Latin rectangle

In combinatorial mathematics, a Latin rectangle is an r × n matrix that has the numbers 1, 2, 3, ..., n as its entries with no number occurring more than once in any row or column where r ≤ n. An n × n Latin rectangle is called a Latin square. If r < n, then it is possible to append n − r rows to an r × n Latin rectangle to form a Latin square, using Hall's marriage theorem.