There are two general strategies for solving a problem. Insight is the sudden realization of a novel idea or problem solution accompanied by an “aha” experience. Analysis occurs in a conscious, deliberate fashion without an “aha” experience. Previous research has shown that brain activity during a preparatory period immediately before a problem is presented can predict whether the subsequently presented problem will be solved by insight or by analysis. Those prior studies used a type of brief verbal problem called compound remote associates (CRA). To determine whether prestimulus activity predicts subsequent insight versus analytic solving for other types of problems, the present study used an anagram task. We examined high-density electroencephalograms (EEGs) immediately preceding the presentation of anagrams and found that during the 2-s prestimulus interval there was greater beta-band activity recorded over right central-parietal cortex prior to analytic solving compared with insightful solving. EEG source reconstruction showed that this activity originated in left mid-cingulate cortex (MCC) and the right postcentral gyrus. In contrast to prior work, we found no evidence of a significant interaction between insight-related prestimulus brain activity and positive mood, although positive mood was associated with greater activity in anterior cingulate cortex and with a larger number of insight solutions. The present MCC results suggest that participants’ anagram-solving strategies may be influenced by allostasis, that is, the estimation and marshalling of neurocognitive resources required to cope with an expected task. Specifically, when a participant adequately prepares for an upcoming problem, then MCC activity is high, enabling solution by resource-intensive analytic processing. Alternatively, when preparation is insufficient for analytic processing, then MCC activity is low and subsequent solving occurs by low-demand insight processing. The current findings and explanatory model differ from those of previous studies that used a CRA task, suggesting the possibility of complex interactions between task-type and procedure-type in determining the nature of prestimulus preparation. Future research examining such interactions may yield results that benefit educators who teach students problem-solving strategies.