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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 andRobber where the zombies (in the cops' role) are of limited intelligence andwill always choose to move closer to a survivor (who takes on the robber'srole). The zombie number of a graph is defined to be the minimum number ofzombies required to guarantee the capture of a survivor on the graph. In thispaper, 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 byFitzpatrick et. al. (2016) that this is the zombie number for the$n$-dimensional hypercube. In proving this result, we also discuss othervariations of Cops and Robber involving active and flexible players.

The Game of Zombies and Survivors on the Cartesian Products of Trees