Tower of London (TOL) is a classic problem solving task to study high-level cognitive processes. In this paper, using the TOL experiment, we aim to investigate the activation and relations of anatomic regions during the planning and execution phases of the problem solving task. We propose a dynamic sparse network representation estimated from the fMRI brain volumes at all time instances. This representation, called Dynamic Mesh Network, enables us to analyze the network properties of the brain under planning and execution stages of a TOL problem. Results indicate that activation during the planing phase is relatively higher than during the execution phase in most of the anatomic regions. Also, the connectivity between the anatomic regions is denser and stronger during the planing phase, compared to the execution phase.