Eight corner blocks can be interchanged (8! ) You can also rotate (3), but you can't flip a corner block alone, so there are always 8! * 3 8 divided by 3 changes the state.

12 side blocks are interchangeable (12! ), you can also flip (2), but you can't flip a side block alone (that is, you can't swap the positions of both sides), so there is always 12! * 2 12 divided by 2*2 changes the state.

In other words, if the Rubik's Cube is disassembled at will, there is a probability of112 that it cannot be restored to its original state. For a Rubik's cube that is disassembled and reassembled at will, the total number of changes is: 8! *3^8* 12! *2^ 12=5 19,024,039,293,878,272,000。

Some Rubik's cubes have directional patterns on all sides. Considering that six central blocks have four orientations, but one of the central blocks cannot rotate 90 degrees, the total number of changes must be multiplied by 4 6 divided by 2. The result at this time is: 8! *3^8* 12! * 2 12 divided by 2*2*3 and then multiplied by 4 6 divided by 2 = 8857,606,706,155,225,088,000.

Extended data:

Singmasternotation was invented in1978+February by DavidBreyerSingmaster, a former professor of mathematics at South Bank University in London. Singmaster notation has become a universal standard, commonly known as "Rubik's cube formula symbol".

Singmaster tag consists of "code number of each layer" and "rotation direction".

1, the code of each layer: each layer of the Rubik's cube is referred to by the English initials. R (right), L (left), U (upper), D (lower), F (front) and B (rear) refer to right, left, top (upper), bottom (lower), front (front) and rear (rear) layers respectively.

2. Rotation direction: rotate 90 clockwise to directly write the codes of each layer; Rotate 90 counterclockwise, and each layer codes suffix' or I'; Rotation 180, with each layer coded with suffix 2 or 2 (default clockwise rotation 180). The complete Singmaster mark can be understood as rotating in the direction from the perspective of the reference layer.

3. For example: r, rotate the right side clockwise by 90 from the angle facing the right side. From the front, that is, the right side turns 90 "upward".

4. Another example: d, from the angle facing the bottom surface, rotate the bottom surface clockwise by 90 degrees. From the front, that is, turn right 90 on the right.

5. Another example: b', rotate the back 90 counterclockwise from the angle facing the back. From the front, that is, turn right 90 degrees from the back. In addition, if you want to record the rotation of the Rubik's cube in more detail, you will also use: m (middle) is used with u, f and l to refer to each middle layer; C(Complete) is used together with U, F and L, indicating that the whole Rubik's Cube rotates in the form of a certain layer.

6. For example, MU, rotate the middle layer 90 clockwise from the top view. From the front, that is, turn left 90 degrees from the second floor above.

7. For example: CF, rotate the whole Rubik's Cube 90 degrees clockwise from the front view. That is, the whole Rubik's cube rotates 90 degrees to the right along the vertical plane.

Baidu encyclopedia-third-order Rubik's cube