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We present three parameters exact solutions with possible black holes in $% 2+1-f\left( R\right) =R^{n}$ modified gravity coupled minimally to a cloud of strings. These three parameters are the cloud of string coupling constant and an integration constant . Although in general one has to consider each set of parameters separately; for an even integer greater than one we give a unified picture providing black holes. For we analyze null / timelike geodesic within the context of particle confinement.

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