Place n points inside the right triangle with vertices (0, 0), (1, 0) and (0, 1), maximizing the smallest triangle formed by any three of them.
Formal definition
ContainerA right triangle with vertices (0, 0), (1, 0) and (0, 1): the region x ≥ 0, y ≥ 0, x + y ≤ 1
SubmissionExactly n points, no three collinear
ConstraintsEvery point lies inside the triangle 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
n = 5 and 6 were proven by Yang, Zhang and Zeng, n = 7 by Sudermann-Merx — see arXiv:2607.15021; everything from n = 8 up is open.