Assume the are $n$ squares $B_1,\ldots, B_n$, each of size 3ft by 3ft. These boxes can be arranged in 2-dimensional space around a given point $c$. The position of the squares shall be optimized such that
1) $B_i \cap B_j = 0$ for $i\neq j$, i.e. they shall not overlap.
2) $min \leftarrow \frac{1}{n} \sum_{i=1}^n dist(B_i, c)$, i.e. the average distance between each square and the point $c$ is minimal.
For $n=4$ an arrangement as a square around $c$ seems to be a natural choice. But how can a solution found for $n >4$ ?
The arrangement as a regular polygon around $c$ does not seem to be optimal.
Thanks for any hint or advice!