The thirty-six officers problem is a mathematical puzzle proposed by Leonhard Euler in 1782.
The problem asks if it is possible to arrange 6 regiments consisting of 6 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;[3] but the problem has led to important work in combinatorics.
Besides the 6 by 6 case the only other case where the equivalent problem has no solution is the 2 by 2 case, i.e. when there are 4 officers.
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