Thirty-six officers problem

Thirty-six officers problem

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Credit: SCIENCE PHOTO LIBRARY

Caption: Thirty-six officers problem. This problem was devised in 1779 by the Swiss mathematician Leonhard Euler (1707-1783). Euler asked if six regiments (colours), with men of six different ranks (pips on shoulder tabs), could be arranged in a 6x6 square so that each row and column would not repeat a rank or regiment. Known as a Graeco-Latin square, this is a form of combinatorics. Latin squares, such as Sudoku, involve non-repetition of one property rather than two. Euler said there was no solution to this problem, but this was not proven until 1901. In 1960, it was shown that all Graeco-Latin squares except the 2x2 and 6x6 cases can be solved.

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Keywords: 1700s, 1779, 18th century, array, artwork, combination, combinations, combinatorics, conjecture, diagram, graeco-latin square, grid, illustration, leonhard euler, mathematical, mathematics, maths problems, military, problem, puzzle, rank, ranks, regiment, regiments, shoulder pips, soldier, soldiers, square, tab, tabs, thirty six officers problem

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