The are 43 quintillion patterns for a Rubik’s

The Rubik’s cube was first invented in 1974 by someone named
Erno Rubik. Although it was invented in 1974, it wasn’t released globally until
1980. Around that time, about 400 million Rubik’s cubes were sold, even though
the Rubik’s cube was never meant to be a toy. It had one the toy of the year in
the UK in both 1980 and 1981. Then later, the Rubik’s cube was no longer in
fashion, but was still there.

When it was no longer the fashion, people were still
participating in Rubik’s cube competitions. The world record for the fastest
person 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.

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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 with
3 stickers on each, with the goal to move all cubes to make each color coordinate
to each other. Such as, 9 red stickers on each side, 9 green stickers on each
side, 9 oranges, yellow, blue, and white stickers on each side. The moves that someone
can make while trying to solve the Rubik’s cube, is called a group, and there
are two ideas that come from the group, which are: Communicators and conjugation.
There are 43 quintillion patterns for a Rubik’s cube, which is really
43,000,000,000,000,000,000. For basic moves for the Rubik’s cube, F= rotate the
front of the Rubik’s cube clockwise. That’s the same for every side, unless it
is prime, which means you move the face counterclockwise. For example, if someone
sees XY, then they would first to the
x move, then the y. Also, with X2 you would do x then x. Same with 3 cubed, its X
then X then X. If you see X-1, then you do the inverse of that move, just
reverse what you did, or if you did clockwise, the do counter clock wise to
undo the move that has been made. If you were to apply the letters that match
with the faces, it would look like U-1. For the multiplication of XY they will not be able to commute, or the
communitive property isn’t available. For example, XY CAN NOT equal YX. But
the 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, you
can make a new move, which is called a conjugate. For example, if X flips one
edge, then ZXZ-1 would flip a different. (keep in mind all the variables are
moves). 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)

conclusion, a Rubik’s cube dates back to 1980, and is composed of 6 faces, and
many, many moves. The moves are not communitive, unless they appy to two moves don’t
affect the same cubies.



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