> In 1779, the Swiss #mathematician Leonhard #Euler posed a #puzzle that has since become famous: Six army regiments each have six officers of six different ranks. Can the 36 officers be arranged in a 6-by-6 square so that no row or column repeats a rank or regiment?

> But after searching in vain for a solution for the case of 36 officers, Euler concluded that “such an arrangement is #impossible, though we can’t give a rigorous demonstration of this.” More than a century later, the French mathematician Gaston Tarry #proved that, indeed, there was no way to arrange Euler’s 36 officers in a 6-by-6 square without repetition. In 1960, mathematicians used #computers to prove that solutions exist for any number of regiments and ranks greater than two, except, curiously, six.

> But whereas Euler thought no such 6-by-6 square exists, recently the game has changed. In a paper posted online and submitted to Physical Review Letters, a group of quantum physicists in India and Poland demonstrates that it is possible to arrange 36 officers in a way that fulfills Euler’s criteria — so long as the officers can have a #quantum #mixture of ranks and regiments.

Euler’s 243-Year-Old ‘Impossible’ Puzzle Gets a Quantum Solution
https://www.quantamagazine.org/eulers-243-year-old-impossible-puzzle-gets-a-quantum-solution-20220110/