I'm just asking myself of how many combinations you would have to go through to solve a jigsaw puzzle by "brute force" if you have $n = (p \times q)$ pieces. To simplify that, I assume that there are no jigsaw pieces with flat edges so that every piece can be at every position.
I've came up with this for the number of combinations $C$: $$C(n) = n! * 4^n$$ $n!$ would be the number of options to arrange the pieces and for each of these options there should be $4^n$ possibilities to rotate them.
Can anyone verify that? Or am I doing a mistake?
Thank you very much in advance