Invariant Arguments Unite Putnam and IMO Windmill Problems — E8 Intelligence Research

Abstract

FINDING: The Putnam problem (likely 1987 A5 or similar) involves a combinatorial or geometric invariant that yields an elegant closed-form solution; the 2011 IMO windmill problem uses a parity/invariant argument on points in general position. | MATH: No explicit equations or constants extracted from search results; typical Putnam/IMO problems involve invariants, combinatorial sums, or geometric configurations (e.g., number of windmill steps = n choose 2 for n points). | CONNECTION: No direct geometric harmony ratios (0.382, 0.618, etc.) or base-60, crystallographic symmetries found in these specific competition problems. | DEPTH: 3 — These are clever problem-solving exercises but do not reveal new universal constants or deep structural symmetries; they refine technique, not fundamental insight. Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com