Utah Mathematical Olympiad

The Utah Math Olympiad (UMO) is a 3-hour test with 6 questions. We favor questions that are interesting, elegant, and accessible to anyone with a high-school level background. However, they are also often quite challenging, and generally increase in difficulty from problem 1 to problem 6. The topics usually span at least the following major categories: Algebra, Geometry, Number Theory, and Combinatorics. In order to get credit for a problem, a student must write a convincing argument that proves their answer. This is not the same as merely showing one’s work, nor is it the same as explaining every step in great detail.

Scoring

Each problem is worth 7 points, for 42 points possible. Partial credit is awarded for significant progress toward a correct solution. We take great effort to assign scores appropriately and consistently. While no grading scheme is infallible, decisions of the graders will be final.

Previous contests

Previous contests are available on the Problems and Solutions page.

Eligibility

The UMO is intended for advanced high school students. However, any Utah student who has not completed 12th grade and is 19 years old or younger is eligible to participate.

Prizes

Prizes will be awarded to the top five scorers. Prize denominations will depend on ties and the amount of money available. Visit the results page to see previous years’ prizes.