What math is used when solving a rubik's cube?

Answer 1

MATHEMATICS OF THE CUBE

The center pieces of each face are always in the same relationship to each other.

Therefore, the number of ways the other pieces can be arranged in relation

to them (ie the possible arrangements of the cube) is:

Total possible arrangements = (possible arrangements of Corner Pieces) x (possible arrangements of Edge Pieces).

Possible Arrangements of Corner Pieces:

There are 8 Corner Pieces. Therefore, the possible different arrangements of them is 8! (ie 8x7x6x5x4x3x2x1) = 40320.

Each Corner Piece has three different orientations, so this must then be

multiplied by 3 to the power 8 (ie 3x3x3x3x3x3x3x3) which equals 6561.

However, with the actual cube, once the second from last Corner Piece is placed, the last piece can have only one automatic orientation so this should be divided by 3 (effectively 3 to the power 7) which equals 2187.

Thus, total possible arrangements of Corner Pieces = 40320 x 2187 = 88,179,840.

Possible Arrangements of Edge Pieces:

There are 12 Edge Pieces. Therefore, the possible different arrangements of them is 12! (ie: 12x11x10x9x8x7x6x5x4x3x2x1) = 479,001,600. However, with the actual Cube (and unlike Corner Pieces) it is impossible to exchange just two Edge Pieces, so once the third from last is placed, the remaining two can have only one possible arrangement, so this total must be divided by 2, which equals 239,500,800.

Each Edge Piece has two different orientations, so this must then be multiplied by 2 to the power 12 (ie 2x2x2x2x2x2x2x2x2x2x2x2) which equals 6561. However, with the actual cube, once the third from last Edge Piece is placed, although the last two pieces will be in fixed positions, one can be reoriented but the last will always have a fixed orientation in relation to it. So this must be divided by 2 (effectively 2 to the power 11) which equals 2048.

Thus, total possible arrangements of Edge Pieces = 239,500,800 x 2048 = 490,497,638,400.

So - Total Possible Arrangements of Rubik's Cube = (possible arrangements of Corner Pieces) x (possible arrangements of Edge Pieces) = 88,179,840 x 490,497,638,400 = 43,252,003,274,489,856,000.

Roughly speaking, 4.3 times 10 to the power 19.

in simple yes, because it uses several mathematical algorithms.

Answer 2

The Rubik's cube is an incredible invention when looking at it from a mathematical point of view. The very intelligent people who produced the solutions to the Rubik's cube spent much time making calculations - very mathematically. Computers can now generate great solutions to Rubik's cubes - by recognizing difficult patterns and finding the best solution using math. Yes, it's all math, math, math....but if you were to learn the beginners method for solving the Rubik's cube, you would not be using math at all. It is basically memorising the turns you have to do in different situations. It may sound easy, compared to what had to be done to make the methods. And it is. But it is far from easy. If you want to learn to solve the Rubik's cube, get a cube and ask 'How do you solve a Rubik's cube?' for my answer.

Answer 3

There are many algorithms you use to solve the Rubik's cube, all involving math.