What is the Euclid Mathematics Contest?
The Euclid Mathematics Contest is the flagship Grade-12 paper of the CEMC — the Centre for Education in Mathematics and Computing at the University of Waterloo. Around 25,000 students worldwide write it each April: ten problems, two and a half hours, one hundred marks, on paper, at school. What sets it apart is the marking: full-solution problems are graded step by step for completeness, clarity and presentation — the writing earns the marks.
“It is very important for students to both learn to solve mathematics problems and learn to write good solutions to these problems.”CEMC · official results booklet
Two kinds of marks, one paper
Every problem is worth 10 marks, but the marks are earned two different ways. Problems 1–8 each carry two or three largely independent parts; problems 9–10 build through linked parts to the hardest finish in the CEMC family. On the booklet itself, a lightbulb symbol marks parts where the final answer alone earns full credit, and a hand symbol marks parts graded as written solutions, step by step.
Two to three short parts per problem — roughly twenty questions across the paper. Early parts sit inside final-year school mathematics; nearly every writer scores here. Answer-only parts reward accuracy, and exact values: graders note that decimal approximations do not earn full marks.
Multi-part, fully-written arguments that chain together — designed, in the CEMC’s words, to “challenge the top students.” In 2026 the world averaged 1.2 / 10 on problem 9 and 0.73 / 10 on problem 10. Partial reasoning still earns marks — a well-written half solution beats an unexplained answer.
Some calculators are permitted, with strict feature limits — the full device policy lives with the contest-day guidelines.
The difficulty cliff, measured
The CEMC publishes the world-average score for every problem. The 2026 gradient tells the whole strategy of the paper: a gentle start almost everyone converts, then a cliff where written arguments decide everything. Reading this chart is the first step of any sensible preparation plan.
Built for Grade 12 — open earlier
The paper targets students in their final year of secondary school (or CÉGEP), and the CEMC explicitly welcomes motivated younger writers. In practice most writers sit it in Grade 11 or 12, with strong Grade 9–10 students entering early for experience.
The contest is written at a registered school or authorized test centre, on paper, under in-person supervision, on the official date. In China, seats run through authorized test centres — the registration guide covers both routes.
Eight topic areas, freely combined
Problems are drawn from curricula up to and including the final year of secondary school — though the CEMC notes some problems may reach beyond the classroom. Its own preparation material organizes the ground into eight areas, and warns that contest problems often combine different topics in a single argument:
Certificates, medals, honour rolls
Certificate of Distinction
Top 25% of writers worldwide. The 2026 line sat at roughly 66 / 100; 2025 at about 68.
Contest Medal
Each school’s champion at or above the medal cutoff — 52 marks in 2026, 54 in 2025.
Honour Rolls & Champions
Zone, provincial, national and international rolls; Canada’s top five earn plaques and prizes. Names publish only with consent.
Schools compete too: a school’s team score is the sum of its three best official papers, feeding zone, provincial and national championships. Five recent years of the world picture, from the official results booklets:
Ordering opens
Schools and test centres begin registering writers for the 2026/27 cycle.
Ordering deadline
The hard stop — orders close a full month before the paper is written.
Hard deadlineThe sitting
April 6 across the Americas; April 7 everywhere else, China included. Written at school, on paper.
Results & certificates
Results reach schools through the supervisor portal; the public results booklet follows.
Five questions about the contest itself
Is the Euclid multiple choice?
No. The Euclid has no multiple-choice section at all. Parts are either final-answer questions — where the exact value earns the marks — or full-solution questions graded line by line on the writing. That structure is exactly why it rewards a different kind of preparation from bubble-sheet contests.
Do wrong answers lose marks?
There is no negative marking. Better: on full-solution parts, correct reasoning earns partial marks even when the final answer is wrong. The costly mistakes are unexplained answers and decimal approximations where exact values are required — both leave earned marks on the table.
How does the Euclid differ from AMC 12?
AMC 12 is 25 multiple-choice questions in 75 minutes — speed and selection. The Euclid is 10 free-response problems in 150 minutes — depth and written argument. Many strong students write both; the skills overlap but the training differs. The related-competitions guide maps the whole landscape.
Can I write both the CSMC and the Euclid?
Yes — they are different sittings in the same CEMC family: the Canadian Senior Mathematics Contest runs in November, the Euclid in April. Waterloo’s Faculty of Mathematics encourages applicants to write at least one of the two for scholarship consideration, and many serious applicants write both.
What happens if a paper is flagged for irregularities?
The CEMC enforces integrity firmly: flagged results can be disqualified, and in severe cases a school can lose access to CEMC contests in following years. Recent seasons have seen anomalous scores cancelled. Appeals run only through the writing school or test centre — contest-day conduct rules are detailed in the guidelines.