This project presents the development of a multi-agent pathfinding (MAPF) algorithm as a core computational component within the GOCHESS robotic chessboard, a smart interactive platform developed by Particula. In this system, multiple mobile robots operate beneath the chessboard surface, maneuvering magnetic actuators to relocate chess pieces autonomously. The primary objective of this work was to design and implement an efficient coordination framework that ensures collision-free, time-efficient motion for all agents operating in a shared environment. The proposed approach integrates two key algorithmic components: (1) path planning based on the A* search algorithm applied over a customized state-space that models spatial dependencies and temporal constraints, and (2) task allocation utilizing the Hungarian algorithm to achieve a near-optimal global assignment between robots and their designated targets. The resulting algorithm demonstrates high robustness, successfully resolving full-board rearrangement scenarios in approximately 90% of experimental trials. This work highlights the practical integration of theoretical principles in graph search, combinatorial optimization, and multi-agent coordination into a physical robotic system.