The third-order Rubik's Cube consists of a central axis connecting six central squares and 20 squares with different structures. When they are connected together, they will form a whole, and either side can rotate horizontally without affecting other building blocks.
The correct calculation formula is as follows:
The symbol "*" is a multiplication symbol;
The symbol "/"is a division symbol;
" ! " This symbol is all time, 8! Namely 8 * 7 * 6 * 5 * 4 * 3 * 2 *1;
This symbol is a power, and 3 8 is the eighth power of 3.
(8! * 3^8 * 12! * 2^ 12)/(3 * 2 * 2)= 43252003274489856000
Numbers separated by thousands:
43 252 003 274 489 856 000
The formula of the total number of changes in the third-order Rubik's cube is as follows:
First of all, the six central blocks are immovable, and they just form a coordinate system because of the different colors. There are 8 angular positions and 12 edge positions in this coordinate system.
For 8 angular positions, we have 8 complete arrangements! Eight small character blocks have three directions, so multiply by 3 8.
For 12 prism block, the same is true, with 12! *2^ 12。
The above two combinations should be combined, and its variation number is the multiplication of these two numbers, which is the molecule (8! * 3^8 * 12! * 2^ 12)。
This result is actually the number of changes we can get after disassembling the Rubik's Cube and assembling it randomly. This figure is 12 times of the above results. That is to say, a randomly assembled Rubik's cube has a probability of112, and it cannot be restored to the same state of six faces.
For the denominator of 3*2*2, their respective meanings are: keeping the position and direction of other color blocks unchanged, it is impossible to flip a prism color block alone (that is, switch its two sides), flip a role block alone, and switch the positions of a pair of color blocks alone.
Or simply put, if we disassemble a prismatic square and turn it over, it can be changed into the shape of 4.3 * 10 19 under all possible changes of the Rubik's cube, but it will never change the appearance of six homochromatic surfaces, and it will never change the 4.3 * 10 65438 that can be derived from six homochromatic surfaces. If we flip a prism quickly, the Rubik's cube will fall into an inner sense and never come back.
Please refer to the following information:
Look down, or search that number. The formulas in the following two web pages are incorrectly written, either missing symbols or numbers. The correct formula is what I wrote above. Moreover, its formula and thinking are correct, and the calculation result is correct.
There are also general changes in the fourth-order and fifth-order Rubik's Cube in the webpage, but I just looked at it and didn't count it.
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