Algorithm: 8 cube corners are arranged in 8 positions, 12 cube corners are arranged in 12 positions, and * * * has 8! × 12 ! Kindness Each cube has two orientations, each cube has three orientations, and there are * * * 3 8× 2 12 kinds. So the number of states of the Rubik's Cube is 8! × 12 ! × 38× 212 = 5 19024039293878272000 species, exceeding 51902 billion.
But in these 20 squares, 18 positions have been determined, and the other two positions have also been determined. So remove factor 2! . Of the eight angles, seven orientations were determined, and the eighth orientation was also determined; In the 12 cube, the orientation of 1 1 is determined, and the orientation of 12 is also determined. This removes the factor of 3 × 2, which is actually112 of the above number, that is, the total is 8! × 12 ! × 3^7 × 2^ 1 1/2=43252003274489856000 .
Consider the divisor 12 above from another angle. If we determine 6 colors, each color is drawn on 9 small squares on the surface of the Rubik's Cube 1. Then we take the Rubik's Cube apart and reassemble it, so not every Rubik's Cube can be restored to its original state. Specifically, there are 5 19024039293878272000 spellings, which can be divided into 12 categories, and each category has 432520032748856000. Any two states in the same class can be transformed into each other, but not between different classes.