The 13th annual PUMaC is scheduled for November 17, 2018. All of the rules are subject to change prior to the competition.

The Main Competition

Teams of eight high school students compete in individual, team, and proof-based math assessments. Afterwards, lunch is served, and students have the option of participating in various scheduled Mini-Events. High-scoring individuals will be invited to take the Individual Finals exam once we finish scoring the individual rounds. Teams will also compete against each other in the fast-paced Live Round, and the day will conclude with an awards ceremony acknowledging and congratulating the best teams and individuals in the competition.

 

Eligibility - Full Teams

  • A full team will consist of 8 members. (Historically, half-teams have been allowed; beginning in 2017, only full teams and individuals may apply.)
  • A team member must not have reached his or her 20th birthday before the PUMaC competition date.
  • A team member must not have been enrolled full-time in a post-secondary institution before the PUMaC competition date.
  • See Registration Info for registration deadlines. Registration deadlines will be strictly enforced and no teams may register after the stated deadline.
  • Generally, teams should come from single high schools, but teams from well-defined geographical regions (comprising members from several schools) coming from a long distance will be allowed for their own convenience. The current Director of the Princeton University Mathematics Competition will have the final word on the legitimacy of teams that do not come from an individual school.
  • When registering, teams may indicate a preference between the A Division and the B Division. The A Division is designed for the more experienced teams, and the B Division is recommended for teams newer to competitions. Teams competing in the A Division will receive more challenging individual tests. The Power Round, Team Round, and Live Round will be identical for both divisions. Awards for the two divisions will be separately calculated. Teams that do not come from a single high school must compete in the A Division. However, teams may petition the PUMaC organizing staff for exceptions. The Director of the Princeton University Mathematics Competition has the final word on which division a team will compete in, and reserves the right to place a team in a division different from the one for which it had a preference.

 

Eligibility- Individuals

  • An Individual must not have reached his or her 20th birthday before the PUMaC competition date.
  • An Individual must not have been enrolled full-time in a post-secondary institution before the PUMaC competition date.
  • Individuals will be combined into teams of 8 for the Power Round and the Main Competition.
  • See Registration Info for registration deadlines. Registration deadlines will be strictly enforced and no Individuals may register after the stated deadline.
  • Individual applicants may register for the A or the B Division. However, the Director of the Princeton University Mathematics Competition reserves the right to move Individuals to a different division based upon perceived strength and application numbers. Individual applicants will be contacted before the change is made.
  • Individual registration will take part in two phases: General Individual Registration and Secondary Individual Registration. The deadlines for these dates are listed on the Registration Info page.
  • During General Individual Registration, Individuals may not apply if they are part of a school or organization that has an active application to compete in the upcoming Main Competition. Failure to abide by this rule may result in the rejection of both the Individual and all teams from the school or organization.
  • During Secondary Individual Registration, only students from schools or organizations all of whose teams were rejected may apply. We will indicate a certain number of students each school or organization can send, based upon space remaining after General Individual Registration.
  • Individual applicants will be granted the opportunity to participate in PUMaC on the basis of merit, just as with full team applicants. They will have the opportunity to indicate their mathematical accomplishments on the registration form. We also wish to encourage students who are part of an underrepresented group in mathematics, or students who would not otherwise have opportunities to participate in math competitions, to apply and indicate this in their application.

 

Test Question and Answer Formats

Any answers and solutions submitted for grading on the Team and Individual Tests and the Live Round should follow the formatting guidelines indicated in this document. Answers and solutions submitted in a format that contradicts what is described below risk being graded as incorrect. Should an appeal arise concerning grading, the current Problem Czar of the Princeton University Mathematics Competition will have the final word.

 

The Power Round

The Power Round is a way for PUMaC to expose a team to what proof-based mathematics is about – questions that may take more than an hour or two and require creative thinking to solve.

  • The Power Round will be made available online for teams a week before the competition date. The exact date and time will be announced to teams via email.
  • The eight students comprising a single team may collaborate on this test. There is no time limit, except that the day of the competition is the due date. As such, the team will have approximately a week to work on the exam.
  • Rules regarding computational aids vary from year to year and will be specified in the Power Round’s instructions.
  • Unless otherwise stated, no outside resources may be during the Power Round. This includes books, internet searches, or other individuals outside the students on the team. In particular, please contact us if you are unsure whether a certain major theorem or fact can be stated without justification. The Power Test will include more information on theorems that can be assumed.
  • Students will be required to submit written solutions with justification. Answers given without any justification will be given no credit unless stated otherwise.
  • The Power Test will have several parts. Results from previous parts may be assumed true in later parts, even if the team is unable to prove these previous results. Students should cite these results when they use them. For example, “From Part II, Question 1, …”
  • Solutions may be handwritten or typed.
  • Solutions should be printed on one side of the paper only. Each page should also have on it the team number (provided upon acceptance) and problem number. Points may be deducted for not following these and other submission guidelines indicated on the Power Round instructions.
  • The team name should not appear anywhere in the submitted solutions.
  • Teams will be allowed to submit their solutions via email or in person during the check-in process. More details about the email submission procedure will be given on the Power Round itself.
  • Teams may submit their solutions only once. If teams submit multiple sets of solutions, the first set received will be the set graded.
  • More detailed instructions will be given on the Power Round itself. If instructions here and on the Power Round itself conflict with one another, the instructions on the Power Round should be followed.

 

INDIVIDUAL TESTS

Each participant of PUMaC will take two Individual Tests from a choice of four: Algebra, Combinatorics, Geometry, and Number Theory. The Individual Tests will have eight problems in the subject areas chosen by the participants. Each Individual Test is 60 minutes. Scoring on these Individual Tests will be described below with all other scoring information.

  • No tools such as calculators, books, protractors, compasses, or rulers will be allowed on any Individual Test. Graph paper is also not permitted. Scratch paper will be provided by proctors.
  • Participants are NOT allowed to collaborate on this part of the competition.
  • Participants must choose two tests from a choice of four. More information on the tests can be found in the FAQ.
  • Participants will be allowed to change which tests they will be taking up until two weeks before the competition. Afterwards, any changes must be approved by PUMaC. No individual will be able to change which tests he or she will be taking when they get to the exam room.
  • Participants should record their answers on an official PUMaC answer sheet that the proctors will provide. After the completion of all Individual Tests, proctors will call up participants individually to enter answers into the computer grading system.
  • For teams not composed of Individual applicants, when computing scores, the top 5 scores per subject are summed per team. This means that if more than 5 people take the same test, the team is implicitly put at a disadvantage. Teams composed of Individual applicants have no restrictions on test numbers.

 

TEAM TEST

The Team Test is an on-site test in which collaboration is allowed (and encouraged). Each team will be given a set of instructions and problems, and they must do their best to finish the exam within the time limit given. This round is not proof-based.

  • No tools such as calculators, books, protractors, compasses, or rulers will be allowed on the Team Test.
  • Team Tests have a time limit of approximately 30 minutes; the precise time limit varies by year and will be announced by proctors on competition day.
  • Participants work on this test together as a team: each team submits one set of answers on an official PUMaC answer sheet that the proctors will provide. Upon the completion of the test, proctors will call up a representative from the team to enter answers into the computer grading system.
  • The Team Test traditionally has a “game” component in which teams have the opportunity to increase their score. The component varies by year. See previous team tests for examples.

 

INDIVIDUAL FINALS

The top 10 individuals in each test, in each division, will be invited to take the Individual Finals exam. This competition is proof-based.

  • The Individual Finals exam has a time limit of one hour.
  • There will be three questions, intended to be in increasing order of difficulty. Participants in different divisions will receive different sets of questions.
  • Participants are NOT allowed to collaborate on this part of the competition.
  • Participants will NOT be allowed to leave early from the exam room.

 

LIVE ROUND

The Live Round is a test which every team takes concurrently. The goal is to provide a test with live scoring so that teams may see everyone's progress in relation to their own, making for a lively atmosphere. You can read a description of the Live Round, as well as complete rules, here: PUMaC Live Round Description.

 

SCORING

We announce at the awards ceremony and post on our website rankings of the top 10 team performances on the Power Round, Team Test, and overall team standings. We also announce and post rankings of the top 10 individual performances for each Individual Test subject, and the top 10 overall individual performances.

The Team Test and Power Round have points assigned to each individual problem. Additionally, each problem on the Individual Finals test is worth 7 points for historical reasons associated with Olympiad grading. In contrast, problems on the Individual Tests do not have pre-assigned point values. Instead, we compute points for each problem based on how many people successfully solve the problem versus how many people attempted it. How we do so and more are described in detail here: PUMaC Scoring Description.

We compute team and individual overall scores by summing up performances in different components:

  • Overall team rankings will be based upon their performance in the Power, Individual, and Team Tests. Individual Finals scores have no bearing on a team’s final score.
  • In the end, each team will have 16 Individual Test scores. For teams not consisting of individuals, only the top 5 scores in each subject will count towards a team’s final score. For example, if a team only takes Algebra and Geometry exams, then only the top five scores in those tests will count toward that team’s final score. However, if a team distributes its team members more evenly among individual tests, then more of their scores can count.
  • Individual overall rankings will be calculated as follows: Each of the two Individual Tests will contribute 25% of a participant’s overall individual score, and Individual Finals will contribute 50%.
  • In the case of a tie in the individual overall rankings, the higher rank will be given to the participant who solved the more difficult questions on the Individual Finals round. If a tie persists, the participant with the more elegant proof will be given the higher rank.
  • In the awards ceremony, ties for Individual Test subject rankings will be broken based on the results of the Individual Finals similarly to how ties in individual overall rankings will be broken. This tiebreaking will not affect the overall team scores.

 

The Power-Only Competition

The Power-Only Competition is a competition designed for teams that are unable to come to campus for the Main Competition. Teams competing in the Power-Only Competition will take only the Power Round of the Main Competition and will send us their solutions to be read and graded.

ELIGIBILITY

  • Teams must consist of 8 members. Individuals may not apply for the Power Competition.
  • Every team member must not have reached his or her 20th birthday before the PUMaC competition date.
  • Every team member must not have been enrolled full-time in a post-secondary institution before the PUMaC competition date.
  • See Registration Info for registration deadlines. Registration deadlines will be strictly enforced and no teams may register after the stated deadline.
  • Generally, teams should come from single high schools, but teams from well-defined geographical regions (comprising members from several schools) coming from a long distance will be allowed for their own convenience. The current Director of the Princeton University Mathematics Competition will have the final word on the legitimacy of teams that do not come from an individual school.

 

TEST RULES

The Power Round rules in the Power-Only Competition are identical to those given in The Main Competition rules section above. Although the test rules and submission guidelines are identical, the actual process of submitting differs (see below).

 

SUBMISSION

Please submit the Power Test as a single file (PDF preferred) by email so that it is received by 8:00 AM Eastern Time (UTC-5) on the day of the competition. An email address to send submissions will be given to all competing teams. Any other means of submission must be approved by PUMaC prior to the start of the competition. Notify us in advance if email is not possible for your team, and we will do our best to accommodate your needs.

Please note that these submission rules apply only to teams competing in the Power-Only Competition. Teams participating in the Main Competition are able to submit their tests in person.