Re-solve the same problem after 1 week, then 1 month. If you solve it instantly, you have internalized the technique. If not, repeat Step 2.
After the hour, read the official solution. Compare it to your attempt. Ask:
The internet is flooded with scanned copies, but finding high-quality, legible, and accurate PDFs requires knowing the right sources. Below are the most reliable venues for free and legal downloads.
Finding reliable PDF collections and translated solutions for Russian Math Olympiads (RMO) requires navigating through historical archives and specialized math communities. The following guide categorizes the best available digital resources. Primary PDF Archives & Solution Banks
These sites host translated problems and solutions ranging from the Soviet era to modern competitions.
IMOmath (Russian Problem Collection): This is one of the most comprehensive archives, featuring problems from 1961 to 2009. It organizes problems by year and competition round. Explore the Russia Problem Collection on IMOmath. russian math olympiad problems and solutions pdf
Art of Problem Solving (AoPS): The gold standard for competition math. Their community wiki and forums contain vast threads for the All-Russian Olympiad (ARO), often including community-vetted solutions. View the All-Russian Olympiad posts on AoPS.
John Scholes' (Kalva) Archive: A historical treasure trove providing detailed solutions for the All-Soviet Union Mathematical Olympiad (1961–1992) and the Russian Mathematical Olympiad (1995–2002). You can find these preserved on Kalva's RMO Archive.
Mathematik Alpha: Offers direct PDF downloads of translated Russian Math Olympiad problems, including complex geometry and logic puzzles. Access their Math Olympiad PDF collection. Curated Books & Compilations
Several foundational books compile these problems into structured formats with instructional solutions.
The USSR Olympiad Problem Book: Written by Shklarsky, Chentzov, and Yaglom, this classic contains 320 unconventional problems in algebra, number theory, and trigonometry. It is available as a free PDF on Archive.org. Re-solve the same problem after 1 week, then 1 month
Moscow Mathematical Olympiads (60-odd Years): Edited by D. Leites, this book provides complete answers and solutions to the prestigious Moscow-specific contests, which are often more difficult than the national rounds. A version is hosted on Scribd's Moscow MO archive.
All-Russian Mathematical Olympiads (The Road to IMO): A series of books available through major retailers like Amazon that provide elementary to advanced problems used for IMO team selection. Practice Problems by Grade Level
For students looking for level-appropriate practice rather than the highest-level "federal" stages:
Russian School of Mathematics (RSM): Provides practice problems and solutions specifically for younger grades (3–8) modeled after the RMO format. Download them from the RSM Competition Preparation page.
Scribd Collections: Various users have uploaded PDFs containing hundreds of problems from specific years, such as the 2012 All-Russian Math Olympiad or recent 2024 problem sets. Practice Problems from the Russian Math Olympiad Russian number theory problems are distinct because they
The file can be saved as a PDF by copying the text into a word processor and exporting as PDF, or using LaTeX (source provided at the end).
Russian number theory problems are distinct because they rely heavily on modular arithmetic and divisibility properties rather than heavy analysis.
This is a classic English-translation book covering problems from Grades 9-11 with deep combinatorial and number theory problems.