The Hardest Easy Geometry Problem: A USAMO-Style Angle Chase Resisting Elementary Solutions — E8 Intelligence Research

FINDING: The "hardest easy geometry problem" is a classic USAMO-style configuration that resists elementary solution, often requiring trigonometric or coordinate methods. | MATH: No explicit equations given in search results; typical such problems involve cyclic quadrilaterals, angle chasing, and ratios like 1:2 or 1:3 in angle measures. | CONNECTION: No direct geometric harmony ratios (0.382, 0.618, etc.) or base-60 links evident from summaries. | DEPTH: 3 — The problem is pedagogically notable but does not reveal new constants or symmetries. FINDING: 2011 IMO Problem 2 (windmill) — a combinatorial geometry problem about rotating lines through points, proving that for any odd number of points, there exists a "windmill" line that visits each point infinitely often. | MATH: Key insight: For \( n \) points in general position (no three collinear), with \( n \) odd, there is a line through one point that rotates, always passing through exactly one other point at any time, and cycles thro Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com