Here's an odd little sliding puzzle:
As you can see, there is currently one free space, in the centre circle. That circle can spin freely, even when it is holding a piece in its 'holder'. Note, however, that if a piece gets moved around via the spinner, it's orientation also will change.
My question, of which the answer I am not sure of yet:
Is it possible to change the order of the numbers such that every tile is still in the correct orientation?
Edit: @somebody has pointed out a very simple construction!
Thus, there remains the question of WHAT orders are possible. I'm suspecting there is some even/odd permutation argument.
For clarification: The intent is to have all numbers having 4 distinct orientations, none of which can be mistaken for another. I did attempt to draw all numbers asymmetrically, and the 6 and 9 distinctly. As of now, I would like the problem as stated to be more straightforward in terms of its mathematical conditions.