The Canadian Mathematical Olympiad (CMO) is Canada’s premier national advanced mathematics competition.
Competitors require an invitation from the Canadian Mathematical Society in order to participate.
The Canadian Junior Mathematical Olympiad (CJMO), also by invitation only, is held at the same time for students up to grade ten. The CJMO is not as challenging as the CMO, however some problems may appear in both competitions.
These 3-hour competitions are held each March at a selected time and date. All official participants write at the same time.
The top students at the CMO can readily expect great scholarship and recruitment offers from universities. They will also be short-listed for the selection for Team Canada at the International Mathematical Olympiad!
The CJMO and CMO competitions were held on Thursday, March 10, 2022.
Results and solutions are now available!
|Gold Medal||Zixiang Zhou||London Central Secondary (London, ON)|
|Silver Medal||Warren Bei||Homeschool (Vancouver, BC)|
|Bronze Medal||Alec Le Helloco||Lycée Blaise Pascal (Orsay, France)|
|Honourable Mention||Cordelia Hu||Farragut High (Knoxville, TN, USA)|
|Evan Lu||Vincent Massey Secondary (Windsor, ON)|
|Kevin Min||Cupertino High (Cupertino, CA, USA)|
|Kaixin Wang||Magee Secondary (Vancouver, BC)|
|Jason Zhang||Canton High (Canton, MI, USA)|
Matthew Brennan Award for Best CMO Solution
The 2022 Award goes to Marvin Mao of Bergen County Academies (Hackensack, NJ, USA) for his solution to problem 3.
Problem 3 asked students to prove an upper and lower bound involving a game, and Marvin had a clever solution to the upper bound. He changed the rules to make the game easier to analyze, and showed that the new game still satisfies the desired upper bound. The idea to change the game was present in a few papers, but Marvin’s version was the most elegant.
|Gold Medal||Christopher Li||TTmath School and William Berczy Public School (Markham, ON)|
|Honourable Mention||Emily Ma||Mark Garneau CI (Toronto, ON)|
|Joshua Wang||Brookfield Central High (Brookfield, WI, USA)|
|Carol Wu||Port Moody Secondary (Port Moody, BC)|
|Daniel Ye||William Lyon MacKenzie CI (Toronto, ON)|
Archive of CMO Problem Sets and Solutions
- 2016: Problem Set – Solutions
- 2015: Problem Set – Solutions
- 2014: Problem Set – Solutions
- 2013: Problem Set – Solutions
- 2012: Problem Set – Solutions
- 2011: Problem Set – Solutions
- 2010: Problem Set – Solutions
- 2009: Problem Set – Solutions
- 2008: Problem Set – Solutions
- 2007: Problem Set – Solutions
- 2006: Problem Set – Solutions
- 2005: Problem Set – Solutions
- 2004: Problem Set – Solutions
- 2003: Problem Set – Solutions
- 2002: Problem Set – Solutions
- 2001: Problem Set – Solutions
- 2000: Problem Set – Solutions
- 1999: Problem Set – Solutions
- 1998: Problem Set – Solutions
- 1997: Problem Set – Solutions
- 1996: Problem Set – Solutions
- 1995: Problem Set – Solutions
- 1994: Problem Set – Solutions
- 1993: Problem Set
- 1992: Problem Set
- 1991: Problem Set
- 1990: Problem Set
- 1989: Problem Set
- 1988: Problem Set
- 1987: Problem Set
- 1986: Problem Set
- 1985: Problem Set
- 1984: Problem Set
- 1983: Problem Set
Prizes and Awards
Official competitors compete for the right to be named the CMO Champion (or CJMO Champion). We also recognize the Silver, Bronze and Honourable Mention competitors as appropriate each year. Typically, this is at least six students for CMO and fewer for CJMO.
The CMO Championship Cup is a full-size trophy that permanently commemorates the Champions. There is no equivalent for the CJMO. The Cup is normally loaned to the CMO Champion’s school to display for a year
Each year a pre-budgeted amount is allocated from the Canadian Mathematical Society and its members and sponsors. Normally, this prize pool is divided up to ensure the CMO Gold medalist gets CAD$2000 (unless there are ties) and Silver, Bronze, and Honourable Mentions also get prize money in decreasing amounts per person.
The CJMO is similar but with considerably smaller cash prizes.
Matthew Brennan Award for Best CMO Solution
In 2021 the CMS and the mathematical community lost one of our most valuable members. Matthew represented Canada twice at the International Mathematical Olympiad, earning a bronze medal in 2011 and a gold medal in 2012. He returned to the IMO as deputy leader observer in 2014 and 2017, and was the leader in 2019. Matt was passionate about Olympiad math, and had served on the Canadian Mathematical Olympiad committee since 2014. He also contributed extensively to problem creation and selection.
In Matthew’s honour, the CMS has created the Matthew Brennan Award for Best CMO Solution. It is awarded every year to the student(s) who have written the best solution to a single problem on that year’s CMO. Their solution will be included in the official solutions, and they will receive a monetary prize.
How to Earn an Invitation
All students require an invitation from the Canadian Mathematical Society in order to participate. Typically 75-100 students are invited each year to write the CMO and a further 20 students are invited to write the CJMO.
Invitations are normally sent out in February.
COMC – Canadian Open Mathematical Challenge
The primary way students to come to our attention to be considered for a CMO/CJMO invitation is by doing very well on the Canadian Open Mathematics Challenge (COMC) in October. We normally invite the top fifty (approx) qualifying COMC students to write the CMO.
CMO Qualifying Repêchage
The next 75 (approx) top qualifying COMC students are invited to write the Repêchage. This is a “take home” week-long exercise held in February. Up to twenty students are selected from this group to write the CMO.
After the Repêchage is complete, we select students for the CJMO. Anyone invited to the CMO is not invited to the CJMO. Remaining Repêchage writers who are in grade ten or less are invited to write the CJMO (normally the maximum is twenty such students). If additional spots are available, then the best qualifying COMC students in grade ten or less, who didn’t get invited to the CMO or Repêchage, are invited.
By traditional arrangement, the top winners from the Alberta High School Mathematics Competition (Part II) and from le Concours de l’Association Mathématique du Québec (AMQ – secondaire) are invited to write the CMO.
Preparing for the Olympiads
It is important to emphasize that any student who is invited to write the Olympiads should be aware that success will require mathematics at a higher level than is taught in most schools, and therefore should prepare specifically for the competition.
In order to be an official participant, all competitors:
- must be a Canadian Citizen or Permanent Resident of Canada (but not necessarily residing in Canada currently),
- must not have formally enrolled at a university or any other equivalent post-secondary institution and must not yet have graduated from high school (or equivalent),
- must be currently attending school full-time since the start of the current school year,
- must be less than 20 years old as of June 30 of the year of the Competition, and
- must not have written the Putnam Competition as an official participant.
Additionally, the CJMO requires that competitors must be in grade ten or earlier.
Students who choose to write the Competition agree to allow the CMS to publish their names and schools when announcing contest results.