To solve a new problem, people spontaneously engage multiple cognitive processes. Previous work has identified a diverse set of oscillatory components critical at different stages of creative problem solving. In this project, we use hidden state modeling to untangle the roles of oscillation processes over time as people solve puzzles. Building on earlier work, we further developed analytical methods, such as incorporating source separating techniques and identifying the optimal number of states using cross-validation. We extracted brain states characterized by spatio-spectral topographies from time-resolved EEG spectral powers. The data driven approach allowed us to infer the dynamic, trial-by-trial, state sequences, and provided a comprehensive depiction of how various oscillation components interact recurrently throughout the trial. The properties of the states suggest their dissociable cognitive functions. For example, we identified three states with dominant activation in alpha bands but having distinct spatial distributions. People were differentially engaged in these states depending on the stages (e.g., onset or response) and outcomes of the trials (solved with insight or analysis). The current approach, applicable to many tasks requiring extended trial duration, can potentially reconcile findings from previous EEG studies and drive new hypotheses to further our understanding of the complex creative process.