Organized by the University of Waterloo in Canada, the Euclid Contest is a significant academic credential for high school students worldwide applying to STEM, Economics, and Computer Science programs. Known for its emphasis on "process, integration, and no calculus," the contest appears moderately difficult but is filled with hidden pitfalls—especially for students accustomed to "only providing the final answer." This article systematically outlines the three core difficulties and provides clear step-by-step solution standards and strategies for high-frequency topics, helping you move from "knowing how to solve" to "getting full marks."
I. Three Core Exam Difficulties
Difficulty 1: Extremely High Requirements for Solution Steps; Differences in Chinese-English Logical Expression Lead to Point Losses
Scoring Mechanism: Uses a "Part Marks" system—even if the final answer is incorrect, you can still earn points as long as key steps are correct; conversely, a correct answer without any process may receive zero or very low points.
Typical Scenarios for Point Loss:
Geometry: Directly writing "△ABC ∽ △DEF" without stating the basis (e.g., AA similarity).
Algebra: Skipping substitution or factorization steps and directly writing the result.
Probability: Failing to list the sample space or define events.
Differences in Chinese vs. English Thinking: Chinese tends toward implicit understanding, while English emphasizes an explicit logical chain. You must use structures like "Because…, therefore…" to clearly articulate causal relationships.
Countermeasure: Write each problem using the three-part structure: "Given → Derivation → Conclusion." Cite the names of key theorems or formulas (e.g., "By the Pythagorean Theorem…").
Difficulty 2: Highly Integrated Knowledge Points; No Single Module Can Solve the Problem
Recent exam data show that over 80% of Questions 8–10 are cross-module integrated problems. Examples include:
| Integration Type | Example from Past Exams |
|---|---|
| Geometry + Algebra | 2024 Q9: Cyclic quadrilateral → set up equations to find side lengths |
| Sequences + Number Theory | 2025 Q10: Recurrence sequence → analyze periodicity modulo 3 |
| Probability + Functions | 2023 Q8: Expected value of a random variable → construct piecewise functions to find extremum |
Countermeasure: Train your "module-switching" ability—when you see a geometry diagram, think about assigning algebraic variables; when you encounter a sequence, consider whether divisibility or periodicity is involved.
Difficulty 3: Complex Problem Statements; Mathematical Modeling Ability Is Key
An increasing number of problems embed real-world contexts (e.g., population growth, investment returns, network paths). Test-takers must first abstract the mathematical structure from the text before applying the appropriate tools to solve it.
Example: 2025 Q7: "Each year, a city's new population is 5% of the previous year plus 2,000 people." → Recognize this as a linear non-homogeneous recurrence sequence.
Countermeasure: Practice "translating the problem statement" into mathematical language (e.g., "increased by 5%" → "× 1.05").
II. High-Frequency Topics & Sprint Strategies
Core Data (2025)
Number of Participants: 27,092
Average Score: 54.8
Top 25% (Certificate of Distinction): ≥ 68 points
Top 5%: ≥ 85 points
Top 1%: ≥ 95 points
Sprint Target Breakdown
| Target | Strategy Focus |
|---|---|
| Top 25% (68+ points) | Perfect score on Q1–7 (≈60 points) + earn 8 points on Q8–9 |
| Top 5% (85+ points) | Maximum 2 points lost on Q1–7 + ≥18 points on Q8–9 + earn step points on Q10 |
| Top 1% (95+ points) | Near-perfect on the entire paper + full solution to Q10 |
List of High-Frequency High-Value Question Types
Combinatorics + Number Theory: Counting with constraints (e.g., three-digit numbers that do not contain the digit 5).
Geometric Extremum Problems: Using symmetry or the triangle inequality to find the shortest path.
Recurrence Sequences: Linear/non-linear recurrences combined with modular arithmetic to analyze periods.
Functional Equations: Finding the form of f(x) given conditions like f(x+y) = f(x) + f(y).
