Mathematician Leonhard Euler’s impossible problem that asks for a 6 x 6 arrangement of military officers can be solved, but only at the quantum level. (Image credit: Pixabay)
18th-century math whiz Leonhard Euler is known for his contributions in physics, astronomy, geography, engineering – pretty much anything to do with numbers. In 1779 Leonhard posed a puzzle that has never been solved - Six army regiments each have six officers of six different ranks. Can the 36 officers be arranged in a 6 x 6 square so that no row or column repeats a rank or regiment? Euler himself declared the puzzle unsolvable, and French mathematician Gaston Tarry agreed a century later. What’s more, with the advent of computers to crunch the numbers, several other mathematicians concluded that the six-by-six square is impossible, but it’s the only size of square other than two-by-two that doesn’t have a solution at all.
Recently, another group of researchers banded together to solve the problem and found that arranging six regiments of six officers of six different ranks in a grid without repeating any rank or regiment more than once in any row or column can be accomplished, but only if the officers are in a state of quantum entanglement. The key is that quantum objects can be in multiple states until they are measured. Think of it like Schrodinger’s cat, where the feline is trapped in a radioactive box and is neither alive nor dead until the box is opened.
In Euler’s problem, each officer has a static regiment and rank. For example, they could be a Lieutenant in a red regiment or a Captain in a blue regiment (colors signify a grid). An officer in a quantum state, on the other hand, can be in more than one regiment or rank at the same time. For example, a red Captain could be a green Lieutenant and a blue Major all simultaneously. So, if officer 1 is a red regiment first Lieutenant, then officer 2 must be a major in the green regiment, and vice versa. It’s that quantum entanglement that solves Euler’s problem - the state of one object informs the state of another. The researchers used computer power to prove their findings. They found that filling that 6 x 6 grid with quantum officers solved the problem as officers are only entangled with others of ranks that are one step below or above them, while regiments are also only entangled with adjacent regiments.
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