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### Abstract Algebra and Puzzles

```
Date: 10/31/98 at 16:34:49
From: Jamie Clarke
Subject: Abstract algebra

I have to do a project about anything I want that relates to abstract
algebra. I want to do something that relates to either science or art.
Do you have any ideas?

Thanks, Jamie
```

```
Date: 10/31/98 at 16:59:43
From: Doctor Barrus
Subject: Re: Abstract algebra

Hi, Jamie!

One thing you might want to look into is how abstract algebra is used
in puzzles like Rubik's Cube and the 15 puzzle(*). Sometimes
principles from group theory can be used to analyze these games. It's
some more material on these topics.

(*) The 15 Puzzle, in case that's not clear, is this: You have a square
frame that contains square tiles with numbers on them. The numbers are
labeled from 1 to 15 and mixed up. There is a blank space you can slide
tiles into. The object is to slide the tiles into order from 1 to 15,
with the blank space ending up in the lower lefthand corner. (You've
probably seen this game before. It's often given away as a party favor.
You can get cheap plastic versions at many toy stores.)

/-------------------\
|  1 |  3 | 13 |  4 |
|----+----+----+----|
|  2 |  6 |  7 |  8 |
|----+----+----+----|
|  9 | 10 |  5 | 12 |
|----+----+----+----|
| 14 | 15 | 13 |    |
\----+----+----+----/

Anyway, that's an idea you may want to look into. If that's not what
you're looking for, you may want to write back to us. One of the other
math doctors may have another idea.

Good luck!

- Doctor Barrus, The Math Forum
http://mathforum.org/dr.math/
```
Associated Topics:
High School Puzzles

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