IMO 2025 Problems: Sunny Lines, Geometry Revenge, and Laser Method — E8 Intelligence Research

FINDING: IMO 2025 Problem 1 ("Sunny Lines") is a combinatorial geometry problem; Problem 2 is a geometry revenge problem; Problem 6 involves a "Laser Method" for board problems. No full solutions extracted from titles alone. | MATH: No explicit equations, constants, or ratios derivable from titles/descriptions. The only concrete mathematical object is "Sunny Lines" — a combinatorial geometry configuration (likely a set of lines where each point is "lit" by a line, a classic IMO-style incidence problem). | CONNECTION: None directly stated. However, "Sunny Lines" in combinatorial geometry often relates to arrangements of lines in the projective plane, which can exhibit affine Weyl group symmetries (e.g., A₂ root system for triangular lattices) — but this is speculative without problem text. | DEPTH: 2/10 — Titles only; no mathematical content extracted. The "Laser Method" for Problem 6 hints at a constructive/algorithmic approach, but no specifics. No harmonic ratios, base-60, or crystal Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com

Authors

Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-08-24
DOI
https://doi.org/10.5281/zenodo.22075896
Primary Topic
Quasicrystal Structures and Properties
Type
preprint
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preprint

IMO 2025 Problems: Sunny Lines, Geometry Revenge, and Laser Method — E8 Intelligence Research

Andrew Stewart Caldin
Zenodo (CERN European Organization for Nuclear Research)
Quasicrystal Structures and Properties
preprint

IMO 2025 Problems: Sunny Lines, Geometry Revenge, and Laser Method — E8 Intelligence Research

Andrew Stewart Caldin
preprint en

Abstract

FINDING: IMO 2025 Problem 1 ("Sunny Lines") is a combinatorial geometry problem; Problem 2 is a geometry revenge problem; Problem 6 involves a "Laser Method" for board problems. No full solutions extracted from titles alone. | MATH: No explicit equations, constants, or ratios derivable from titles/descriptions. The only concrete mathematical object is "Sunny Lines" — a combinatorial geometry configuration (likely a set of lines where each point is "lit" by a line, a classic IMO-style incidence problem). | CONNECTION: None directly stated. However, "Sunny Lines" in combinatorial geometry often relates to arrangements of lines in the projective plane, which can exhibit affine Weyl group symmetries (e.g., A₂ root system for triangular lattices) — but this is speculative without problem text. | DEPTH: 2/10 — Titles only; no mathematical content extracted. The "Laser Method" for Problem 6 hints at a constructive/algorithmic approach, but no specifics. No harmonic ratios, base-60, or crystal Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com

Zenodo (CERN European Organization for Nuclear Research)
Quasicrystal Structures and Properties
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