The Euclid Mathematics Contest is organized by the Centre for Education in Mathematics and Computing (CEMC) at the University of Waterloo, Canada. It is known as the "TOEFL of the Math World" and is one of the most prestigious math competitions for students in grade 12 and below applying to top science and engineering programs in North America and the UK. The 2026 contest was held on April 2. Based on student feedback and question analysis, this year's contest is characterized by "stable early questions, challenging later questions, and high differentiation."
I. 2026 Euclid Contest In-Depth Difficulty Review
1. Questions 1–6: Foundation Points – Must Be Secured
Content Covered: Algebraic operations, linear/quadratic equations, basic number theory (divisibility, modular arithmetic), introductory analytic geometry (lines, circles), and simple applied problem modeling.
Difficulty Level: Comparable to in-class AP Precalculus / A-Level Maths – considered "easy points."
Target Score: 55–60 points (out of approximately 60). This is the absolute foundation for achieving Distinction (top 25%).
Key Reminder: Any mistake could directly cost you an award. Ensure zero computational errors.
2. Question 7: Difficulty Jumps – Abstract Thinking Emerges
Topics: Logarithmic functions + piecewise function iteration.
Challenge: Requires understanding the domain transfer and range constraints of nested functions, demanding a complete logical chain.
Typical Pitfall: Ignoring piecewise conditions, leading to an expanded solution set.
3. Questions 8–10: The "Arena" for Top Competitors
| Question | Core Topics | Difficulty Analysis |
|---|---|---|
| Q8 | Geometric properties of circles + number theory counting | Part (b) combines triangle side-length inequalities with the floor function, requiring construction of inequality systems and enumeration of feasible solutions – extremely prone to missing solutions. |
| Q9 | Cubic polynomials + Diophantine equations | Involves factorization, the Rational Root Theorem, and integer solution constraints. Heavy computation and complex steps – one mistake can ruin the entire solution. |
| Q10 | Brand new "internal peak" combinatorics | Defines a new concept, "internal peak," requiring on-the-spot understanding and construction of recurrence relations or dynamic programming models. No set pattern to follow – highly creative. |
II. 2026 Euclid Contest Score Predictions
Due to the increased difficulty of the last three questions, and despite the relative stability of the first six questions, the number of high-scoring candidates is likely to decrease. The Distinction cutoff is expected to drop slightly.
| Award | 2025 Cutoff | 2026 Estimated Cutoff | Explanation |
|---|---|---|---|
| Distinction (Top 25%) | 68 | 65–67 | Q8–Q10 lower the mean for high-scoring segment. |
| Honor Roll (Top 5%) | ≈80 | 78–80 | Almost no one scored full marks on Q10. |
| Perfect Score (100) | Very few | Extremely unlikely | Q10 is a completely new type of problem, making a perfect score very difficult. |
Official Release: CEMC typically releases official cutoffs and results 5–6 weeks after the exam (i.e., mid-May 2026).
III. Post-Exam Golden Planning Guide
Phase 1: Before Results (April–Mid-May) – Consolidation & Expansion
Synchronize with In-Class Knowledge: The topics tested in Euclid (functions, polynomials, trigonometry, sequences, analytic geometry, number theory, etc.) heavily overlap with AP Calculus, IB HL Math, and A-Level Further Math. Strike while the iron is hot to avoid forgetting.
Plan Next Competitions:
Lower grades (G9–G10): Prepare for AMC10/12, Kangaroo Math, CEMC Fryer/Galois/Hypatia.
Upper grades (G11–G12): If you did well, consider challenging AIME or the Canadian COMC.
Phase 2: After Results (Late May Onward) – Precise Positioning
Save Your Results: Log in to the CEMC official website to download your PDF certificate and archive it with standardized naming.
Adjust Your Academic Strategy Based on Score:
| Score Type | Recommended Direction |
|---|---|
| Top 2.5%+ (≥85) | Aim for pure mathematics, theoretical physics, theoretical CS; consider preparing for advanced competitions like BMO or Putnam. |
| Steady Top 25% (65–75) | Suitable for applied science and engineering fields such as engineering, electronics, materials, data science – a "lane-changing advantage." |
| No Award (<60) | Timely pivot to humanities, social sciences, business (non-quantitative tracks), art & design, etc., leveraging other strengths. |
