  "Zombies and Survivor" is a variant of the well-studied game of "Cops and
Robber" where the zombies (cops) can only move closer to the survivor (robber).
We consider the deterministic version of the game where a zombie can choose
their path if multiple options are available. The zombie number, like the cop
number, of a graph is the minimum number of zombies, or cops, required to
capture the survivor. In this short note, we solve a question by Fitzpatrick et
al., proving that the zombie number of the Cartesian product of two graphs is
at most the sum of their zombie numbers. We also give a simple graph family
with cop number $2$ and an arbitrarily large zombie number.
