Number of puzzle states wrong

[simulatedScience]

Currently the number of puzzle states is calculated as the number of permutations of the puzzle pieces that can be reached with the defined moves.
However, this doesn't take into account that some states may not be differentiable because several peices may look identical.

For puzzles like a rubiks cube (2x2x2 and 3x3x3) this still provides the correct result, for others like the 2_rings or 4x4x4 rubiks cube, it dramatically overestimates the number of states.

[simulatedScience]

if exact computation is not feasible, an easy alternative is to just provide upper and lower bounds for the state space size.
upper = current group order
lower = group order divided by number of permutations of indistinguishable pieces.

e.g. for 2 rings puzzle, lower bound is |G| / (n-1)!² when each ring contains n points.