It turns out that the latter number is smaller. To show this, first count the number of cube positions that exist in total, then count the number of positions achievable using at most 17 moves starting from a solved cube. It can be proven by counting arguments that there exist positions needing at least 18 moves to solve. Note that these letters are usually lowercase instead. As with regular turns, a 2 signifies a half rotation and a prime (') indicates a quarter rotation in the opposite direction. These cube rotations are used in algorithms to make the algorithms smoother and faster. Z signifies the rotation of the cube on the F direction. Y signifies the rotation of the cube in the U direction.

X signifies rotating the cube in the R direction. The letters X, Y and Z are used to signify cube rotations. As with regular turns, a 2 signifies a double turn and a prime (') indicates a quarter turn anticlockwise. E represents turning the layer between the U and D faces 1 quarter turn left to right, clockwise as seen from the bottom. S represents turning the layer between the F and B faces 1 quarter turn clockwise, as seen from the front.

M represents turning the layer between the R and L faces 1 quarter turn top to bottom. The letters M, S and E are used to denote the turning of a middle layer. A counterclockwise quarter turn is indicated by appending a prime symbol ( ′ ). Half turns are indicated by appending a 2. The letters L, R, F, B, U, and D indicate a clockwise quarter turn of the left, right, front, back, up, and down face respectively. To denote a sequence of moves on the 3×3×3 Rubik's Cube, this article uses 'Singmaster notation', which was developed by David Singmaster. Main article: Rubik's Cube § Move notation An algorithm that solves a cube in the minimum number of moves is known as God's algorithm. There are many algorithms to solve scrambled Rubik's Cubes. In STM (slice turn metric), the minimal number of turns is unknown. These numbers are also the diameters of the corresponding Cayley graphs of the Rubik's Cube group. The maximal number of face turns needed to solve any instance of the Rubik's Cube is 20, and the maximal number of quarter turns is 26. A move to turn an outer layer two quarter (90°) turns in the same direction would be counted as two moves in the quarter turn metric (QTM), but as one turn in the face metric (FTM, or HTM 'Half Turn Metric', or OBTM 'Outer Block Turn Metric'). The second is to count the number of outer-layer twists, called 'face turns'. The first is to count the number of quarter turns. There are two common ways to measure the length of a solution. Optimal solutions for Rubik's Cube refer to solutions that are the shortest.

Rubiks cube flip one middle end pice