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Suppose that a cup is installed at every point of a planar setP, and that somebody pours water into the cups. The total rate atwhich the water flows into the cups is 1. A player moves in theplane with unit speed, emptying the cups. At any time, the playersees how much water there is in every cup. The player has noinformation on how the water will be poured into the cups in thefuture; in particular, the pouring may depend on the player’smotion. The backlog of the player is the maximum amount of water inany cup at any time, and the player’s objective is tominimise the backlog. Let D be the diameter of P. If the water ispoured at the rate of 1/2 into the cups at the ends of a diameter,the backlog is Ω(D). We show that there is a strategy for theplayer that guarantees the backlog of O(D), matching the lowerbound up to a multiplicative constant. Note that our guarantee isindependent of the number of the cups.