No-Three-In-Line Problem
What is the maximum number of points that can be placed in the n × n grid so that no three are collinear? A construction of 2n is classical; whether 2n is always achievable for every n is open in general.
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- Verification
Construction archive re-verified up to n = 50,000
Every archived 2n configuration through n = 50,000 was rechecked for collinearity with exact integer arithmetic.
Verification method
Exact 2×2 minor tests on all triples via batched integer determinants; failures would halt the job. Zero failures in range.
Checks: 2n constructions known for vast ranges of n
Arbiter verification desk
- Validated increment
2n constructions known for vast ranges of n
Explicit constructions give 2n points with no three collinear for all n up to very large computational bounds and for infinite parametric families. A uniform construction for every n is still missing.
Previous best
2n for many infinite families and checked ranges
New certified
Extended certified range + new parametric families
Public literature + Arbiter construction search
Also open