Permutations without repeats Consider this matrix:
A B C D E
D C A E B
B A E C D
E D B A C
C E D B A

The letters are arranged so that no row and no coulumn contains the same letter twice (Sudoku style).
Let's call the number of diffent letters $n$ (5 in the above example). When writing the first row, I have $n!$ permutations to choose from.
How many permutations can I choose between when writing the second row? And the third row? Etc.

When entering the second row, it has to be a derangement of the first row. When $n=5$ there are $44$ derangements. But from the third row onwards
the number of possibilities will depend on exactly what the previous rows
contain.
