The impossible Euler’s 6x6 puzzle gets a quantum solution

In an effort to solve the quantum version of Euler’s 243-year-old math problem, a group of scientists from Indian Institute of Technology Madras (IITM) and Jagiellonian University in Poland came up with a novel solution. This work got published in the prestigious journal Physical Review Letters on 25th February 2022 and has generated tremendous interest in the scientific community. We had the opportunity to discuss with Prof Arul Lakshminarayan and his PhD student, Suhail Ahmad Rather, on their phenomenal achievement.

Proposed by the Swiss mathematician Leonhard Euler in 1779, Euler’s puzzle became a challenging problem among academicians. The challenge is to arrange 36 officers belonging to six different ranks and six different regiments in a 6x6 square in such a way that no row or column repeats a rank or regiment. Mathematically speaking, this involves creating an orthogonal Latin square, which is an n × n square (where n is a natural number) where n objects (each having n possible colours) are arranged in such a way that they are not repeated in any row or column. As depicted in the illustration above, definite solutions are possible for 3x3, 4x4 and 5x5 squares, however a solution for the 6 x 6 square remains elusive. In 1900, the problem was proved unsolvable by the French mathematician Gaston Tarry.