Verified PDF collections typically fall into three categories: official national archives, specialized geometry collections, and historical problem books. IMOmath Problem Collection

Properties of integers, divisibility, and modular arithmetic.

provides a central repository for the All-Russian Mathematical Olympiad, including printable PDF collections for recent years, such as the 2019 All-Russian Olympiad . John Scholes (Kalva) Archive

The Russian Math Olympiad is a prestigious mathematics competition that has been held annually in Russia since 1964. The competition is designed to identify and encourage talented young mathematicians, and its problems are known for their difficulty and elegance. In this paper, we will present a selection of problems from the Russian Math Olympiad, along with their solutions.

board like a standard chessboard with alternating black and white squares. A board has exactly 50 black squares and 50 white squares.

The sum of an odd number of odd numbers is always odd . Therefore, 25 T-tetrominoes must cover an odd number of black squares. However, our board contains exactly 50 black squares, which is an even number. Conclusion: It is impossible to cover a board with 25 T-tetrominoes. Top Resources for Verified RMO Problems and Solutions PDFs

AoPS maintains a community-vetted archive of the problems. These are often translated into English and include discussion threads for various solution methods.

Spotting concyclic points and exploiting the properties of inscribed angles.