Olympiad Problems and Solutions
This page contains problems and solutions to several USA contests, and a few others.
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}
New: Thanks to the great work of Rustam Turdibaev and Olimjon Olimov, we now have an enormous 336problem 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.
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.
See some statistics for recent years.
 USAMO 1996 (problems and solutions)
 USAMO 1997 (problems and solutions)
 USAMO 1998 (problems and solutions)
 USAMO 1999 (problems and solutions)
 USAMO 2000 (problems and solutions)
 USAMO 2001 (problems and solutions)
 USAMO 2002 (problems and solutions)
 USAMO 2003 (problems and solutions)
 USAMO 2004 (problems and solutions)
 USAMO 2005 (problems and solutions)
 USAMO 2006 (problems and solutions)
 USAMO 2007 (problems and solutions)
 USAMO 2008 (problems and solutions)
 USAMO 2009 (problems and solutions)
 USAMO 2010 (problems and solutions)
 USAMO 2011 (problems and solutions)
 USAMO 2012 (problems and solutions)
 USAMO 2013 (problems and solutions)
 USAMO 2014 (problems and solutions)
 USAMO 2015 (problems and solutions)
 USAMO 2016 (problems and solutions)
 USAMO 2017 (problems and solutions)
 USAMO 2018 (problems and solutions)
 USAMO 2019 (problems and solutions) (Math Jam)
 USAMOO 2020 (problems and solutions) (video)
 USAMO 2021 (problems and solutions) (video)
 JMO 2010 (problems and solutions)
 JMO 2011 (problems and solutions)
 JMO 2012 (problems and solutions)
 JMO 2013 (problems and solutions)
 JMO 2014 (problems and solutions)
 JMO 2015 (problems and solutions), featuring Steve!
 JMO 2016 (problems and solutions)
 JMO 2017 (problems and solutions)
 JMO 2018 (problems and solutions)
 JMO 2019 (problems and solutions) (Math Jam)
 JMOO 2020 (problems and solutions) (video)
 JMO 2021 (problems and solutions) (video)
USA TST Selection Test (TSTST)#
For an explanation of the name, see the FAQ on the USA IMO team selection.
 TSTST 2011 (problems) (solutions)
 TSTST 2012 (problems) (solutions)
 TSTST 2013 (problems) (solutions)
 TSTST 2014 (problems) (solutions)
 TSTST 2015 (problems) (solutions)
 TSTST 2016 (problems) (solutions)
 TSTST 2017 (problems) (solutions)
 TSTST 2018 (problems) (solutions) (statistics)
 TSTST 2019 (problems) (solutions) (statistics)
 TSTST 2020 (problems) (solutions) (statistics) (video 1) (video 2) (video 3)
 TSTST 2021 (problems) (solutions) (statistics)
 TSTST 2022 (problems) (solutions) (statistics)
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 (problems)
 USA Team Selection Test 2001 (problems)
 USA Team Selection Test 2002 (problems)
 USA Winter TST for IMO 2012 (problems)
 USA Winter TST for IMO 2013 (problems)
 USA Winter TST for IMO 2014 (problems) (solutions)
 USA Winter TST for IMO 2015 (problems) (solutions)
 USA Winter TST for IMO 2016 (problems) (solutions)
 USA Winter TST for IMO 2017 (problems) (solutions)
 USA Winter TST for IMO 2018 (problems) (solutions) (statistics)
 USA Winter TST for IMO 2019 (problems) (solutions) (statistics)
 USA Winter TST for IMO 2020 (problems) (solutions) (statistics)
 USA Winter TST for IMO 2021 (problems) (solutions) (statistics) (video)
 Because of the pandemic, there was no USA Winter TST for IMO 2022.
International Math Olympiad#
 IMO 1998 (problems and solutions)
 IMO 1999 (problems and solutions)
 IMO 2000 (problems and solutions)
RUSG1 USAA1 BLRA5 HUNC1 RUSN3 RUSG8  IMO 2001 (problems and solutions)
KORG2 KORA6 GERC8 CANC2 ISRG8 BGRN5  IMO 2002 (problems and solutions)
COLC1 KORG3 ROMN6 ROMN2 INDA4 UKRG6  IMO 2003 (problems and solutions)
BRAC1 BGRN3 POLG6 FING1 IRLA4 FRAN6  IMO 2004 (problems and solutions)
ROMG1 KORA4 ESTC7 KORA1 POLG4 IRNN5  IMO 2005 (problems and solutions)
ROMG2 NLDN2 KORA5 POLN1 POLG4 ROMC6  IMO 2006 (problems and solutions)
KORG1 SRBC2 IRLA6 USAN1 ROMN4 SRBG10  IMO 2007 (problems and solutions)
NZLA1 LUXG4 RUSC6 CZEG1 UNKN6 NLDA7  IMO 2008 (problems and solutions)
RUSG1 AUSA2 LITN6 KORA1 FRAC4 RUSG7  IMO 2009 (problems and solutions)
AUSN1 RUSG2 USAA6 BLGG1 FRAA3 RUSC7  IMO 2010 (problems and solutions)
FRAA1 HKGG4 USAN5 POLG2 NLDC4 IRNA7  IMO 2011 (problems and solutions)
MEXA1 UNKC3 BLRA6 IRNC1 IRNN5 JPNG8  IMO 2012 (problems and solutions)
GREG1 AUSA3 CANC6 SAFA1 CZEG5 SRBN7  IMO 2013 (problems and solutions)
JPNN2 AUSC2 RUSG6 THAG1 BGRA3 RUSC7  IMO 2014 (problems and solutions)
AUSA1 HRVC3 IRNG5 GEOG1 LUXN3 AUTC5  IMO 2015 (problems and solutions)
NLDC2 SRBN5 UKRG6 GREG2 ALBA4 AUSC5  IMO 2016 (problems and solutions)
BELG1 AUSC4 RUSN7 LUXN3 RUSA6 CZEC7  IMO 2017 (problems and solutions)
SAFN1 ALBA6 AUTC5 LUXG2 RUSC4 USAN7  IMO 2018 (problems and solutions)
GREG1 SVKA2 IRNC4 ARMC2 MNGN4 POLG6  IMO 2019 (problems and solutions)
SAFA1 UKRG3 HRVC5 SLVN1 USAC3 INDG7  IMO 2020 (problems and solutions) (video)
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)
ELMO#
See also general ELMO information.
 ELMO 2010 (problems) (solutions)
 ELMO 2011 (problems) (solutions)
 ELMO 2012 (problems)
 ELMO 2013 (problems) (solutions) (shortlist) (broken Chinese)
 ELMO 2014 (problems) (solutions) (shortlist)
 ELMO 2016 (problems) (solutions) (ELSMO)
 ELMO 2017 (problems) (shortlist with solutions) (ELSMO) (ELSSMO)
 ELMO 2018 (problems) (shortlist with solutions) (ELSMO)
 ELMO 2019 (problems) (shortlist with solutions) (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 shortanswer problems.

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