In this paper, we aim to measure the information content of brain anatomic regions using the functional magnetic resonance images (fMRI) recorded during a complex problem solving (CPS) task. We, also, analyze the brain regions, activated in different phases of the problem solving process. Previous studies have widely used machine learning approaches to examine the active anatomic regions for cognitive states of human subjects based on their fMRI data. This study proposes an information theoretic method for analyzing the activity in anatomic regions. Briefly, we define and estimate two types of Shannon entropy, namely, static and dynamic entropy, to understand how complex problem solving processes lead to changes in information content of anatomic regions. We investigate the relationship between the problem-solving task phases and the Shannon entropy measures suggested in this study, for the underlying brain activity during a Tower of London (TOL) problem solving process. We observe that the dynamic entropy fluctuations in brain regions during the CPS task provides a measure for the information content of the main phases of complex problem solving, namely planning and execution. We, also, observe that static entropy measures of anatomic regions are consistent with the experimental findings of neuroscience. The preliminary results show strong promise in using the suggested static and dynamic entropy as a measure for characterizing the brain states related to the problem solving process. This capability would be useful in revealing the hidden cognitive states of subjects performing a specific cognitive task.