MathDB

n\times n

Latin square is a

n\times n

grid that is filled with

n

1

's,

n

2

's,

\dots

, and

n

n

's such that each column and row of the grid contains exactly one of each

1

2

\dots

n

. For example, the following is a valid

2\times2

Latin square:

\textstyle\begin{bmatrix}2&1\\1&2\end{bmatrix}

, but this is not:

\textstyle\begin{bmatrix}2&1\\2&1\end{bmatrix}

. How many

4\times4

Latin squares are there?

22