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Linearly independent quantum states can be unambiguously discriminated, but linearly dependent ones cannot. For linearly dependent quantum states, however, if C copies of the single states are available, then they may form linearly independent states, and can be unambiguously discriminated. We consider unambiguous discrimination among N = D + 1 linearly dependent states given that C copies are available and that the single copies span a D-dimensional space with equal inner products. The maximum unambiguous discrimination probability is derived for all C with equal a priori probabilities. For this classification of the linearly dependent equidistant states, our result shows that if C is even then adding a further copy fails to increase the maximum discrimination probability. [ABSTRACT FROM AUTHOR]