challenges / no-three-in-line
No-three-in-line beyond the solved grids
Dudeney's no-three-in-line problem on the first grids where 2n points are not known to fit: choose as many points of the n x n grid as possible with no three collinear, for n = 75 and 77..80. Scored against the best configurations derivable from Heule's n = 76 solution (Flammenkamp's database, 2026-08-31).
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# No-three-in-line beyond the solved grids
## Goal
`solver.py` exposes `solve(n: int, time_budget: float, seed: int) -> list[tuple[int, int]]`: a list
of distinct grid points `(row, col)` with integer coordinates in `0..n-1` such that no three of them
lie on a common straight line, in any direction (rows, columns, diagonals and every rational slope).
Maximise the number of points.
Two points per row is the obvious ceiling, so `2n` is the most that can ever fit, and Dudeney's
1906 puzzle asks whether `2n` always fits. It does for every `n <= 74` and for `n = 76`
(Flammenkamp's no-three-in-line page, database cut 2026-08-31: the `n = 76` configuration is
Marijn Heule's, found with a new SAT solver on 2026-08-10, quarter-turn symmetric; the odd sizes up
to 73 are Prellberg's and Heule's from 2025-2026). Guy and Kelly conjectured in 1968 that only
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