Can 36 officers be arranged in a 6 by 6 square so that
each of 6 regiments and each of six ranks appear in each row and column
exactly once?
The question is equivalent to finding two orthogonal latin
squares of order 6.
The first solution was given in 1901 by Col. Tarry, who simply listed every possible latin square of order 6 and saw that no two of them were orthogonal. The best solution is by D. Stinson in 1988.
You can also read my solution:
A Coding-Theoretic Solution to the 36 Officer Problem -- Designs,
Codes and Cryptography, 4, 123-128, 1994.
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