Place n points in the unit square, maximizing the smallest distance between any two of them.
Formal definition
ContainerThe unit square: the origin (0, 0) at its lower-left corner, (1, 1) at its upper right
SubmissionExactly n points, no two coinciding
ConstraintsEvery point lies inside the square or on its boundary
ObjectiveMake the smallest pairwise distance as large as possible; compared internally by its square, exactly
Getting a feel for it
Where the room for improvement is
Spreading points IS packing equal circles: discs of half the minimum distance around each point must not overlap. Optima are jammed contact structures, and the container shape decides everything.
Where the frontier is
Spreading points in a square is dual to packing equal circles in one; proofs in the csq table transfer. n = 2, 4, 5 and 9 are proven here by elementary arguments, and the rest follow csq's progress.