Orthogonal Latin Squares of Order 6 do not Exist/Historical Note

Historical Note on Orthogonal Latin Squares of Order 6 do not Exist
This problem was posed by, who couched it as follows:
 * Place $36$ officers,
 * comprising a colonel, lieutenant-colonel, major, captain, lieutentant and sub-lieutenant
 * from each of $6$ regiments,
 * in a square array
 * so that no rank or regiment will be repeated in any row or column.

This turns out to be impossible to do.