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Processor Allocation schemes play a significant role in obtaining high performance in parallel computing paradigms. Finding available processors for incoming task with the constriction of minimizing overhead is the chief objective of task allocation. Various processor allocation schemes have been proposed with series of performance measures and complexities of space and time. Optimality of allocation schemes too plays a vital role apart from the performance measures. Existing allocation schemes like Frame Sliding and Quick Allocation schemes expends scanning overhead. In our paper we propose a best-fit strategy titled "Heuristic Processor Allocation in Mesh-Connected Systems via a Coloring Mechanism" (HPAM), which achieves optimality, efficient processor allocation and also simplified scanning overhead. By using game playing i.e. Tetris Game approach and a heuristic function incorporating a penalty factor at each step of allocation process, ensures optimality. Performance comparison shows that our scheme by and large has lesser allocation overhead than all other existing allocation algorithms, while delivering competitive performance.