Princeton University Mathematics CompetitionPUMaC

A full team is eight students. PUMaC states that teams need not come from a single high school — regional and homeschool teams are allowed — but they must represent a well-defined geographic region. One catch matters a lot for Irvine families assembling an ad-hoc squad: multi-school teams are normally required to compete in Division A, the experienced division, unless the organizers grant an exception. Confirm your division with them before you register.

Yes. PUMaC stopped accepting half-team applications in 2017 but still takes individual entrants for the Main Competition at the same $15 per-student fee. Two procedural points matter. First, an adult must create a coach account to be responsible for the student. Second, individual registration runs in two phases: in the first, students whose school has an active team application may not apply; the second opens only to students whose school's teams were all rejected.

Division B is for newer or less experienced teams; Division A is for established ones. The Power Round and Team Round are identical across divisions — only the individual subject tests differ in difficulty. A new school team should start in B, since placing in Division B says more than finishing last in Division A. Bear in mind, though, that teams assembled across multiple schools are usually placed in Division A, so factor that in when forming the roster.

Yes. PUMaC runs a Power Competition for teams that cannot attend: you complete only the proof-based Power Round remotely, and the remaining problems are posted after the event. A team registers for either the Main Competition or the Power Competition, never both. For a California team, it is a low-cost way to sample PUMaC's proof-writing style without flying to New Jersey, then decide about attending in person the following year.

Two official pages disagree, so check carefully. The newer Registration Info page lists $15 per student — $120 for an eight-person team and $15 for an individual entrant — while the FAQ page still shows older, lower prices. Go with Registration Info and email the organizers to confirm before paying. Registration typically opens in September and closes in mid-October, decisions are made on a rolling basis so early applicants hear sooner, and financial hardship requests are considered.

Yes, and that is one of PUMaC's distinctive features. Each student picks two of algebra, combinatorics, geometry, and number theory, with eight problems in sixty minutes per subject. Watch the scoring, though: the top ten in each subject and division advance to Individual Finals, and those finals count for fifty percent of the individual score — three proof-based problems in ninety minutes. A student who can compute answers but not write proofs will not place highly.

The Power Round is a proof-based team round released online roughly a week before the tournament; the whole team may collaborate on it across that week and submit before competition day. It is nothing like a timed exam — it behaves more like a small research project. Divide up the reading, agree on notation, set an internal deadline, and leave time to unify the write-up and hunt for logical gaps. Do not start it the night before it is due.

Each team must be accompanied by one adult, and individual entrants need a coach-account holder responsible for them in an emergency — a parent can fill either role. The competition is held in person on the Princeton campus in New Jersey, usually on a Saturday in late November, and other family members may attend although lunch is not guaranteed for them. California families should book flights and lodging as soon as acceptance is confirmed; the mid-October deadline leaves little margin.