each of a more specific set of possible permutations of the latest layer's pieces, performing orientation and permutation of both edges and corners in fewer sequences (and total moves) than the shorter but more repetitive beginner algorithms. The 6-color Megaminx comes with an additional challenge which is not immediately obvious (and which does not occur on the 12-color puzzle). Its edge pieces come in visually identical pairs, because of the duplicated colors of opposite faces. However, although visually indistinguishable, they are nevertheless mathematically bound in a parity relationship. In any legal position (reachable from the solved state without disassembling the puzzle), there is always an even number of swapped pairs of edges. However, since swaps may be between visually identical edges, one may find that having solved almost the entire puzzle, one is left with a pair of swapped (distinct) edges that seems to defy all attempts to exchange them. The solution is to swap a single pair of 'identical' edges to resolve the parity issue, and then restore the rest of the puzzle. This property is absent in the 12-color Megaminx, because all its edges are distinguishable, and it would be immediately obvious that there is another pair of swapped edges besides the pair one is working with. "Impossible" permutations of a 12-color Megaminx, causing behaviors inconsistent with the expectations of a solving method, are the result of manipulations not possible solely by turning the faces during a scramble or solve. The most common is a "corner twist", an often-necessary side effect of puzzles designed to allow some misalignment of a face when beginning rotation of an adjacent face (so-called "corner-cutting"). The looser tolerances allow a corner to be rotated in place, independent of any other face or corner, placing the puzzle in a permutation that face turns alone cannot solve. Most other "impossible" permutations of the puzzle are the result of improper assembly, and are avoided by always reassembling the puzzle into a solved state after disassembly for cleaning, maintenance or adjustment. Variations There are many similar puzzles with different numbers of layers, most of which change the "mega" in the puzzle's name to another metric prefix. They are the Kilominx (2 layers), Master Kilominx (4 layers), Gigaminx (5 layers), Elite Kilominx (6 layers), Teraminx (7 layers), 8×8 Kilominx (8 layers), Petaminx (9 layers), Examinx (11 layers), Zettaminx (13 layers), Yottaminx (15 layers), and Atlasminx Or Quettaminx (19