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.
Grade Levels
Grades 7-12 (Ages 12-18)
Format
Proof-Based · 4 questions · 3-4 hours
Scoring
Rigorous scoring. Full proofs required. Solutions must be complete and well-structured.
Participants
Hundreds
March
Competition held in March-April
Registration
Automatic qualification from Euclid results
Prizes & Recognition
National medals. Top Lyceum performers invited to Greek Mathematical Olympiad selection.
About This Competition
The Archimedes Mathematical Competition (Μαθηματικός Διαγωνισμός «Αρχιμήδης») is the final qualifying stage before the Greek Mathematical Olympiad, named after Archimedes of Syracuse (c. 287-212 BC). At this level, problems approach international olympiad difficulty.
Only students who excelled at Euclid are invited to participate. The competition requires complete, rigorous mathematical proofs across number theory, combinatorics, algebra, and geometry. Top performers, primarily from lyceum, are selected for the Greek Mathematical Olympiad, which serves as the final selection for Greece's IMO, BMO, and EGMO teams.
How to Prepare
Train with Olympiad-Level Problems
Archimedes is the final national stage before the Olympiad. Solve problems from past Archimedes and BMO rounds to calibrate your level.
Write Rigorous, Complete Proofs
Partial marks are given for clear reasoning. Structure each proof with definitions, lemmas, and a logical conclusion. Graders reward rigor.
Study Advanced Problem-Solving Books
Books like 'Solving Mathematical Problems' by Terence Tao and EME's advanced problem collections are excellent preparation for this level.
Persevere Through Difficult Problems
At the Archimedes level, problems are designed to be challenging. Spending 30-60 minutes on a single problem is normal. Don't give up too quickly.
Frequently Asked Questions
What level is the Archimedes competition?
Archimedes is the most advanced stage before the Greek Mathematical Olympiad. Problems approach international olympiad difficulty, particularly for lyceum students. Only students who excelled at Euclid are invited.
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.
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.
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.