We used behavioral and functional magnetic resonance imaging (fMRI) methods to probe the cerebral organization of a simple logical deduction process. Subjects were engaged in a motor trial-and-error learning task, in which they had to infer the identity of an unknown 4-key code. The design of the task allowed subjects to base their inferences not only on the feedback they received but also on the internal deductions that it afforded (autoevaluation). fMRI analysis revealed a large bilateral parietal, prefrontal, cingulate, and striatal network that activated suddenly during search periods and collapsed during ensuing periods of sequence repetition. Fine-grained analyses of the temporal dynamics of this search network indicated that it operates according to near-optimal rules that include 1) computation of the difference between expected and obtained rewards and 2) anticipatory deductions that predate the actual reception of positive reward. In summary, the dynamics of effortful mental deduction can be tracked with fMRI and relate to a distributed network engaging prefrontal cortex and its interconnected cortical and subcortical regions.