  The general position number ${\rm gp}(G)$ of a connected graph $G$ is the
cardinality of a largest set $S$ of vertices such that no three pairwise
distinct vertices from $S$ lie on a common geodesic. The $n$-dimensional grid
graph $\pn$ is the Cartesian product of $n$ copies of the two-way infinite path
$P_\infty$. It is proved that if $n\in {\mathbb N}$, then ${\rm
gp}({P_\infty^n}) = 2^{2^{n-1}}$. The result was earlier known only for $n\in
\{1,2\}$ and partially for $n=3$.
