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Math Coding

CEMC Contests

University of Waterloo Centre for Education in Mathematics and Computing Contests

Canada's national contest ladder, from grade 7 puzzles to the Canadian Computing Olympiad.

Run by University of Waterloo

Key facts

Eligible grades
A ladder of contests by grade. Gauss for grades 7 and 8; Pascal for grade 9; Cayley for grade 10; Fermat for grade 11; Euclid for senior secondary, designed for grade 12; CIMC for grades 9 and 10; CSMC for grades 11 and 12 and CÉGEP students; Fryer, Galois and Hypatia as full-solution contests for grades 9, 10 and 11 respectively.
Motivated students in lower grades are welcome to write a higher contest, and students working ahead a grade or more may choose the more advanced one. But a participant may write only ONE of Pascal, Cayley and Fermat in a school year, and only one of the Gauss contests. Choose deliberately.
Source, checked 2026-09-02
Official divisions
A ladder with a contest per grade: Gauss for grades 7 and 8, Pascal grade 9, Cayley grade 10, Fermat grade 11, Euclid designed for grade 12, plus full-solution contests Fryer, Galois and Hypatia for grades 9, 10 and 11. You may write only one of Pascal, Cayley and Fermat in a year, so choose the one matching your course.
Based on the organiser's own divisions.
Eligible ages
Not confirmed. This organiser may set eligibility by grade rather than age. We do not convert one into the other.
CEMC sets eligibility by grade, not age.
Individual or team
Individual · Individual, with an optional school Team Competition on some contests where the team score is the sum of the three highest-scoring participants. Schools may opt out of the team competition. New in 2026, CEMC no longer provides team honour rolls or awards at zone, provincial or national levels.
Where it runs
In person · Canada, International
Entry cost
A modest per-student fee paid by the schoolCEMC charges the school for contest orders rather than publishing a per-student price, and schools pass on varying amounts. One Toronto school charged students $7 for Pascal, Cayley or Fermat. Ask your school. Separately, all CEMC practice resources, past contests and problem sets are free with no registration required.
Registration deadline
Set locally, not published as a single national date CEMC begins accepting contest orders for 2026-27 in September 2026. There is no single student deadline: your school sets its own, typically about four weeks before each contest. In a recent cycle one school's Pascal, Cayley and Fermat registration closed 30 January for a 25 February contest.
Competition dates
Tentative 2026-27 dates published by CEMC: Canadian Senior and Intermediate Mathematics Contests 19 November 2026; Canadian Computing Competition 18 February 2027; Pascal, Cayley and Fermat 25 February 2027; Euclid 7 April 2027; Fryer, Galois and Hypatia 8 April 2027; Canadian Team Mathematics Contest 14 April 2027 or later; Gauss 10 to 21 May 2027; Team Up Challenge 1 June 2027 or later.
Difficulty
Some preparation neededYou will want a few weeks of targeted practice. Most motivated students place respectably.
Prizes
Certificates, medals and Waterloo scholarship considerationRecognition through honour rolls and results booklets rather than cash prizes. CEMC reserves the right to disqualify students or withhold publication of results at its discretion.

What CEMC Contests is

The University of Waterloo runs a full family of mathematics and computing contests spanning grades 7 to 12: Gauss, Pascal, Cayley, Fermat, Fryer, Galois, Hypatia, Euclid, and the Canadian Computing Competition. They are written at schools worldwide, not only in Canada, and Waterloo publishes every past paper with full solutions for free, which makes this the best-documented contest family in the world.

How the competition works

Formats differ by contest. Pascal, Cayley, Fermat and Gauss are one-hour multiple-choice. Euclid is 10 questions in 2.5 hours, mixing final-answer and full-solution, scored out of 100. CIMC and CSMC are 9 questions in 2 hours, 6 answer-only and 3 full-solution, scored out of 60. For the full-solution contests each solution is assessed for completeness, clarity and presentation style: a correct solution that is poorly presented will not earn full marks. All are written in school on paper, individually, with some calculators permitted.

Eligibility notes

Contests are matched to grade: Gauss for grades 7 and 8, Pascal for grade 9, Cayley for grade 10, Fermat for grade 11, Euclid for senior students. You may write a contest above your grade level but not below.

How to register

  1. Ask your maths or computer science teacher whether the school already writes CEMC contests. Many international schools do.
  2. If not, a teacher registers the school as a contest centre on the CEMC site and orders papers for the contests they want to run.
  3. Write the contest at school on the scheduled date.
  4. Results and certificates are returned to the school.

Register on the official site

What skills you need

  • Algebra
  • Geometry
  • Number theory
  • Full-solution writing for Euclid
  • Programming in C++, Python or Java for the CCC

How to prepare

The CEMC publishes every past paper since the 1990s with complete official solutions, plus free online courseware. No other contest family gives you this much free material, so preparation is entirely a matter of working through the archive systematically.

What to study

Multiple-choice contests
Gauss, Pascal, Cayley and Fermat cover school curriculum content stretched into contest problems. Speed and accuracy matter more than advanced material.
Euclid
Ten full-solution problems in 150 minutes. Written work is marked, so presentation and complete reasoning earn marks that a bare answer does not.
Canadian Computing Competition
Junior division tests implementation and basic algorithms; Senior division tests graphs, dynamic programming and data structures.

Full preparation guide, including a week-by-week plan

Recommended resources

  • CEMC past contests archive Past problems · free

    Every past paper with full official solutions, free, going back decades.

  • CEMC Courseware Course · free

    Free structured online courses in mathematics and computer science, written by the contest organisers.

  • CEMC At Home problem sets Practice · free

    Free graded problem sets with solutions.

Past problems and materials

Only materials the organiser or an authorised archive publishes openly are listed here.

Helpful videos

Frequently asked questions

Can students outside Canada write CEMC contests?

Yes. Schools worldwide register as contest centres and write the same papers on the same dates. International participation is substantial.

Which CEMC contest should I write?

Match it to your grade: Gauss for grades 7 and 8, Pascal for grade 9, Cayley for grade 10, Fermat for grade 11. Euclid is for senior students regardless of grade. You may write above your grade but not below.

Does Euclid actually matter for Waterloo admission?

Waterloo states that Euclid results are used in admissions and scholarship decisions for its mathematics and computer science programmes. If Waterloo is on your list, it is one of the few competitions with a direct, documented admissions effect.

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