Place n points inside a circle of radius 1, maximizing the smallest distance between any two of them.
Formal definition
ContainerA circle of radius 1 centred at (1, 1), so both coordinates run from 0 to 2
SubmissionExactly n points, no two coinciding
ConstraintsEvery point lies inside the circle or on it
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 disc is dual to packing equal circles in it: a point set with spacing d is a packing of radius d/2. Proofs in the cci table transfer; n = 4 is proven here, and the rest open or close as cci does.