The Final Boss

Master-Level Problems in the Spirit of IMO Problem 6

A demanding collection of 99 olympiad problems for readers ready to explore the deepest end of high-school mathematics.

Inspired by Problem 6 of the International Mathematical Olympiad (IMO), this book is for ambitious students, coaches, and mathematical problem-solvers who want to go beyond routine exercises. The problems are designed to reward creative insight, careful reasoning, and persistence—not memorized templates. They draw on elementary mathematics, pushed to a high level, and do not require university-level calculus or abstract algebra.

What’s inside

The collection spans all four core olympiad disciplines: algebra, geometry, number theory, and combinatorics. The problems are calibrated in the 35M–50M+ range on Evan Chen’s Math Olympiad Hardness Scale (MOHS), the challenging territory associated with the hardest olympiad problems.

Across the book, you will encounter functional equations, inequalities, and polynomials; geometric configurations and projective ideas; Diophantine equations and modular methods; and combinatorial problems involving extremal reasoning, invariants, graphs, and games.

Each problem is presented in competition style, followed by a carefully pitched hint and a full solution. The solutions conclude with takeaways that highlight useful strategies and ideas to carry into future problems. The appendices provide reference toolkits across the four subjects, a problem-and-technique cross-reference, and recommended further reading.

How to use the collection

Give each problem a serious attempt before turning to its hint. If you remain stuck, use the hint as a nudge, then return to the problem and develop the argument yourself. Afterward, study the complete solution, check the details of your proof, and reflect on the takeaways. The problems are demanding by design; working carefully through a selection can be more valuable than rushing through the whole book.

Who it’s for

This book is intended for strong high-school students preparing for national olympiads and the IMO, coaches looking for advanced training material, and readers who enjoy challenging, non-routine mathematics. It assumes comfort with standard high-school mathematics and a willingness to write complete proofs. The problems are not a gentle introduction to olympiad problem-solving; they are for readers ready to tackle its most difficult style of challenge.

Author: Vu Hung Nguyen

Book: The Final Boss: Master-Level Problems in the Spirit of IMO Problem 6

Contents: 99 problems across algebra, geometry, number theory, and combinatorics, with hints, full solutions, takeaways, and appendices.