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Olympiad Problems and Solutions

This page contains problems and solutions to the International Math Olympiad and several USA contests, and a few others. Check the AoPS contest index for even more problems and solutions, including most of the ones below.

International Math Olympiad#

Premier USA Contests

USA Math Olympiad (USAMO)#

Despite being part of the USA team selection process, these are not the “official” solution files, rather my own personal notes. In particular, I tend to be more terse than other sources.

My understanding is that the internal problems and solutions, from the actual USA(J)MO committee, are copyrighted by MAA. To my knowledge they are not published anywhere. The Math Magazine has recently resumed publishing yet another version of the problems and solutions of the olympiad.

Recent statistics for USAMO

Download statistics for 2015-present (PDF).

Problems and solutions to USAMO

USA TST Selection Test (TSTST)#

For an explanation of the name, see the FAQ on the USA IMO team selection.

USA Team Selection Test (TST)#

These exams are used in the final part of the selection process for the USA IMO team.

Other contests


Also listed on the USEMO page.


See also general ELMO information.

Taiwan Team Selection Test#

These are the problems I worked on in high school when competing for a spot on the Taiwanese IMO team. These problems are in Chinese; English versions here.


In high school, I and some others ran two online contests called NIMO (National Internet Math Olympiad) and OMO (Online Math Open). Neither contest is active at the time of writing (April 2021) but I collected all the materials and put them in a Google Drive link since the websites for those contests is not currently online. Most of the problems are short-answer problems.

Hardness scale#

Here is an index of many problems by my opinions on their difficulty and subject. The difficulties are rated from 0 to 50 in increments of 5, using a scale I devised called MOHS.1

In 2020, Rustam Turdibaev and Olimjon Olimov, compiled a 336-problem index of recent problems by subject and MOHS rating. In addition, the linked file also contains a hyperlink to each of the corresponding solution threads on Art of Problem-Solving.

This document will probably see a lot of updates. Anyway, I cannot repeat enough the disclaimer that the ratings (and even philosophy) are my own personal opinion, rather than some sort of indisputable truth.

  1. The acronym stands from “math olympiad hardness scale”, pun fully intended

Updated Mon 13 May 2024, 19:04:50 UTC by 734e8ff1f776