  A Latin square of order $n$ is an $n\times n$ array which contains $n$
distinct symbols exactly once in each row and column. We define the adjacent
distance between two adjacent cells (containing integers) to be their
difference modulo $n$, and inner distance of a Latin square to be the minimum
of adjacent distances in the Latin square. By first establishing upper bounds
and then constructing squares with said inner distance, we found the maximum
inner distance of an $n \times n$ Latin square to be
$\left\lfloor\frac{n-1}{2}\right\rfloor$. We then studied special kinds of
Latin squares such as pandiagonals (also known as Knut-Vik designs), as well as
Sudoku Latin squares. This research was conducted at the REU at Moravian
College on Research Challenges of Computational and Experimental Mathematics,
with support from the National Science Foundation.
