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120-year-old dissection puzzle - mklabgr - 07-29-2026 120-year-old dissection puzzle Summary Researchers from the Japan Advanced Institute of Science and Technology (JAIST) and MIT have solved a 120-year-old math challenge by proving that Henry Ernest Dudeney’s famous 1907 dissection puzzle—cutting an equilateral triangle and rearranging its pieces into a square—is optimal with four pieces. While Dudeney originally demonstrated a four-piece hinged solution, mathematicians had never formally established whether a three-piece dissection was geometrically possible.  By introducing a novel proof technique that converts piece arrangements into discrete graph structures called "matching diagrams," the team rigorously demonstrated that no valid dissection exists using three or fewer polygonal pieces without flipping, establishing a pioneer methodology for proving optimality in geometric dissection problems with practical applications in fields like computational geometry, robotics, and manufacturing. ARTICLE