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#

• IMO 1997 (PDF) (TeX)
• IMO 1998 (PDF) (TeX)
• IMO 1999 (PDF) (TeX)
• IMO 2000 (PDF) (TeX)
• IMO 2001 (PDF) (TeX)
• IMO 2002 (PDF) (TeX)
• IMO 2003 (PDF) (TeX)
• IMO 2004 (PDF) (TeX)
• IMO 2005 (PDF) (TeX)
• IMO 2006 (PDF) (TeX)
• IMO 2007 (PDF) (TeX)
• IMO 2008 (PDF) (TeX)
• IMO 2009 (PDF) (TeX)
• IMO 2010 (PDF) (TeX)
• IMO 2011 (PDF) (TeX)
• IMO 2012 (PDF) (TeX)
• IMO 2013 (PDF) (TeX)
• IMO 2014 (PDF) (TeX)
• IMO 2015 (PDF) (TeX)
• IMO 2016 (PDF) (TeX)
• IMO 2017 (PDF) (TeX)
• IMO 2018 (PDF) (TeX)
• IMO 2019 (PDF) (TeX)
• IMO 2020 (PDF) (TeX) (video)
• IMO 2021 (PDF) (TeX)
• IMO 2022 (PDF) (TeX)
• IMO 2023 (PDF) (TeX)
• IMO 2024 (PDF) (TeX)

European Girls Math Olympiad#

• EGMO 2012 (PDF) (TeX)
• EGMO 2013 (PDF) (TeX)
• EGMO 2014 (PDF) (TeX)
• EGMO 2015 (PDF) (TeX)
• EGMO 2016 (PDF) (TeX)
• EGMO 2017 (PDF) (TeX)
• EGMO 2018 (PDF) (TeX)
• EGMO 2019 (PDF) (TeX)
• EGMO 2020 (PDF) (TeX)
• EGMO 2021 (PDF) (TeX)
• EGMO 2022 to be written
• EGMO 2023 to be written
• EGMO 2024 to be written

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

• USAMO 1996 (PDF) (TeX)
• USAMO 1997 (PDF) (TeX)
• USAMO 1998 (PDF) (TeX)
• USAMO 1999 (PDF) (TeX)
• USAMO 2000 (PDF) (TeX)
• USAMO 2001 (PDF) (TeX)
• USAMO 2002 (PDF) (TeX)
• USAMO 2003 (PDF) (TeX)
• USAMO 2004 (PDF) (TeX)
• USAMO 2005 (PDF) (TeX)
• USAMO 2006 (PDF) (TeX)
• USAMO 2007 (PDF) (TeX)
• USAMO 2008 (PDF) (TeX)
• USAMO 2009 (PDF) (TeX)
• USAMO 2010 (PDF) (TeX)
• USAMO 2011 (PDF) (TeX)
• USAMO 2012 (PDF) (TeX)
• USAMO 2013 (PDF) (TeX)
• USAMO 2014 (PDF) (TeX)
• USAMO 2015 (PDF) (TeX)
• USAMO 2016 (PDF) (TeX)
• USAMO 2017 (PDF) (TeX)
• USAMO 2018 (PDF) (TeX)
• USAMO 2019 (PDF) (TeX) (Math Jam)
• USAMOO 2020 (PDF) (TeX) (video)
• USAMO 2021 (PDF) (TeX) (video)
• USAMO 2022 (PDF) (TeX)
• USAMO 2023 (PDF) (TeX)
• USAMO 2024 (PDF) (TeX)
• JMO 2010 (PDF) (TeX)
• JMO 2011 (PDF) (TeX)
• JMO 2012 (PDF) (TeX)
• JMO 2013 (PDF) (TeX)
• JMO 2014 (PDF) (TeX)
• JMO 2015 (PDF) (TeX), featuring Steve!
• JMO 2016 (PDF) (TeX)
• JMO 2017 (PDF) (TeX)
• JMO 2018 (PDF) (TeX)
• JMO 2019 (PDF) (TeX) (Math Jam)
• JMOO 2020 (PDF) (TeX) (video)
• JMO 2021 (PDF) (TeX) (video)
• JMO 2022 (PDF) (TeX)
• JMO 2023 (PDF) (TeX)
• JMO 2024 (PDF) (TeX)

USA TST Selection Test (TSTST)#

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

• TSTST 2011 (probs) (sols) (TeX)
• TSTST 2012 (probs) (sols) (TeX)
• TSTST 2013 (probs) (sols) (TeX)
• TSTST 2014 (probs) (sols) (TeX)
• TSTST 2015 (probs) (sols) (TeX)
• TSTST 2016 (probs) (sols) (TeX)
• TSTST 2017 (probs) (sols) (TeX)
• TSTST 2018 (probs) (sols) (TeX) (stats)
• TSTST 2019 (probs) (sols) (TeX) (stats)
• TSTST 2020 (probs) (sols) (TeX) (stats)
  • (video 1) (video 2) (video 3)
• TSTST 2021 (probs) (sols) (TeX) (stats)
• TSTST 2022 (probs) (sols) (TeX) (stats)
• TSTST 2023 (probs) (sols) (TeX) (stats)
• TSTST 2024 (probs) (sols) (TeX) (stats)

USA Team Selection Test (TST)#

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

• USA Team Selection Test 2000 (probs)
• USA Team Selection Test 2001 (probs)
• USA Team Selection Test 2002 (probs)
• USA Winter TST 2012 (probs)
• USA Winter TST 2013 (probs)
• USA Winter TST 2014 (probs) (sols) (TeX)
• USA Winter TST 2015 (probs) (sols) (TeX)
• USA Winter TST 2016 (probs) (sols) (TeX)
• USA Winter TST 2017 (probs) (sols) (TeX)
• USA Winter TST 2018 (probs) (sols) (TeX) (stats)
• USA Winter TST 2019 (probs) (sols) (TeX) (stats)
• USA Winter TST 2020 (probs) (sols) (TeX) (stats)
• USA Winter TST 2021 (probs) (sols) (TeX) (stats) (video)
• Because of the pandemic, there was no USA Winter TST for IMO 2022.
• USA Winter TST 2023 (probs) (sols) (TeX) (stats)
• USA Winter TST 2024 (probs) (sols) (TeX) (stats)

Other contests

USEMO#

Also listed on the USEMO page.

• USEMO 2019 (problems) (solutions+results)
  • (video 1) (video 2)
• USEMO 2020 (problems) (solutions+results)
  • (video 1) (video 2)
• USEMO 2021 (problems) (solutions+results)
  • (video 1) (video 2)
• USEMO 2022 (problems) (solutions+results)
• USEMO 2023 (problems) (solutions+results)

ELMO#

See also general ELMO information.

• ELMO 2010 (problems) (solutions)
• ELMO 2011 (problems) (solutions)
• ELMO 2012 (problems)
• ELMO 2013 (problems) (solutions) (shortlist) (中文)
• ELMO 2014 (problems) (solutions) (shortlist)
• ELMO 2016 (problems) (solutions) (ELSMO)
• ELMO 2017 (problems) (shortlist) (ELSMO) (ELSSMO)
• ELMO 2018 (problems) (shortlist) (ELSMO)
• ELMO 2019 (problems) (shortlist) (ELSMO)
• ELMO 2020 (problems) (ELSMO)
• ELMO 2021 (problems) (ELSMO)
• ELMO 2022 (problems) (ELSMO)

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.

• Taiwan TST 2014 Round 1 (problems)
• Taiwan TST 2014 Round 2 (problems)
• Taiwan TST 2014 Round 3 (problems)

NIMO / OMO#

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.