Rubik's Cube

Most of us have seen a Rubik’s cube before and possibly even solved one. This fascinating little toy was not always a toy. It was created in 1974 by a gentleman named Erno Rubik who was a Hungarian architect and teacher. Erno had created this masterpiece as a new method for teaching in relation to geometry. It was first named the magic cube and was much larger and heavier. I guess it is magical in that any plane of the cube, even the middle, can rotate independent of the others. When Rubik created the cube it took him a month just to solve it. Since it hit the shelves in 1980 and estimated 350 million have been sold.

If you are curious, the number of possible positions of a Rubik’s cube is
\(\frac{8!\cdot 12!\cdot 3^8\cdot 2^{12}}{2\cdot 3\cdot 2}=43252003274489856000\)

So it will keep you busy.

In the 1980’s the cube a record holder had solved it in about 20 seconds while today the current record holder solved it in under 5 seconds.

Most people don’t realize that there is a general pattern that you can follow from any scrambled cube in order to solve the puzzle and it’s not very complicated. According to Rubik’s website it is only a six stage process. However, the pros can recognize patterns and solve it in multiple ways.

Machines can do it even faster, and you have to imagine some discrete mathematics was involved.

“Mathematically the Rubik’s Cube is a permutation group. 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. We can rotate the 6 faces of the cube so we can define 6 basic operations or permutations which rearrange the ordered list in a certain way. Repeating and combining these permutations we can define new permutations, which rearrange the list in an other way” (Ruwix).

Possible Exam Question

In total, how many little blocks make up the Rubik's Cube and how many colors does it consist of?