No-three-in-line $D(42)$
The largest number of points of the $42 \times 42$ grid with no three on a line.
Value: $84$ Verified lower bound
Verified bounds
Verified bounds come with a certificate that is checked automatically: a formal proof in Lean, or an explicit construction checked by a program. Submit a certificate.
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Lower bound:
$84$
Checked construction
no-three-in-line-42-lower-84, submitted by daniel-munro, 2026-11-05
[construction from The No-Three-in-Line Problem, Achim Flammenkamp, 2026-10-28] - Upper bound: None yet
Updates from the literature
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Upper bound: $84$
Trivial or easy according to the secondary source.
[via No-three-in-line problem - Wikipedia] -
1992-07
Lower bound: $84$
A. Flammenkamp, Progress in the no-three-in-line problem, Journal of Combinatorial Theory, Series A 60 (1992) 305-311.
[via The No-Three-in-Line Problem, Achim Flammenkamp, 2026-10-28]