Thirty-six officers problem

The thirty-six officers problem is a mathematical puzzle proposed by Leonhard Euler in 1782.

The problem asks if it is possible to arrange six regiments consisting of six officers each of different ranks in a 6 × 6 square so that no rank or regiment will be repeated in any row or column. Such an arrangement would form a Graeco-Latin square. Euler correctly conjectured there was no solution to this problem, and Gaston Tarry proved this in 1901, but the problem has led to important work in combinatorics.

Besides the 6 × 6 case the only other case where the equivalent problem has no solution is the 2 × 2 case, i.e. when there are four officers.

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