P24 · Extremal configurations · Formed here

The smallest triangle in an L

Place n points inside an L (a 2 × 2 square with its top-right 1 × 1 removed) so that the smallest triangle formed by any three of them is as large as possible.

Formal definition

ContainerThe container is a square of side 2 with its top-right 1 × 1 quarter removed: the origin (0, 0) is its lower-left corner and the missing piece is where x and y are both greater than 1.
SubmissionExactly n points, no three collinear
ConstraintsEvery point lies inside the container 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

Our own variant: Heilbronn's problem in an L (a 2 × 2 square with its top-right 1 × 1 removed) was posed here, and there is no literature for it. Every n is unstudied; the standing record is all anybody knows.