HMMT Preparation: Harvard MIT Tournament Guide

HMMT preparation starts with a choice most students make carelessly: which of the two tournaments to enter. A competitor may take part in only one per season, and the two are different events.

Two tournaments, one entry

The Harvard-MIT Mathematics Tournament has run since 1998 and is organised entirely by students at Harvard, MIT and nearby schools, many of them former competitors. There are two tournaments each season: HMMT November at Harvard and HMMT February at MIT, each drawing close to a thousand students.

November is officially pitched from mid-AMC to upper-AIME difficulty, and its team round is short answer. February is pitched from mid-AIME to national olympiad level, and its team round is proof-based with partial credit.

Our advice is usually straightforward. A student new to tournament mathematics should write November and treat it as the year that teaches the format. A student already comfortable at AIME level should write February, where the ceiling is high enough to justify the trip.

Ten problems in fifty minutes

The individual tests are 10 problems in 50 minutes, short answer. February splits them by subject across three tests: Algebra and Number Theory, Geometry, and Combinatorics.

Five minutes a problem sounds generous and is not. These are not AMC problems; several will take a capable student twelve minutes or defeat them entirely.

The skill that separates scores at this level is triage: recognising within ninety seconds that a problem is not going to yield, and leaving it without the lingering doubt that costs another four minutes. We train that explicitly, because it feels like giving up and is not.

The February team round is a different examination

November's team round asks for 10 short answers in 60 minutes, so no proof experience is required. February's asks for proofs, with partial credit available.

This catches out strong teams. Four students who can each solve a problem may still score poorly if nobody can write the argument so that a grader awards it. Partial credit cuts both ways: it rewards a team that writes up an incomplete idea cleanly, and quietly penalises one that solves a problem in conversation and submits three lines of notation.

A real part of HMMT preparation for February goes to proof writing for this round specifically, including how a team divides a proof-based paper — which is not the same as dividing a short-answer one.

Guts is a tactical round

The Guts round is 36 questions in 80 minutes, delivered in sets, with a team submitting one set before receiving the next. November uses 12 sets of 3; February uses 9 sets of 4.

Because the sets are sequential, pace is a team decision taken repeatedly under pressure: submit a set with one problem unsolved and move on, or spend another three minutes and risk the sets that follow.

Teams that have never practised this lose marks that have nothing to do with their mathematics. Teams that have practised develop a default rule and stop re-deciding from scratch each time.

Topic coverage

The mathematics is the standard olympiad spread worked to speed.

Algebra and number theory covers polynomials, functional equations and modular arithmetic. Geometry covers circles, cyclic configurations, power of a point, and both trigonometric and coordinate methods — because at 50 minutes for 10 problems the fastest available method matters more than the most elegant. Combinatorics covers counting in bijection, recursion, generating functions, probability and extremal arguments.

Students who find combinatorics the limiting factor, as many do at this level, will get more from our combinatorics course than from general practice.

Preparing as a team, not only as an individual

Two of the rounds are collaborative, and almost all mathematics practice is solitary. That gap is where ordinary teams lose to coordinated ones.

The questions that decide a team round are organisational: who takes which problem, how do you check someone's work without re-solving it, and what happens when two people disagree with four minutes left. These are rehearsable and almost nobody rehearses them.

Team composition rules are specific — members must attend the same in-person school or live within 150 miles of one another, with at least one adult coach — so the team is usually fixed early and can practise together across a season.

What the November Theme round asks for

One November feature deserves its own mention because it has no equivalent elsewhere. Alongside the General round, November sets a Theme round built around a single theme that changes each year.

Students sometimes assume this means the mathematics is unusual. It is not; the topics are the standard spread. What differs is that the problems share a context, so an idea developed in an early question frequently applies later in the round.

That rewards a particular habit: noticing when you have already done most of the work. A student who treats each problem as independent will redo the same construction three times, which on a 50-minute round is fatal. Reading the whole round briefly before starting is worth the ninety seconds it costs.

A realistic preparation timeline

For a student already at AMC 12 level, three to four months of focused HMMT preparation before a tournament is a reasonable frame.

The first stretch should close topic gaps at tournament depth, worked untimed. The middle stretch moves to 50-minute individual sets, which is where triage is learned and where most of the score improvement actually comes from.

The final stretch adds the collaborative rounds, and this is the part teams skip. Guts practice in particular needs the real format — sets submitted sequentially, no going back — because the decision it trains cannot be rehearsed any other way.

Where HMMT fits

HMMT is a tournament rather than a qualifier, so it sits alongside the AMC and AIME pathway rather than replacing it. The topic overlap is almost complete and the formats differ.

For students who want more team-based tournaments, PUMaC and the Stanford Math Tournament run comparable events with different round structures, and PUMaC in particular offers a route for teams that cannot travel.

Dates, entry caps, team sizes and the online tournament option are set each season by the organisers. Check hmmt.org for the current year rather than relying on figures reproduced on a coaching page.