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