Mathematics Behind Rubik S Cube

There is an identity element e g such that e g g e g.

Mathematics behind rubik s cube. The immediate math to be done with those numbers is the total number of ways you can scramble a rubik s cube. The basic operations there are 6 faces and two directions for each so 12 of them correspond to some generators of the group. Demaine and his colleagues recognized that under some circumstances a single sequence of twists could move multiple squares into their proper places cutting down the total number of moves. The set of positions of a rubik s cube is indexed by the element of a group named the rubik s cube group.

Sp 268 the mathematics of the rubik s cube the operation is associative so for any elements f g and h f g h f g h. 2 12 represents the permutation of the edge pieces. Represents the 12 edge pieces that can be arranged in 12. It has 6 different colors and each color is repeated exactly 9 times so the cube can be considered as an ordered list which has 54 elements with numbers between 1 and 6 each number meaning a color being repeated 9 times.

The number of possible positions of a rubik s cube is. Six center pieces which do not move relative to each other. Every element in g has an inverse g 1relative to the operation such that g g 1 g 1 g e. In the mathematics of the rubik s cube it is noted that by measuring the number of individual cubes changed by performing a sequence of moves the required additional moves needed to reverse unwanted changes can be determined.

That approach will indeed yield a worst case solution that s proportional to n 2. Written in a more mathematical way that number is 3 8 8. Twelve edge cubies each with two stickers on them. This impressive figure is the number of tile combinations possible in the rubik s cube also known as the magic cube the most famous puzzle of all times.

The mathematical mystery behind rubik s cube. Represents the 8 corner piece that can be arranged in 8. Mathematically the rubik s cube is a permutation group. The rubik s cube is an instance of what s called a configuration problem the best known example of which involves finding the most efficient way to reorganize boxes stacked in a warehouse.

The standard way to solve a rubik s cube demaine explains is to find a square that s out of position and move it into the right place while leaving the rest of the cube as little changed as possible. Michael hutchings uc berkeley the mathematics of rubik s cube julia robinson math festival 1 26 elements of rubik s cube the cube contains. It follows that useful pairs of moves typically only change a small number of individual pieces. Eight corner cubies each with three stickers on them.

The mathematics is the following.