Describe how to create an \(n \times n\) Latin square.

The following procedure will generate only 1 of many possible Latin squares:

Take an ordered sequence of \(n\) integers and use it for the first row. Then pick a direction (left or right). To create the next row, take a previous row and rotate it in the initially chosen direction by one (consistently rotate all rows in the same direction). Repeat the rotation and appending of the next row \(n-1\) times to get the full square.

To generate all possible \(n \times n\) Latin squares do the following:

• Generate all \(n!\) permutations of \(n\) elements
• Generate all possible \(n\) groups of those permutations which don’t share any element in the same position (called derangements) as rows of an \(n \times n\) square
• Permute rows of each square generated with the procedure above.