Euclid Contest Problems and Solutions: Past Papers & Examples

The Euclid Contest is a senior-level Canadian mathematics competition organized by the Centre for Education in Mathematics and Computing (CEMC) at the University of Waterloo. It is designed mainly for students in their final year of secondary school and CÉGEP students, while strong younger students may also participate. The contest has 10 questions, 100 marks, and 2.5 hours. Some parts require short answers. Others require complete written solutions.

The best way to prepare is to solve official Euclid Contest past papers. CEMC provides recent contests, official solutions, and results for free. The current archive includes the 2026 through 2017 contests. For students planning ahead, our guide to the Euclid Contest 2027 covers the latest exam date, registration deadline, eligibility, format, and preparation information.

What Is the Euclid Contest Format?

The Euclid Contest contains 10 problems worth 10 marks each. The contest lasts 150 minutes. Questions become more challenging as the paper progresses. Full-solution parts are graded for completeness, clarity, and presentation. A correct answer without a clear solution may not receive full marks.

The contest mainly uses mathematics from the senior secondary curriculum. Some problems may require students to apply ideas beyond what they have learned in class.

Euclid Contest at a Glance

The current format is important because Euclid is not only an answer-solving contest. Written reasoning is part of the score.

What Topics Appear on Euclid Contest Problems?

Euclid problems can combine several areas of high school mathematics. Recent official papers include:

• Algebra
• Geometry
• Number theory
• Counting and combinatorics
• Probability
• Functions
• Sequences and patterns
• Trigonometry
• Coordinate geometry
• Logical and strategic reasoning

The 2026 paper shows this range clearly. Early questions include algebra, digit patterns, averages, and equations. Later questions include probability, geometry, functions, triangle problems, and combinatorics.

The key pattern is application. Students often need to combine familiar ideas in an unfamiliar setting.

Where Can You Find Euclid Contest Past Papers and Solutions?

The official CEMC archive is the best source for Euclid Contest past papers and solutions. It currently lists Euclid contests from 2026 back to 2017, with the contest paper, official solution, and results for each year.

Official CEMC Past Contests archive: Euclid Contest past papers, solutions and results

CEMC states that past contests can be used to understand the format and difficulty of the competition and to prepare for future contests.

What Does the 2026 Euclid Contest Look Like?

The 2026 Euclid Contest was held on March 31 in North and South America and April 1 elsewhere. The official paper contains 10 questions and follows the standard 2.5-hour, 100-mark format.

The 2026 paper gives a useful picture of the current question style.

Early Questions: Core Skills

The first questions use familiar skills in short problems.

Examples include:

• solving a rational equation;
• finding the smallest integer with a specified digit sum;
• counting three-digit integers with a given digit-product property;
• solving a system of equations.

These questions reward accuracy and speed.

Middle Questions: Multi-Step Reasoning

The middle of the 2026 paper combines several skills.

Examples include:

• probability with dice;
• averages and rates;
• a parabola and triangle area;
• a square related to a parabola;
• percentage relationships.

These problems require students to connect multiple steps.

Final Questions: Deeper Reasoning

The last questions become more proof-oriented.

The 2026 paper includes:

• geometry with isosceles triangles;
• a proof about the number of possible triangles;
• integer side lengths;
• permutation and peak-counting problems.

This progression is one reason past papers are valuable. Students can see how Euclid moves from direct calculations to deeper reasoning.

What Are the Best Euclid Contest Problems to Practice?

Students do not need to solve every past paper immediately.

A better approach is to practice in stages.

Stage 1: Learn the Format

Start with one recent paper.

Try 2026 or 2025.

Learn:

• how the 10 questions are structured;
• where short answers appear;
• where full solutions appear;
• how much space is needed for written work.

Stage 2: Practice Recent Papers

Next, solve:

• 2024
• 2023
• 2022

These papers give several recent examples of CEMC problem design.

Stage 3: Compare Your Solutions With CEMC Solutions

Do not check only the final answer.

Compare:

1. Did you choose a valid method?
2. Did you show enough work?
3. Did every step follow logically?
4. Did you explain important claims?
5. Could another student follow your solution?

This matters because CEMC explicitly evaluates full solutions for completeness, clarity, and presentation.

Are Calculators Allowed on the Euclid Contest?

Yes, calculators are allowed under CEMC restrictions. A calculator cannot have internet access, communication functions, stored student information, a computer algebra system, or dynamic geometry software. Students must still show and justify mathematical work.

This is an important update because older Euclid preparation articles may state that calculators are prohibited. That information is no longer correct for the current contest format.

How Difficult Is the Euclid Contest?

The Euclid Contest becomes harder as the paper progresses.

The first questions usually reward strong fundamentals.

The later questions require:

• deeper problem solving;
• proof;
• mathematical modeling;
• flexible use of multiple topics;
• clear written reasoning.

The 2026 results show a mean score of 52.2/100, while the Certificate of Distinction cutoff was 66/100. The 2026 contest had 23,985 contestants.

These numbers should be used as reference points, not as a fixed definition of difficulty. The distribution changes from year to year.

What Is the Best Way to Prepare for Euclid Contest Problems?

The most effective preparation combines topic review, timed past papers, and solution writing.

A simple weekly routine can work well:

The CEMC also provides free preparation resources and courseware for high school students. Its official resources include past contests, courseware, Math Circles materials, and a Problem of the Week.

FAQ

1. Where can I find Euclid Contest past papers?

On the official CEMC website.

The University of Waterloo CEMC provides free Euclid Contest papers, official solutions, and results. The current archive lists 2026 through 2017.

2. Are Euclid Contest solutions provided by CEMC?

Yes.

CEMC publishes official solutions for previous Euclid contests. These solutions are especially important because full-solution questions are graded for completeness, clarity, and presentation.

3. Is the Euclid Contest only for Grade 12 students?

No, but Grade 12 is the main target.

CEMC describes the contest as intended for students in their final year of secondary school and CÉGEP students. Motivated students in lower grades may also write the contest.

4. Can you use a calculator on the Euclid Contest?

Yes, with restrictions.

The calculator cannot access the internet, communicate with other devices, store student materials, use CAS, or use dynamic geometry software. Students must still show mathematical reasoning.

Conclusion: Use Past Euclid Problems as Your Main Practice Tool

The best Euclid Contest preparation is not memorizing hundreds of formulas. It is solving official past problems, studying the CEMC solutions, and improving the way you write mathematical arguments.

The official CEMC archive is the best starting point, because it provides free Euclid Contest past papers, solutions, and results in one place.

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Nathan, a graduate of the University of New South Wales, brings over 9 years of expertise in teaching Mathematics and Science across primary and secondary levels. Known for his rigorous yet steady instructional style, Nathan has earned high acclaim from students in grades 1-12. He is widely recognized for his unique ability to blend academic rigor with engaging, interactive lessons, making complex concepts accessible and fun for every student.