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### Rubik's Cube

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Date: 12/03/98 at 23:19:16
From: S. Smith
Subject: Rubik's cube

I just wanted to know about the Rubik's Cube. Who made it and how it
can help me learn math?

Thanks.
```

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Date: 12/04/98 at 12:46:05
From: Doctor Rick
Subject: Re: Rubik's cube

Hi, welcome to Dr. Math's office.

Rubik's Cube was invented in the 1970s by a Hungarian named Erno Rubik.
Playing with Rubik's Cube makes you think about 3-dimensional shapes,
visualize what will happen if you turn a face of the cube a certain
way, and plan ahead. You have to make the cube look worse before it can
get better, so you can't just do it one step at a time. You learn
certain patterns - sequences of 3 or 5 or 15 rotations that move the
little cubes in a certain way. These things are good for stretching
your mind even if it doesn't seem like math.

A warning, though: it doesn't replace doing homework. The Cube can be
habit-forming, so be careful with it!

There is math in Rubik's Cube that you haven't learned yet. The math
in Rubik's Cube is a branch of mathematics called Group Theory. Instead
of multiplying or adding numbers, you rotate faces of the cube, and
this kind of math helps to describe what happens when you do several
rotations in a row.

For instance, in regular math, 3 times 2 is 6 and 2 times 3 is also 6.
But in the "group" that is Rubik's Cube (the set of rules that it
follows), turning the top counterclockwise and then turning the front
clockwise is NOT the same as doing these two "operations" in the
reverse order. We say that the group is not "commutative".

I don't think you'd understand it yet, but in case you'd like to see
what the math looks like, you could try to find an old copy of
Scientific American magazine in the library. In March 1981, Douglas
learned how to solve the Cube by studying this article, but I must
admit that 9-year-olds with no idea of the math involved could solve
it faster than I. I have no idea how they did it!

For another advanced source, this one on the Internet, you could try
the lecture notes by Professor W. D. Joyner for a class on the
mathematics of the Rubik's Cube:

http://web.usna.navy.mil/~wdj/rubik_nts.htm

- Doctor Rick, The Math Forum
http://mathforum.org/dr.math/
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