  We construct multi-center, non-supersymmetric four-dimensional solutions
describing a rotating anti-D6-D2 black hole and an arbitrary number of D4-D2-D0
black holes in a line. These solutions correspond to an arbitrary number of
extremal non-BPS black rings in a Taub-NUT space with a rotating three-charge
black hole in the middle. The positions of the centers are determined by
solving a set of "bubble" or "integrability" equations that contain cubic
polynomials of the inter-center distance, and that allow scaling solutions even
when the total four-dimensional angular momentum of the scaling centers is
non-zero.
