Euclid
The second phase of Greece's EME competition pipeline. By invitation only for top Thales performers. More challenging proof-based problems requiring sophisticated mathematical reasoning.
Grade Levels
Grades 7-12 (Ages 12-18)
Format
Proof-Based · 5 questions · 3 hours
Scoring
Each problem scored with partial credit. Higher difficulty than Thales.
Participants
Several thousand
January
Competition held in January
Registration
Automatic qualification from Thales results
Prizes & Recognition
Distinctions and certificates. Top scorers qualify for Archimedes.
About This Competition
The Euclid Mathematical Competition (Μαθηματικός Διαγωνισμός «Ευκλείδης») is the second stage of the EME competition pipeline, named after Euclid of Alexandria (c. 300 BC), the father of geometry. Only students who performed well in the Thales competition qualify to participate.
At this level, problems require significantly more sophisticated mathematical reasoning than Thales. Students must construct complete proofs and demonstrate deep understanding of mathematical concepts. The competition serves as a critical filter, identifying students with genuine mathematical talent from the broader Thales participant pool.
Top performers at Euclid advance to the Archimedes competition in March, the final qualifying stage before the Greek Mathematical Olympiad.
How to Prepare
Deepen Your Proof Techniques
Euclid problems demand elegant proofs. Study proof by contradiction, proof by induction, and the pigeonhole principle, as these appear frequently.
Allocate Time per Problem Wisely
With fewer, harder problems than Thales, spend time understanding each problem fully before writing. A clear plan saves time and avoids dead ends.
Use EME Publications and Past Papers
EME publishes detailed solutions for Euclid problems. Study these to understand the expected rigor and learn proof patterns favored by the examiners.
Embrace the Challenge of Hard Problems
It's normal not to solve every problem. Even partial progress shows understanding. Focus on writing clear, logical steps even if you can't reach the final answer.
Frequently Asked Questions
How do I qualify for the Euclid competition?
Students qualify by achieving a top score (approximately top 20-30%) in the Thales competition held in October-November. There is no separate registration.
How hard is the Euclid competition compared to Thales?
Euclid is significantly more challenging than Thales. Problems require more sophisticated mathematical reasoning and complete proofs. It represents the intermediate stage of EME's competition pipeline.
Related Competitions
Pythagoras
The Hellenic Mathematical Society's math skills competition for students in grades 2-9 (elementary and gymnasium). Features 20 multiple-choice questions testing mathematical reasoning, not rote knowledge. Held annually on a single Saturday in March.
Kangourou Greece
The Greek chapter of Math Kangaroo, the world's largest mathematics competition. Open to all grades 1-12 with multiple-choice format and emphasis on making mathematics fun and engaging.
Thales
The first phase of Greece's secondary school math competition pipeline (grades 7-12). Open to all students, with top performers qualifying for Euclid. Proof-based format requiring full written solutions.
Archimedes
The third and final qualifying stage of Greece's EME pipeline before the National Olympiad. Olympiad-level proof problems for top performers from Euclid.
Greek Mathematical Olympiad
Greece's national mathematical olympiad, the final selection stage for the IMO team. By invitation only for top Archimedes performers. IMO-style format with 6 problems over 2 days.
Balkan Mathematical Olympiad
Regional olympiad for Balkan countries including Greece, Romania, Bulgaria, and Cyprus. Important stepping stone toward IMO for participating nations.