This design is a slight variation of the CrossCode Burr #3 puzzle, whereby I've strategically moved the exit paths in order to make it much more tricky to find the right configuration that allows each piece to be removed. There is indeed some underlying logical rule that dictates what those configuration are, yet the logic is subtle enough that it seems random, and as such I think this puzzle concept crosses the line into territory where the increased difficulty takes away from the fun of playing with it.