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The end of Moore's law for CMOS technology has prompted the search for low-power computing alternatives, resulting in several promising proposals based on magnetic logic[1-8]. One approach aims at tailoring arrays of nanomagnetic islands in which the magnetostatic interactions constrain the equilibrium orientation of the magnetization to embed logical functionalities[9-12]. Despite the realization of several proofs of concepts of such nanomagnetic logic[13-15], it is still unclear what the advantages are compared to the widespread CMOS designs, due to their need for clocking[16, 17] and/or thermal annealing [18,19] for which fast convergence to the ground state is not guaranteed. In fact, it seems increasingly evident that "beyond CMOS" technology will require a fundamental rethinking of our computing paradigm[20]. In this respect, a type of terminal-agnostic logic was suggested[21], where a given gate is able to "self-organize" into its correct logical states, regardless of whether the signal is applied to the traditional input terminals, or the output terminals. Here, we introduce nanomagnetic self-organizing balanced logic gates, that employ stray-field coupled nanomagnetic islands to perform terminal-agnostic logic. We illustrate their capabilities by implementing reversible Boolean circuitry to solve a two-bit factorization problem via numerical modelling. In view of their design and mode of operation, we expect these systems to improve significantly over those suggested in Ref.[21], thus offering an alternative path to explore memcomputing, whose usefulness has already been demonstrated by solving a variety of hard combinatorial optimization problems[22].