Sunny Lines: Combinatorial Geometry in IMO 2025's Easiest Problem — E8 Intelligence Research

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Authors

Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-09-01
DOI
https://doi.org/10.5281/zenodo.22224677
Primary Topic
Computational Geometry and Mesh Generation
Type
preprint
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preprint

Sunny Lines: Combinatorial Geometry in IMO 2025's Easiest Problem — E8 Intelligence Research

Andrew Stewart Caldin
Zenodo (CERN European Organization for Nuclear Research)
Computational Geometry and Mesh Generation
preprint

Sunny Lines: Combinatorial Geometry in IMO 2025's Easiest Problem — E8 Intelligence Research

Andrew Stewart Caldin
preprint en

Abstract

FINDING: IMO 2025 Problem 1 ("Sunny Lines") is a combinatorial geometry problem involving line arrangements and point sets, with multiple solution videos confirming its status as the "easiest" problem of the set. | MATH: The problem concerns a finite set of points in the plane and lines that partition the set into two non-empty subsets ("sunny lines"). Key combinatorial invariants: number of such lines ≤ n(n-1)/2 (trivial bound from pairs), but the actual extremal count depends on point configuration (collinearities, convex hull size). No explicit constants or equations are given in the video titles; the core is a counting/parity argument over line arrangements. | CONNECTION: The phrase "Sonnige Leitungen" (sunny lines) and "Kombinatorische Geometrie" suggests a configuration-space problem. The underlying structure — lines through pairs of points, partitions of a point set — is a discrete analogue of hyperplane arrangements in root systems (e.g., A_n, D_n). The extremal counting of "su Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com

Zenodo (CERN European Organization for Nuclear Research)
Computational Geometry and Mesh Generation
DOIOpen Access PDFOpenAlex
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Sunny Lines: Combinatorial Geometry in IMO 2025's Easiest Problem — E8 Intelligence Research — Andrew Stewart Caldin · Zenodo (CERN European Organization for Nuclear Research) (2026) | TGRS Research Map | TGRS