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In order to address the energy imbalance issue of a series-connected lithium-iron battery pack, this paper proposes an active equalization method based on a reduced-order solving strategy for the Hanoi Tower problem. The proposed scheme utilizes a combined structure of a switching-network circuit and a bidirectional Cuk converter and leverages an ultracapacitor cell as the energy-transfer carrier. Simulation and comparison demonstrate that the exchange of unbalanced energy within the battery pack can be achieved. The proposed approach can effectively achieve various balancing modes such as cell-to-cell, cell-to-string, string-to-cell, and string-to-string with a relatively fast balancing speed.