An important question for understanding the neural basis of problem solving is whether the regions of human prefrontal cortices play qualitatively different roles in the major cognitive restructuring required to solve difficult problems. However, investigating this question using neuroimaging faces a major dilemma: either the problems do not require major cognitive restructuring, or if they do, the restructuring typically happens once, rendering repeated measurements of the critical mental process impossible. To circumvent these problems, young adult participants were challenged with a one-dimensional Subtraction (or Nim) problem [Bouton, C. L. Nim, a game with a complete mathematical theory. The Annals of Mathematics, 3, 35–39, 1901] that can be tackled using two possible strategies. One, often used initially, is effortful, slow, and error-prone, whereas the abstract solution, once achieved, is easier, quicker, and more accurate. Behaviorally, success was strongly correlated with sex. Using voxel-based morphometry analysis controlling for sex, we found that participants who found the more abstract strategy (i.e., Solvers) had more gray matter volume in the anterior medial, ventrolateral prefrontal, and parietal cortices compared with those who never switched from the initial effortful strategy (i.e., Explorers). Removing the sex covariate showed higher gray matter volume in Solvers (vs. Explorers) in the right ventrolateral prefrontal and left parietal cortex.