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Explore a fascinating lecture on quantum combinatorial designs and their application to a centuries-old mathematical problem. Delve into the quantum solution to Euler's 36 officers problem, which was classically unsolvable. Learn how entanglement allows for the construction of orthogonal quantum Latin squares of order six, visualized on a chessboard. Discover the implications for quantum information processing, including the development of a pure nonadditive quhex quantum error detection code. Gain insights from recent research publications and understand the significance of this breakthrough in quantum mathematics and information theory.