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Solving the Hardest Problem from the 1986 International Math Olympiad

Wrath of Math via YouTube

Overview

Explore a detailed mathematical analysis of Problem 3 from the 1986 International Mathematical Olympiad (IMO) in Warsaw, Poland - considered the most challenging problem that only 11 students solved correctly. Learn the step-by-step solution used by 10 of these successful participants, involving a pentagon with integers assigned to its vertices and a specific replacement algorithm. Understand the problem statement involving positive sums, vertex assignments, and the transformation rule (x, y, z) → (x + y, −y, y + z) when y is negative. Follow along through examples, solution functions, and proof of the algorithm's termination through decreasing function analysis, culminating in a comprehensive understanding of this historic IMO problem.

Syllabus

Intro
The Problem
Example
The Solution Function
The Function is Decreasing
Conclusion

Taught by

Wrath of Math

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