English

Constraint Satisfaction Programming for the No-three-in-line Problem

Combinatorics 2026-02-10 v1

Abstract

Using a constraint satisfaction approach, we exhibit configurations of 2n2n points on the n×nn\times n grid for all n60n\le60 with no three collinear. Consequently, the smallest nn for which it is unknown whether D(n)=2nD(n)=2n increases from 4747 to 6161.

Keywords

Cite

@article{arxiv.2602.07751,
  title  = {Constraint Satisfaction Programming for the No-three-in-line Problem},
  author = {Thomas Prellberg},
  journal= {arXiv preprint arXiv:2602.07751},
  year   = {2026}
}

Comments

16 pages, 6 figures, supplementary material on https://github.com/ThomasPrellberg/no-three-in-line---CP-SAT

R2 v1 2026-07-01T10:26:21.397Z