11. The reasoning is this : A Latin square is the multiplication table of a quasigroup. 12. :The minimum number of transversals of a Latin square is also an open problem. 13. See small Latin squares and quasigroups. 14. A Graeco-Latin square can therefore be decomposed into two " orthogonal " Latin squares. 15. A Graeco-Latin square can therefore be decomposed into two " orthogonal " Latin squares . 16. Every column and row includes all six numbers-so this subset forms a Latin square . 17. Another type of operation is easiest to explain using the orthogonal array representation of the Latin square . 18. For each, the number of Latin squares altogether is times the number of reduced Latin squares. 19. For each, the number of Latin squares altogether is times the number of reduced Latin squares . 20. Since this applies to Latin squares in general, most variants of Sudoku have the same maximum.
