The Harvard-MIT Mathematics Tournament (HMMT) is a high school competition that is held in Cambridge, MA and the competition location typically alternates between Harvard University in November and MIT in February. This tournament attracts many top students in mathematics from everywhere. Like PUMaC, HMMT is also organized by student volunteers who are currently attending Harvard and MIT.
I never participated in the November contest but got a chance to participate in the February one. The differences between the two are listed here. November one can have 6 students and the February one can have 8 students in one team. I have to admit that this is not an easy contest and so guidelines of knowing your level and participating in the right one is important. For example, if you can do first few problems of AIME comfortably, then participate in the November one where as if you can do later AIME problems and AMO problems, then participate in the February one.
Overall, I was exhausted at the end of the day after doing many hours of math. We started in the morning with the Team (Proof based) round first then you get 3 individual tests for Algebra, Geometry, and Combinatorics which are 50 minutes each. These problems are like harder AIME problems and I was able to solve four in each category. We got a nice lunch break after the individual round and then proceeded to the Guts round. This is a fun round where you can see how your team is doing on a big screen in the MIT Math building. At one point, my team was in the top 15 teams which made me feel very proud. The best way to prepare for this contest is to practice using previous tests which are here. I also really enjoyed practicing with my team a few weeks prior to the test. We met for a few days on the weekends.
Overall, the student volunteers at Harvard and MIT did a wonderful job in organizing the event with close to 1000 high school students on the campus. I also got a chance to visit MIT and sit through their information session.