Latin Square Problem

A Latin square is a square with n rows and n columns, and each cell contains an integer 1 to n such that each row and each column have distinct numbers.
Example of a Latin square

Part 1. How many 3×3 Latin squares are there? You can use the interactive Latin square designer to help you.

Part 2. How many 4×4 Latin squares are there?
Part 3. Devise a formula L(n) for the number of n×n Latin squares. This is one of the unsolved problems of mathematics since the formula is not known yet. The number of n×n Latin squares is known to increase very fast, in fact L(n) is larger than
  .

Solution - none exists yet!

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