PUMaC prep
PUMaC is the Princeton University Mathematics Competition, run by the Princeton Math Club, with a Power Round, individual tests in four subjects, a team round and an invited-only Individual Finals.
PUMaC at a glance
- Individual tests
- Each student takes two of four subjects: Algebra, Combinatorics, Geometry and Number Theory.
- Divisions
- Division A for experienced teams and Division B for newer ones, with harder individual tests in A.
- Individual Finals
- The top individuals in each test and division are invited to a three-problem, proof-based final.
Who this is for
Picking two subjects out of four is the unusual part of PUMaC, and it makes the tournament an easy one to specialize for. If you already know your two strongest subjects, you can spend most of your practice on them.
Take the matching individual tests from past years, and leave the Power Round for a practice session with your team.
PUMaC problems carry subject tags, and a Custom set on Number Theory or Combinatorics draws on the same material the tests do.
What Lemmas has for PUMaC
- Problems in the bank
- 168
- Years covered
- 2022 to 2025
- Median difficulty, out of 100
- 55
PUMaC has 168 problems on Lemmas, taken from 21 tests between 2022 and 2025. The ratings run from 22 to 77, and the median of 55 is 7 points above the AIME's 48.
Arena has 21 PUMaC tests, each with 8 problems. The middle half of the ratings sits between 42 and 62; the About page says how the scale is built.
Division A against Division B
Division A problems have a median rating of 59, and Division B problems 47. Within a test, problems 1 and 2 rate 37 at the median and problems 7 and 8 rate 63.
- Division A, median rating
- 59
- Division B, median rating
- 47
PUMaC problems by subject
Number Theory comes first in the PUMaC bank with 53 problems and Geometry comes last with 32.
- Number Theory, 32% of the bank
- 53
- Algebra, 27% of the bank
- 46
- Combinatorics, 22% of the bank
- 37
- Geometry, 19% of the bank
- 32
PUMaC after the AIME
Written proofs appear in two places at PUMaC, the Power Round and the Individual Finals, while the AIME takes only integer answers from 0 to 999. A student arriving from the AIME also chooses two subjects out of four and sits tests built for them.
Questions about PUMaC
Which subjects can I pick at PUMaC?
Two of Algebra, Combinatorics, Geometry and Number Theory. The team events are the same for every team.
What is the difference between Division A and B?
Division A is for experienced teams and gets harder individual tests. Division B is recommended for newer teams.
Is PUMaC proof-based?
Parts of it are. The Power Round and the Individual Finals ask for written proofs.
Where the PUMaC problems come from
PUMaC's organizers gave written permission, by email, for these problems to appear on Lemmas, and each one is credited to the Princeton University Mathematics Competition.
PUMaC on the Princeton University Math Club website (opens in a new tab)
Make an account and try your first problem.
Username, email and password. No card.