems. All answers must be clear in logic; numerical or incomplete answers will receive no or partial credit. The top performers will be invited to the Mathematical Olympiad Summer Program (MOSP or MOP). Then six elite students will represent the USA at the annual International Mathematical Olympiad (IMO), the toughest math competition for high school students. Typically, being qualified for USAMO or USAJMO is an amazing feat because there are only about 500 students combined who have the honor to take the test.