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An array is  row‐Latin  if no symbol is repeated within any row. An array is  Latin  if it and its transpose are both row‐Latin. A  transversal  in an    n  ×  n    array is a selection of  n  different symbols from different rows and different columns. We prove that every    n  ×  n    Latin array containing at least(  2  −   2   )    n  2distinct symbols has a transversal. Also, every    n  ×  n    row‐Latin array containing at least1  4    (  5  −   5   )    n  2distinct symbols has a transversal. Finally, we show by computation that every Latin array of order 7 has a transversal, and we describe all smaller Latin arrays that have no transversal.

Transversals in Latin Arrays with Many Distinct Symbols