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post finishing is also very important to get smooth operation. I sand every piece smooth after printing, but this process is very time consuming (around 10 hours of sanding per puzzle)

For a basic 3x3 mechanism you can get by with 0 tolerances between the pieces. If you do a complete sanding it will also remove material creating a small amount of tolerances. In my own puzzles, the sanding process removes about .1mm from the surface.