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 
pretty interesting stuff. Your professor could probably help you find 
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/