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

TL;DR

This paper applies constraint satisfaction programming to find point configurations on an n×n grid with no three collinear points, extending known results up to n=60 and raising the minimal n where the problem is unresolved.

Contribution

It introduces a constraint satisfaction approach to the no-three-in-line problem, improving bounds on the minimal n with unknown D(n) values.

Findings

Configurations found for all n ≤ 60 with no three collinear points.

The minimal n with unknown D(n)=2n increases from 47 to 61.

Demonstrates the effectiveness of constraint programming in combinatorial geometry.

Abstract

Using a constraint satisfaction approach, we exhibit configurations of $2n$ points on the $n\times n$ grid for all $n\le60$ with no three collinear. Consequently, the smallest $n$ for which it is unknown whether $D(n)=2n$ increases from $47$ to $61$.