Parity Invariant Solves IMO 2011 Windmill Problem via Finite Configuration Space — E8 Intelligence Research

FINDING: The 2011 IMO windmill problem (Q2) is a combinatorial geometry problem that unexpectedly requires a parity-based invariant and a finite configuration space argument, not a direct geometric ratio. | MATH: The problem: Given a finite set of points in the plane, no three collinear, a "windmill" process rotates a line through a point, switching pivot when hitting another point. The invariant: The number of points on each side of the line modulo 2 remains constant. The proof uses the fact that the total number of points is odd (2n+1) to guarantee a point exists such that the windmill visits all points infinitely often. No explicit equations or constants. | CONNECTION: No direct geometric harmony ratios (0.382, 0.618, etc.) or base-60 or crystallographic symmetries. The problem is purely combinatorial with a parity invariant. | DEPTH: 3 — The problem is a clever combinatorial geometry puzzle but reveals no new universal constants, ratios, or deep mathematical structure beyond its ow Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com