  In this paper, we present the clockwise-algorithm that solves the extension
in $k$-dimensions of the infamous nine-dot problem, the well-known
two-dimensional thinking outside the box puzzle. We describe a general strategy
that constructively produces minimum length covering trails, for any $k \in
\mathbb{N}-\{0\}$, solving the NP-complete $(3 \times 3 \times \cdots \times
3)$-point problem inside $3 \times 3 \times \cdots \times 3$ hypercubes. In
particular, using our algorithm, we explicitly draw different covering trails
of minimal length $h(k)=\frac{3^k-1}{2}$, for $k=3, 4, 5$. Furthermore, we
conjecture that, for every $k \geq 1$, it is possible to solve the $3^k$-point
problem with $h(k)$ lines starting from any of the $3^k$ nodes, except from the
central one. Finally, we cover a $3 \times 3 \times 3$ grid with a tree of size
$12$.
