number of possible number arrangements

Following up on sneaklyfox's question in the Timed Puzzle Bonus thread:

"How many combinations are there for the solution arrangement for a 4x4 puzzle?"

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Latin squares.

To get the number for 4x4, multiply the given number L(4, 4) = 4 by (n - 1)! x n!:

4! x 3! x 4 = 24 x 6 x 4 = 576.

The numbers get interesting for larger n...

Not going to run out of 9x9 puzzles anytime soon, for example

(and this is not counting the cage and operator arrangements (!!))

Patrick