The Rubik’s cube was first invented in 1974 by someone namedErno Rubik. Although it was invented in 1974, it wasn’t released globally until1980. Around that time, about 400 million Rubik’s cubes were sold, even thoughthe Rubik’s cube was never meant to be a toy. It had one the toy of the year inthe UK in both 1980 and 1981.

Then later, the Rubik’s cube was no longer infashion, but was still there.When it was no longer the fashion, people were stillparticipating in Rubik’s cube competitions. The world record for the fastestperson to solve the Rubik’s cube, which is Mats Valk, coming in at 5.55 seconds.

Now days, Robots a solve a Rubik’s cube in 3.25 seconds.A Rubik’s cube contains six center pieces with one sticker,12 edge mini cubes with two stickers on each, and eight corner mini cubes with3 stickers on each, with the goal to move all cubes to make each color coordinateto each other. Such as, 9 red stickers on each side, 9 green stickers on eachside, 9 oranges, yellow, blue, and white stickers on each side. The moves that someonecan make while trying to solve the Rubik’s cube, is called a group, and thereare two ideas that come from the group, which are: Communicators and conjugation.

There are 43 quintillion patterns for a Rubik’s cube, which is really43,000,000,000,000,000,000. For basic moves for the Rubik’s cube, F= rotate thefront of the Rubik’s cube clockwise. That’s the same for every side, unless itis prime, which means you move the face counterclockwise.

For example, if someonesees XY, then they would first to thex move, then the y. Also, with X2 you would do x then x. Same with 3 cubed, its Xthen X then X. If you see X-1, then you do the inverse of that move, justreverse what you did, or if you did clockwise, the do counter clock wise toundo the move that has been made. If you were to apply the letters that matchwith the faces, it would look like U-1.

For the multiplication of XY they will not be able to commute, or thecommunitive property isn’t available. For example, XY CAN NOT equal YX. Butthe ONLY exception, is that if the two variables don’t affect the same ‘Cubies’,then they can commute. Another move on a Rubik’s cube is Y and Z. With these, youcan make a new move, which is called a conjugate. For example, if X flips oneedge, then ZXZ-1 would flip a different.

(keep in mind all the variables aremoves). Although there are many, many things you can do with a Rubik’s cube,there are few things you cannot. You cannot flip a single edge, or a single corner.(Math Berkeley, Michael Hutchings and Julia Robinson)Inconclusion, a Rubik’s cube dates back to 1980, and is composed of 6 faces, andmany, many moves. The moves are not communitive, unless they appy to two moves don’taffect the same cubies.