cp's OEIS Frontend

Not every position can be reached using this restricted set of moves. Total number of positions that can be reached = 192.

Total number of positions = 88179840. Here a half-turn is counted as a single move.

Total number of positions = 88179840. Here a half-turn is counted as two moves.

Not every position can be reached using this restricted set of moves. Total number of positions that can be reached = 2592.

From Ben Whitmore, Dec 27 2024: (Start)

An alternative description is number of positions of the subgroup of the Rubik cube at a distance of n moves from the solved state, in the slice-quarter-turn metric.

The slice-quarter-turn metric counts quarter-turns of outer faces and inner slices as 1 move, and half-turns of outer faces and inner slices as 2 moves.

The M slice is the middle layer between the left and the right faces, and an M move is a clockwise move of this slice when viewed from the left face.

The total number of positions is 6! * 2^5 * 4 * 2 = 184320.

The two positions requiring 23 moves can be reached by applying the following algorithm, or its inverse, to a solved cube: U M U M U M U M U' M U M' U M U M' U M U' M' U2 M. (End)

Not every position can be reached using this restricted set of moves. Total number of positions that can be reached = 768.

Not every position can be reached using this restricted set of moves. Total number of positions that can be reached = 6144. This is for 2q or anti-slice moves.

Not every position can be reached using this restricted set of moves. Total number of positions that can be reached = 6144.

Not every position can be reached using this restricted set of moves. Number of inequivalent positions that can be reached = 50.