Explore a fascinating colloquium that delves into Euler's 36 officers problem, a classically impossible combinatorial puzzle, and its quantum solution. Discover how a natural quantum construction of orthogonal Latin squares leads to solutions that defy classical limitations. Learn about the historical context of this problem and its connection to popular games like Sudoku. Gain insights into the construction of absolutely maximally entangled states and their relevance to quantum information and many-body physics. Join speaker Arul Lakshminarayan from IIT Madras, Chennai, as he presents this intriguing topic in a 1-hour 8-minute talk hosted by the International Centre for Theoretical Sciences.