When designing ANOVA experiments, these are often used to limit experimental interactions.
When designing ANOVA experiments, these are often used to limit experimental interactions. In 1900, Tarry proved that no orthogonal ones of order 6 exist, and in 1960 Bose, Shrikhande, and Parker proved that for all other orders of the form 4n + 2, there do exist orthogonal ones. The problem was initially proposed by Euler in 1783 as the "36 officers problems," where one attempts to arrange six grades of officers from six regiments into a grid such that each row has each kind of officer and each column has a representitive from each regiment. A Japanese puzzle operating on a similar concept, Sudoku, is gaining popularity. For ten points, name these n by n grids where each column and row contains the numbers 1  to n exactly once.
When designing ANOVA experiments, these are often used to limit experimental interactions.
Latin or Euler (before mentioned) or Graeco-Roman squares/rectangles