et's ignore the top middle piece, since it does not really take part in the puzzle. The other 8 movable pieces and the blank space have 9! permutations, but as with most sliding piece puzzles only half of these can actually be achieved. They can therefore be mixed in 9!/2 ways. Each of the 8 pieces can also be oriented independently of one another, in 4 ways. This gives a total of 48·9!/2 = 23,781,703,680.
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