# Combinations of a jigsaw

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

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One of your many combinations $C(n)$ is also a solution of the puzzle, but upside down, i.e., rotated 180 degrees. Would that also solve your puzzle? I was (jokingly) suggesting that the worst case scenario would be one step faster. –  Hendrik Jan Jan 6 '13 at 11:14