People can solve problems in more than one way. Two general strategies involve (A) methodical, conscious, search of problem-state transformations, and (B) sudden insight, with abrupt emergence of the solution into consciousness. This study elucidated the influence of initial resting brain-state on subjects' subsequent strategy choices. High-density electroencephalograms (EEGs) were recorded from subjects at rest who were subsequently directed to solve a series of anagrams. Subjects were divided into two groups based on the proportion of anagram solutions derived with self-reported insight versus search. Reaction time and accuracy results were consistent with different cognitive problem-solving strategies used for solving anagrams with versus without insight. Spectral analyses yielded group differences in resting-state EEG supporting hypotheses concerning insight-related attentional diffusion and right-lateralized hemispheric asymmetry. These results reveal a relationship between resting-state brain activity and problem-solving strategy, and, more generally, a dependence of event-related neural computations on the preceding resting state.