2017 Princeton University Mathematics Competition

The **2017 Princeton University Mathematics Competition** is the 12th annual PUMaC competition. The competition took place on November 18, 2017.

## Registration Info

Beginning in 2017, no half teams were allowed, but individuals applications for the main competition were allowed.

There are two separate competitions the Main Competition, and the Power Competition. Teams were only allowed to register for one of the competitions.

### Full Team Registration

#### Schedule

 Friday, September 22 (5 PM Eastern Time)
 Friday, September 29
 Friday, October 20
 Friday, October 27
 Friday, November 3
 Saturday, November 11
 Saturday, November 18

#### Payment Info

* The cost of each student is $12.50, for a total of $1000 per team. PUMaC accepts check and credit card payments.
* Teams do not send in payment if they haven't been accepted.
* teams are allowed to pay by cash/check on the day of the main competition, but most notify PUMaC with their intent to do so.
* All payments include the team member issued to the team after acceptance.
* Payments include the team numbers of all teams that the payment covers (this is only for multiple teams coming from the same school/organization).
* If an accepted and registered team doesn't pay before the fee payment deadline (October 20), that team might be replaced with a team on the waitlist).
* If a team pays its fees and withdraws, refunds will be given one week before Contest Day.

#### Additional Info

* teams should check their emails often for updates regarding registration.
* Full teams rejected from the main competition have the opportunity to join the Power Competition on a first-come, first-served, basis.
* Teams accepted to the Main Competition and don't show up or participate without notifying PUMaC beforehand may be barred from competing I the future (this is up to the discretion of the PUMaC Director).

## Test Rules

### The Main Competition

#### Eligibility - Full Teams

* Teams of eight students compete in individual, team, and proof-based math assessments. Teams will also compete in mini-events and a fast-paced live round. The day concludes with an awards ceremony.

* A full-team consists of 8 members.
* There are no-half teams available this year.
* A team member must be less than 20 years old and not enrolled in a post-secondary institution before the PUMaC competition date.
* Teams should come from a single high school, and teams from well-defined geographical regions will be allowed; the director of the Princeton University Mathematics Competition will have the final say on eligibility of teams.
* Teams also have a preference between the A Division and B Division. The A Division has more challenging individual tests, but the team, power, and live tests are the same. The A Division is for more experienced teams, and the B Division is for newer teams. Teams not from a single high school, however, must compete in the A Division.

#### Eligibility - Individuals

* An individual must be less than 20 years old and not enrolled in a post-secondary institution before the PUMaC competition date.
* Individuals will be randomly assigned to teams of 8 for the Power Round the Main Competition.
* Individuals at apply for the A or B Division, but they could be moved to a different division due to perceived strength and application numbers, but the individual gets notified beforehand.
* The registration takes part in two stages: General individual Registration and Secondary Individual Registration.
* Only students coming from schools whose teams were rejected may apply.
* 8 individuals have the opportunity to participate in PUMaC as if they were on a full team. They also have the opportunity to indicate their math achievements on their registration form.

#### The Power Round

*Main article: Power Round*

* The purpose of the Power Round is to introduce teams and individuals to proof-based mathematics - questions that may take hours and creative thinking to solve.
* The Power Round is made available online for teams a week before the competition date. There is no time limit, but the due date of the competition is the due date.
* No outside resources may be used for the PUMC Round.
* Teams and individuals must submit written solutions with justification - answers given without justification will receive no credit.
* The Power Test consists of several posts - results from previous parts can be assumed true in later parts - regardless of whether or not the team was able to prove these results.
* Solutions may be handwritten or typed, but solutions should be printed on only one side of the paper. The team shouldn't be anywhere in the submitted solutions. Teams will be allowed to submit their solutions through email or in person.
* Teams submit only one set of solutions.
* Point values are assigned to each problem on the Power Round.

#### Individual Tests

*Main article: Individual Tests*

* Every participant of PUMaC takes two Individual Tests from a choice of four: Algebra Combinatorics, Geometry, and Number Theory.
* Each Individual test will consist of 8 problems in the subject areas chosen by each participant, and it lasts 60 minutes.
* No tools are allowed on any Individual Tests, except for scratch paper, which is provided by the proctor.
* Participants aren't allowed to collaborate on this part of the competition.
* Participants may change which tests they are taking up to two weeks before the main competition.
* Participants record their answers on an official PUMaC sheet, and after all individual tests are completed, proctors call up students individually to enter answers in the computer grading system.
* For teams not composed of individual applicants, the top 5 scores per subject are summed per team when computing the individual portion of the team core.
* problems on these tests do not have pre-assigned point values, points are computed based on how many people successfully solved a problem versus how many people attempted it.

#### Team Test

*Main article: Team Test*

* The team test is a test taken at the main competition in which collaboration is allowed and encouraged. Each team is give a set of problems and they do their best in finish the round within the time limit given. This round is not proof-based.

* No tools are allowed on the Team Test.
* The time limit is 35 minutes.
* Participants work on this test together as a team, each team submits one set of answers on an official PUMaC sheet. At the end of the test, a representative of the team will be called up to enter answers into the computer grading system.
* The team test has a game component in which teams have the opportunity to increase their scene. The game component is where a team will have to come up with a second answer in which the team things that other teams will get the answer. Each team gets nk/150 points for each problem, where k is the point value of the problem, and n is the number of teams who submit that answer as their first response. No extra points are awarded if the first and second answers are the same and/or if the second answer is the correct answer.

#### Individual Finals

*Main article: Individual Finals*

* The top 10 individuals in each test, in each division, is invited to take the Individual Finals exam, which is proof-based.
* There are three questions intended to be in increasing order of difficulty, all worth 7 points, and the competition has a time limit of 60 minutes. There are different set of questions for participants in each division.
* Participants are not allowed to collaborate or leave the exam room early during the competition.
* Scores from the individual finals do not affect the team rank.
* individual overall rankings and scores will be calculated with Individual Finals counting 50%, and both of the Individual tests counting 25%.

## Mini-Events

*Main article: Mini-Events*

* Talk by Matt Weinberg
* Orange Key Tours
* Puzzle Hunt
* Board Games and Chess
* Cubing Events
* Math Bowl
* SIG Estimation Contest

## Results

* Short Results
* Extended Results

 Miscellaneous