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We theoretically analyze the Cops and Robber Game for the first time in amultidimensional 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 setof cop strategies for which $n$ cops are provably sufficient to catch therobber. Further, for two-dimensional grid, we provide an efficient cop strategyfor which the robber is caught even by a single cop under certain conditions.

On Necessary and Sufficient Number of Cops in the Game of Cops and Robber in Multidimensional Grids