This study triangulates executive planning and visuo-spatial reasoning in the context of the Tower of London (TOL) task by using a variety of methodological approaches. These approaches include functional magnetic resonance imaging (fMRI), functional connectivity analysis, individual difference analysis, and computational modeling. A graded fMRI paradigm compared the brain activation during the solution of problems with varying path lengths: easy (1 and 2 moves), moderate (3 and 4 moves) and difficult (5 and 6 moves). There were three central findings regarding the prefrontal cortex: (1) while both the left and right prefrontal cortices were equally involved during the solution of moderate and difficult problems, the activation on the right was differentially attenuated during the solution of the easy problems; (2) the activation observed in the right prefrontal cortex was highly correlated with individual differences in working memory (measured independently by the reading span task); and (3) different patterns of functional connectivity were observed in the left and right prefrontal cortices. Results obtained from the superior parietal region also revealed left/right differences; only the left superior parietal region revealed an effect of difficulty. These fMRI results converged upon two hypotheses: (1) the right prefrontal area may be more involved in the generation of a plan, whereas the left prefrontal area may be more involved in plan execution; and (2) the right superior parietal region is more involved in attention processes while the left homologue is more of a visuo-spatial workspace. A 4CAPS computational model of the cognitive processes and brain activation in the TOL task integrated these hypothesized mechanisms, and provided a reasonably good fit to the observed behavioral and brain activation data. The multiple research approaches presented here converge on a deepening understanding of the combination of perceptual and conceptual processes in this type of visual problem solving.