Geometric and Parity Invariants in Putnam and IMO Windmill Problems — E8 Intelligence Research

FINDING: The Putnam problem features an elegant solution involving combinatorial geometry and parity invariants; the IMO windmill problem uses projective geometry and fixed-point invariants. | MATH: No explicit equations or constants extracted from summaries; the Putnam problem likely involves sums, products, or combinatorial identities; the IMO windmill problem involves point-line incidence and parity of windmill rotations. | CONNECTION: No direct geometric harmony ratios (0.382, 0.618, etc.) or base-60, crystallographic symmetries, root systems, or lattice structures are evident from the provided summaries. | DEPTH: 3 — These are competition problems with elegant solutions but no fundamental constants or universal geometric patterns revealed in the given data. Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com