We present new supersymmetric solutions of five-dimensional minimal supergravity that describe concentric black rings with an optional black hole at the common center. Configurations of two black rings are found which have the same conserved charges as a single rotating black hole; these black rings can have a total horizon area less than, equal to, or greater than the black hole with the same charges. A numerical investigation of these particular black-ring solutions suggests that they do not have closed timelike curves.
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