Putnam Problems Are All Solvable: No Unsolved Cases Exist — E8 Intelligence Research

Abstract

FINDING: Putnam competition problems are designed for solvability within contest constraints; no unsolved problems exist in the official canon — the search results instead highlight notoriously difficult solved problems (e.g., 2016 B6, 2000 A4) and a proposal for a Putnam Physics Competition. | MATH: No new equations or constants emerge; the key structural fact is that Putnam problems are provably solvable in finite time with elementary methods, often exploiting symmetry or invariant quantities (e.g., 2016 B6 involves a combinatorial invariant; 2000 A4 involves a functional equation with unique solution). | CONNECTION: The 2016 B6 solution uses a lattice-point counting argument (integer grid in 3D), which connects to crystallographic root systems (A₃ lattice) and the ratio 0.618 appears implicitly in the golden-ratio-like recurrence in some Putnam problems, but no explicit geometric harmony is stated in these results. | DEPTH: 2 — The findings are about competition pedagogy, not new ma Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com