  We theoretically analyze the Cops and Robber Game for the first time in a
multidimensional grid. It is shown that for an $n$-dimensional grid, at least
$n$ cops are necessary to ensure capture of the robber. We also present a set
of cop strategies for which $n$ cops are provably sufficient to catch the
robber. Further, for two-dimensional grid, we provide an efficient cop strategy
for which the robber is caught even by a single cop under certain conditions.
