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In the game of Cops and Robbers, the capture time of a graph is the minimum number of moves needed by the cops to capture the robber, assuming optimal play. We prove that the capture time of the n-dimensional hypercube is Θ (n n). Our methods include a novel randomized strategy for the players, which involves the analysis of the coupon-collector problem.arXiv:1308.3354v1 fatcat:qgofi32f6fezpmowoxzgti2rhy