Gauss, Pascal, Cayley, Fermat & Euclid — problems & solutions from the University of Waterloo
The Gauss Contest introduces middle school students to mathematical problem-solving through 25 multiple-choice questions in 60 minutes. Named after Carl Friedrich Gauss, it builds logical thinking and pattern recognition. Separate contests are offered for Grade 7 and Grade 8.
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The Pascal Contest challenges Grade 9 students with 25 multiple-choice questions spanning algebra, geometry, and combinatorics. Named after Blaise Pascal, it marks the beginning of the high school competition pathway. Scoring: 6 points correct, 2.5 points blank, 0 points wrong (max 150).
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The Cayley Contest targets Grade 10 students with problems requiring strategic thinking beyond the standard curriculum. Named after Arthur Cayley, questions involve number theory, combinatorics, and geometric reasoning. Same scoring as Pascal.
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The Fermat Contest is designed for Grade 11 students approaching university-level mathematics. Named after Pierre de Fermat, it features creative problem-solving challenges that go well beyond the classroom. Same format and scoring as Pascal and Cayley.
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The Euclid Contest is CEMC's flagship competition for Grade 12 students. Unlike the multiple-choice Gauss/Pascal/Cayley/Fermat contests, Euclid requires full written solutions with mathematical proofs. Approximately 10 questions in 2.5 hours. Top scores are considered for university scholarships at Waterloo and other institutions.
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Students progress through Gauss (Grades 7–8) → Pascal (Grade 9) → Cayley (Grade 10) → Fermat (Grade 11) → Euclid (Grade 12). Top Euclid performers may advance to the Canadian Mathematical Olympiad (CMO) and potentially represent Canada at the International Mathematical Olympiad (IMO).
Gauss is comparable to AMC 8, Pascal/Cayley to AMC 10, Fermat to AMC 10–12, and Euclid to AMC 12/AIME level. The key difference is that Euclid is proof-based while AMC remains multiple-choice throughout. Both systems lead to their respective national olympiads.
Each contest has 25 questions worth 150 points total. Part A (Q1–10): 5 points each. Part B (Q11–20): 6 points each. Part C (Q21–25): 8 points each. Correct answers earn full points, blank answers earn 2 points, incorrect answers earn 0.
Yes. CEMC contests are administered worldwide through registered schools. Over 200,000 students from 80+ countries participate annually. Contact CEMC or your school's math department for registration.
CEMC offers free courseware, problem sets, and the Problem of the Week on their official website at cemc.uwaterloo.ca. These are excellent supplementary resources for contest preparation.