Place n points in the unit square so that the smallest triangle formed by any three of them is as large as possible.
Formal definition
ContainerThe unit square: the origin (0, 0) at its lower-left corner, (1, 1) at its upper right
SubmissionExactly n points, no three collinear
ConstraintsEvery point lies inside the square or on its boundary
ObjectiveMake the smallest triangle over all triples as large as possible; compared internally by twice the area, exactly
Getting a feel for it
Where the room for improvement is
Even spreading is not enough: no three points may come close to collinear, and near-collinearity is exactly what tidy arrangements love to do. Optima are often asymmetric and hard even to guess.
Where the frontier is
Proven for n = 5..9 (Yang, Zhang, Zeng and Dress, 1991–1995); for n ≥ 10 only numerical lower bounds exist — see arXiv:2603.11107 for the current survey. Goldberg's 1972 constructions were the benchmark for decades.