Classic Putnam and IMO Hardest Problems: Combinatorial Geometry and Number Theory — E8 Intelligence Research

Abstract

FINDING: Putnam problem with elegant solution (likely 1985 A6 or similar) | MATH: No explicit equation given; problem involves combinatorial geometry or number theory | CONNECTION: None identified from summary | DEPTH: 3 — Classic contest problem, no universal constant or symmetry revealed. FINDING: IMO hardest problem ever (likely 1988 Problem 6 or 2005 Problem 3) | MATH: No equation given; typical IMO hardest problems involve functional equations, inequalities, or number theory (e.g., Vieta jumping) | CONNECTION: None identified | DEPTH: 4 — High difficulty but isolated to contest math, no geometric harmony. FINDING: Insane limit problem from India's hardest exam (JEE Advanced) | MATH: Limit problem, likely involving nested radicals or series; no specific equation given | CONNECTION: None identified | DEPTH: 2 — Standard calculus trick, no deep constant. FINDING: 2011 IMO Q2 windmill problem | MATH: Combinatorial geometry — given finite set of points in plane, prove existence of a Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com