Sharygin Geometry Olympiad
Type: International Geometry Olympiad
Focus: Pure Euclidean Geometry (Synthetic Geometry)
Organized by: Moscow Center for Continuous Mathematical Education (MCCME)
About: Named after Igor Fedorovich Sharygin, a renowned Russian mathematician and author of many geometry books.
- Correspondence (Qualifying) Round (Online Qualifier)
- Held online and open internationally
- Students are given a set of challenging geometry problems (typically 6–8)
- They submit detailed written solutions with full proofs
- Problems range from classical to creative and non-standard
- Final Round (Onsite in Dubna, Russia, or online in recent years)
- Top scorers are invited to the final round in Russia (or online alternative)
- Consists of proof-based problem solving over one or two days
- Includes individual and sometimes team competitions
- Open to middle and high school students globally
- Separate age categories:
- Junior group (typically grades 7–9)
- Senior group (grades 10–11)
Problems are usually available in Russian and English
Submissions can typically be written in English or Russian
Diplomas and Certificates of Participation
Special prizes for elegant solutions
Iranian Geometry Olympiad (IGO)
Type: International Geometry Olympiad
Focus: Pure Euclidean Geometry (proof-based)
Founded: 2014
Organized by: Iran’s National Organization for Development of Exceptional Talents (NODET), in collaboration with the Iranian Mathematical Society
Goal: Promote interest in geometry and encourage creative mathematical thinking among students worldwide
Key Features
International Participation: Students from many countries (over 50) participate every year
Exclusively Geometry: All problems involve classical or advanced synthetic
Emphasis on Proofs: Participants must provide full, clear, and rigorous mathematical proofs geometry
1. Levels
There are 4 levels, based on age/grade:
| Level | Grade Range | Approx. Age |
| E | Grades 6–7 | 11–13 |
| B | Grades 8–9 | 13–15 |
| C | Grades 10–11 | 15–17 |
| E | Grades 12 | 17–18 |
2. Rounds
– Single-Round Exam (organized locally in each participating country or online)
– Students receive a set of 3–4 geometry problems, with a time limit of 4 hours
– All solutions must be handwritten and submitted as scanned PDFs (if online)
– Gold, Silver, Bronze Medals, and Honorable Mentions
– Certificates for all participants
– Recognition among global math and Olympiad communities
– Strong track record of participants later succeeding at IMO and other top contests
– Problems are provided in English and Persian
– Students may write solutions in English, Persian, or other approved languages
– Open to middle and high school students globally
– Students usually participate through:
– National math societies or Olympiad training centers
– Direct registration (if allowed by the organizers)
– Most students are selected by their school, city, or national-level competitions
– Schools or national organizations must register on the IGO portal during the announced period
– The exam is either:
– Held onsite in registered centers
– Conducted online under proctoring guidelines
International Zhautykov Olympiad (IZhO)
Hosted by: Kazakhstan, but with major Russian academic involvement.
Type: International Math, Physics, and Computer Science Olympiad
Eligibility: High school students (Grades 10–12)
Format: Teams of 3 from each subject area; individuals also awarded.
Participation Route (India): Through school nominations, math training camps, or by applying directly if invited.
Focus: Problems include algebra, number theory, geometry, combinatorics
Language: English, Russian
Tournament of Towns
Highly respected international Olympiad created in Russia, now global
Open to Indian students through many schools or math clubs
Two levels: Junior and Senior
Rounds: Fall and Spring (2–3 hours per paper)
Problems: Very conceptual; focus on cleverness over technique
Official site: https://www.turgor.ru
Indian Access: Conducted in collaboration with some math teachers, clubs, or as self-submissions
Moscow Math Olympiad
One of Russia’s most prestigious city-level Olympiads
Access: Not open to international students officially, but many of its problems and past papers are available in English
Use: Ideal as practice material for high-level problem-solving
Where to find: AoPS, math olympiad archives, books like *Problems from the Moscow Math Olympiads*
Russian Math Open Competitions (Unofficial/Collaborative)
Occasionally, Russian universities or training centers organize open competitions (e.g. via MCCME or Skoltech), and sometimes invite international students.
- How Indian Students Participate:
- Through math enrichment programs in India
- International math circles
- Direct email invitations or online rounds
How Indian Students Can Access Russian Olympiads
Self-Participation
Through Schools or Math Circles
Via Olympiad Camps
Direct Registration
European Girls’ Mathematical Olympiad (EGMO)
Full Name: European Girls’ Mathematical Olympiad
First Held: 2012 (in the UK)
Inspired by: The International Mathematical Olympiad (IMO)
Purpose: To encourage more female students to participate in advanced mathematics and international competitions
Who Can Participate?
Eligibility
- Female students under the age of 20
- Not enrolled in any university course before the event
- Typically high school students
Team Composition
- Each participating country sends a team of 4 girls
- Accompanied by 1 leader and 1 deputy leader
Countries
- Open to European countries and invited guest teams from other continents (e.g., India, USA, Japan, Brazil)
Competition Format
Duration
2 consecutive days
Problems
Time
4.5 hours per day
Scoring
Maximum score: 42 points
Awards and Prizes
Gold, Silver, Bronze Medals, and Honourable Mentions
Team Rankings (unofficial, based on total team score)
Certificates and memorabilia
High scorers gain visibility and are often invited to math training programs worldwide
AMC 8 and AMC 10
AMC = American Mathematics Competitions
Organized by the Mathematical Association of America (MAA), the AMC contests are a series of international-level mathematics competitions designed to promote problem-solving skills and identify mathematical talent at the school level.
AMC 8 (American Mathematics Contest 8)
- Target Group: Students in Grade 8 or below
- Age Limit: Must be under 14.5 years on the day of the exam
- Format
- 25 multiple-choice questions
- Time: 40 minutes
- No calculators allowed
- Topics
- Algebra, geometry, number theory, combinatorics, probability
- Based on pre-high school math curriculum
- Scoring
- Each correct answer = 1 point
- No penalty for wrong answers
- Max score: 25
AMC 10 (American Mathematics Contest 10)
- Target Group: Students in Grade 10 or below
- Age Limit: Under 17.5 years
- Format
- 25 multiple-choice questions
- Time: 75 minutes
- No calculators allowed
- Topics
- High-school level math (up to Algebra II)
- Geometry, coordinate geometry, combinatorics, number theory, basic inequalities
- Scoring
- Correct answer: 6 points
- Blank answer: 1.5 points
- Wrong answer: 0 points
- Max score: 150
Asian Pacific Mathematics Olympiad (APMO)
Organized by: The Asia-Pacific Mathematical Olympiad Organization
Target Audience: High school students from Asia-Pacific regions
India’s Participation: India sends a team of selected students to this competition, which is similar to the IMO but focuses on the Asia-Pacific region.
Competition Format: The APMO involves several challenging mathematical problems similar to those in IMO.
Website: http://www.apmo-official.org
National Mathematics Talent Contest (NMTC)
Organized by: Association of Mathematics Teachers of India (AMTI)
(A highly reputed organization promoting math education in India since 1965)
Eligibility and Categories
NMTC is open to students from Grade 5 to 12, divided into the following categories:
| Category | Name | Eligible Classes |
| Sub-Junior | Primary (PRM) | Classes 5–6 |
| Junior | Sub-Junior (SUB-JR) | Classes 7–8 |
| Intermediate | Junior (JR) | Classes 9–10 |
| Senior | Inter (INT) | Classes 11–12 |
| College | Senior Level | Undergraduate |
Exam Structure
Stage 1: Preliminary Round
Objective-type questions (usually multiple-choice or short answer)
Duration: 2 hours
Conducted around September/October
Stage 2: Final Round
Descriptive/written answer format — emphasis on proofs and explanations
Held in December or January
More advanced, Olympiad-style questions
Syllabus & Topics
Topics include
Geometry
Algebra
Logical Reasoning
Combinatorics & Puzzles (especially in higher categories)
Awards and Recognition
Prizes and Medals for top scorers at each level
Top scorers may be invited to higher training camps
Recognition by Olympiad training centers and top math schools
How to Register
Individual registration is rare unless a student connects directly with AMTI or a test center.
Website: https://amtionline.com
International Mathematica Olympiad (IMatO)
Organized by: Mathematical Association of America
Target Audience: High school students worldwide
Competition Format: Students solve a series of advanced problems that require both individual ingenuity and collaboration.
India’s Participation: Indian students can compete in the Indian Mathematical Olympiad and be selected for international competitions like IMatO.
Website: https://www.maa.org
International Science and Mathematics Olympiad (ISMO)
Organized by: The World Academy of Science (WAS)
Target Audience: High school students
India’s Participation: Indian students can compete at regional stages and progress to the international stage.
Competition Format: Involves multiple rounds covering mathematics and science problems, including theoretical and applied aspects.
Website: https://www.was.org
Romanian Master of Mathematics (RMM)
Organized by: Romania
Target Audience: High school students from around the world
Competition Format: Six problems over two days, focusing on algebra, geometry, combinatorics, and number theory.
India’s Participation: Indian students are selected through INMO and represent India in RMM.
Website: https://www.rmm.ro
International Kangaroo Mathematics Contest
Organized by: International Association Kangaroo (Kangourou sans Frontières)
Target Audience: School students (up to 12th grade)
Competition Format: The contest consists of a set of problems based on logical reasoning, arithmetic, and problem-solving. The questions are accessible to a wide range of students.
Website: https://www.kangaroo.net
How Indian Students Can Participate in These Competitions
National Olympiads and Selection
Preparation
Application Process
Benefits of Participating in International Competitions
Global Recognition: These competitions offer international recognition, showcasing your skills on a global stage.
University Admissions: Top universities like MIT, Harvard, Oxford, and Stanford often highly value the participation and success in international competitions.
Scholarships: Success in these competitions can open doors to scholarships and internship opportunities in various institutions worldwide.
Networking: It offers students an opportunity to connect with like-minded peers and professionals.
Would you like more details about the application processes or preparation strategies for these competitions?