Many boys (even some grown up ‘boys’) have a fascination with toy soldiers. The great mathematician Euler [pronounced ‘oiler’] (1707 – 1783) was also iterested in soldiers. He posed the following problem:
Given that (a) an officer may have one of six different ranks, (b) there are six regiments, no two officers from the same regiment having the same rank, how can 36 officers be arranged on parade in a 6 x 6 square so that no row or column will contain two officers of the same rank or of the same regiment?
In fact the problem has no solution. The problem involves mutually orthogonal Latin squares!
