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The paper presents a problem motivated by the hidden subgroup problem, for which the "standard approach" is to use the oracle to produce the coset state. Abstractly, one is given a set of quantum states on a d-dimensional Hilbert space, with the property that the pairwise fidelities are bounded. The question is: How many copies of the unknown state does one need to be able to distinguish them all with high reliability? The minimal state will depend on the precise geometric position of the states relative to each other, but useful bounds can be obtained simply in terms of the number N and the fidelity F.