Consider $n$ points $p_j$ inside a simply connected, compact plane domain (for example $n$ points inside the interior of a simple continuous plane loop). Find the positions such that the total distance $D$ between them is maximized. $D$ is the sum of the distances between all pairs of points: $2D=\sum_{i,j=1}^{n} d(p_i,p_j)$.

Let $ C $ be a connected and simply connected compact subset of the plane $ \mathbb{R}^{2} $. How can we pick $ n $ points, denoted $ x_{1},\ldots,x_{n} $, lying in $ C $ such that the total sum $ \displaystyle D \stackrel{\text{df}}{=} \sum_{i,j = 1}^{n} d(x_{i},x_{j}) $ of their pairwise distances is maximized? For example, $ C $ could be the region consisting of a simple closed curve and its interior.

Have n (finite number) points inside a connected, simple connected, compact plane domain (for example N points inside the interior of a simple continuous plane loop). Find the points positions such that the total distance D between them is maximized. D is the sum of the distance between all pairs of points, D={sum}_{i,j=1}^{n} d(i,j).

Consider $n$ points $p_j$ inside a simply connected, compact plane domain (for example $n$ points inside the interior of a simple continuous plane loop). Find the positions such that the total distance $D$ between them is maximized. $D$ is the sum of the distances between all pairs of points: $2D=\sum_{i,j=1}^{n} d(p_i,p_j)$.