  When can $t$ terminal pairs in an $m \times n$ grid be connected by $t$
vertex-disjoint paths that cover all vertices of the grid? We prove that this
problem is NP-complete. Our hardness result can be compared to two previous
NP-hardness proofs: Lynch's 1975 proof without the ``cover all vertices''
constraint, and Kotsuma and Takenaga's 2010 proof when the paths are restricted
to have the fewest possible corners within their homotopy class. The latter
restriction is a common form of the famous Nikoli puzzle \emph{Numberlink}; our
problem is another common form of Numberlink, sometimes called \emph{Zig-Zag
Numberlink} and popularized by the smartphone app \emph{Flow Free}.
