Constraint satisfaction programming for the no-three-in-line problem

Using a constraint satisfaction formulation with rotational symmetry reduction, we exhibit configurations of 2 n points on the n × n grid for every 2 ≤ n ≤ 60 with no three collinear. These computations resolved every previously open case through n = 60 . We describe the formulation, computational search, and empirical scaling of the method.

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Publication Details

Journal
Journal of Combinatorial Theory Series A
Published
2026-08-14
DOI
https://doi.org/10.1016/j.jcta.2026.106244
Primary Topic
Complexity and Algorithms in Graphs
Type
article
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article

Constraint satisfaction programming for the no-three-in-line problem

Thomas Prellberg
Journal of Combinatorial Theory Series A
Complexity and Algorithms in Graphs
article

Constraint satisfaction programming for the no-three-in-line problem

Thomas Prellberg
article en

Abstract

Using a constraint satisfaction formulation with rotational symmetry reduction, we exhibit configurations of 2 n points on the n × n grid for every 2 ≤ n ≤ 60 with no three collinear. These computations resolved every previously open case through n = 60 . We describe the formulation, computational search, and empirical scaling of the method.

Journal of Combinatorial Theory Series AVol. 225
Queen Mary University of London (GB)
Openalex Percentile: Top 83%
Complexity and Algorithms in Graphs
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Constraint satisfaction programming for the no-three-in-line problem — Thomas Prellberg · Journal of Combinatorial Theory Series A (2026) | TGRS Research Map | TGRS