mc ☕<p>> In 1779, the Swiss <a href="https://qoto.org/tags/mathematician" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>mathematician</span></a> Leonhard <a href="https://qoto.org/tags/Euler" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>Euler</span></a> posed a <a href="https://qoto.org/tags/puzzle" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>puzzle</span></a> 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?</p><p>> But after searching in vain for a solution for the case of 36 officers, Euler concluded that “such an arrangement is <a href="https://qoto.org/tags/impossible" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>impossible</span></a>, though we can’t give a rigorous demonstration of this.” More than a century later, the French mathematician Gaston Tarry <a href="https://qoto.org/tags/proved" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>proved</span></a> that, indeed, there was no way to arrange Euler’s 36 officers in a 6-by-6 square without repetition. In 1960, mathematicians used <a href="https://qoto.org/tags/computers" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>computers</span></a> to prove that solutions exist for any number of regiments and ranks greater than two, except, curiously, six.</p><p>> 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 <a href="https://qoto.org/tags/quantum" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>quantum</span></a> <a href="https://qoto.org/tags/mixture" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>mixture</span></a> of ranks and regiments.</p><p>Euler’s 243-Year-Old ‘Impossible’ Puzzle Gets a Quantum Solution<br><a href="https://www.quantamagazine.org/eulers-243-year-old-impossible-puzzle-gets-a-quantum-solution-20220110/" rel="nofollow noopener" target="_blank"><span class="invisible">https://www.</span><span class="ellipsis">quantamagazine.org/eulers-243-</span><span class="invisible">year-old-impossible-puzzle-gets-a-quantum-solution-20220110/</span></a></p>