Most years, the University of Northern Colorado offers a math contest for students in grades 7-12. Check the Dates page for this year’s schedule.

The contest is for all interested students in Colorado. It is designed for students in grades 7-12, but younger students are welcome to participate if they have an interest.

The contest consists of two rounds, a First Round in the fall and a Final Round in January. All grade levels are given the same questions. Each round is a paper and pencil exam with about 9-12 problems. Students compete individually and no electronic devices are to be used in working the problems.  Both rounds challenge students to exercise their creativity and ingenuity to solve problems in geometry, algebra, combinatorics, probability, logic, and number theory. All the old contest questions are archived on the Problems & Solutions page.

The First Round of the contest is administered in late October or early November in schools around the state by volunteer teachers, math coaches, and parents. Students send their answers are sent to UNC electronically for grading. Students are allowed ninety minutes to work the First Round problems.

All schools in the state, including public, private, and home are invited to administer the contest. Unschooling parents are welcome, as well. Students should ask their teachers about the contest at their schools. If your school is not offering the contest, but you would like to participate, then you can ask a teacher to register and offer the contest at your school, you can email us at, or you can call us at (682) 330-3952. We want every student in the state who is interested to be able to participate. Teachers are welcome and encouraged to administer the contest even if just one student is interested. They are also welcome to offer the contest to entire classes. Home schooled and unschooled students should ask their parents or supervisors to register for them. Go to the Registration pages.

The First Round Solutions Seminar is held on a weekend soon after the First Round. Anyone who is interested is invited to the UNC Campus in Greeley for a discussion of the problems and solutions. UNC faculty will discuss solutions. Contest participants are invited to present their solutions if they would like to do that. Parents and teachers are also welcome.

Invitation to participate in the Final Round is based on performance on the first round. We also consider petitions from students who have not qualified by score on the first round, but who would nevertheless like to participate. To send us a petition, email and explain that you understand that the questions on the Final Round are seriously challenging and that you want to come and try them. There is no need to try to convince us you can do well. All we want to know is that you want to try the questions and that you understand that they will be difficult! All students who participate in the Final Round are asked to register on this website before coming. They should go to the Registration page and provide an email address to which a summary of the results of the Final Round can be sent.

The Final Round is held on the UNC campus in Greeley in late January.  The Final Round is similar in spirit to the First Round, but the problems are significantly more challenging. Students are allowed three hours to work the Final Round problems. All written work is carefully examined and partial credit is awarded wherever it is warranted. Students are asked to show all their work and to justify their answers. Rank depends on the work shown. A better presentation or more elegant solution may earn higher rank. Students should show work even for problems they have not found a final answer for: such work will be evaluated. It is traditional for some of the problems on the Final Round to have roots in questions from the First Round. Participants are encouraged to study the problems from the First Round carefully in the weeks between the two rounds. It is also a good idea to look at old contest questions.

While the students work on the problems during the Final Round, parents, teachers, and others who have come with their contest participants to Greeley are invited to the Final Round Solution Seminar, where the problems and their solutions will be discussed with some of the contest writers.  Attendees will be prepared to discuss the contest with their contest participants after the contest!

We try to have results of the Final Round posted on this website and emailed to registered participants within a week to ten days after the contest.  We post general results, we rank the top two dozen papers, and we select papers for honorable mention, but we do not compute individual scores. We do read carefully all the work that every student gives us. The primary goal of the contest is to promote engagement in mathematics as a pleasurable challenge, and no numerical scoring system can measure the passion, creativity, and resourcefulness that so many students display.

Winners of the Final Round are invited, along with their families and a math teacher, to attend an Awards Banquet held on the UNC campus in April.

This year’s schedule  can be found on the Dates page.


The University of Northern Colorado State Math Contest was founded in 1992 by Richard Grassl. It has been directed since 2011-12 by Ricardo and Katie Diaz, with assistance from Dean Zeller, Rocke Verser, Richard Grassl, Oscar Levin, and Rich Morrow. The contest was inspired by the Polya Competitions at Stanford, and the intention has been to maintain the spirit and standards set forth by Polya.

Past participants in the UNC Math Contest have enjoyed success in a wide range of intellectual and academic pursuits, and many have reported that the intellectual stimulation and sense of accomplishment they acquired at this age gave them the confidence to undertake even greater challenges in later years.

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