A Group Game

from Scientific American

 

Science

(continued)

We have a game for you to play.  It involves 12 scrambled numbers and two moves.  The idea is to unscramble the numbers.  You can play by clicking here

The  two moves are inversion and merge.  Inversion just switches positions.  If we denote this in cyclic notation this would be

I = (1,12)(2,11)(3,10)(4,9)(5,8)(6,7)

Merge is more complicated.  Play with it to see what it does and make yourself a little diagram.  One way to  learn what it does is to not randomize and just see where the numbers 1 to 12 go.

(next column)

24/04/2009 09:23 PM

In cyclic notation merge looks like this:

M = (1)(2,3,5,9,8,10,6,11,4,7,12).

In this notation, in each parenthesis, each number is moved to the position of the next number, and the last number moves back to the first.

Maybe we can go further with this sometime by replacing the numbers 1 to 12 with the 12 musical notes and playing you the solution.  It might be interesting eh?

It's  not an easy game.  It is kind of like Rubrics cube, with no manual dexterity.  If you want the solution click here 

Groups are mathematical entities
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