  We consider the game of Zombies and Survivors as introduced by Fitzpatrick,
Howell, Messinger and Pike (2016) This is a variation of the game Cops and
Robber where the zombies (in the cops' role) are of limited intelligence and
will always choose to move closer to a survivor (who takes on the robber's
role). The zombie number of a graph is defined to be the minimum number of
zombies required to guarantee the capture of a survivor on the graph. In this
paper, we show that the zombie number of the Cartesian product of $n$
non-trivial trees is exactly $\lceil 2n/3 \rceil$. This settles a conjecture by
Fitzpatrick et. al. (2016) that this is the zombie number for the
$n$-dimensional hypercube. In proving this result, we also discuss other
variations of Cops and Robber involving active and flexible players.
