Parity Invariant and Point Ordering in the 2011 IMO Windmill Problem — E8 Intelligence Research

FINDING: The 2011 IMO windmill problem (Q2) is a combinatorial geometry problem that unexpectedly requires a parity-based invariant and a careful point-ordering argument, not a direct harmonic ratio. | MATH: No explicit equations or constants; the proof uses a finite set of points in general position, a line rotating about a point, and an invariant (the number of points on each side of the line changes by ±1 per windmill step). The key is that the line always passes through exactly one point (the pivot) and the process cycles through all points as pivots. | CONNECTION: No direct link to 0.382, 0.618, 0.786, 1.618, 2.618, base-60, or crystallographic symmetries. The problem involves rotational symmetry of the process but not geometric harmony ratios. | DEPTH: 4 — The problem is a clever combinatorial geometry puzzle but does not reveal new universal constants or deep structural symmetries. It is a pedagogical example of invariant thinking, not a fundamental mathematical discovery. FIND Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com