Discussion:  All Topics 
Topic:  Towers of Hanoi Applet 
Related Item:  http://mathforum.org/mathtools/tool/407/ 
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Subject:  RE: Towers of Hanoi Applet 
Author:  Michael McKelvey 
Date:  Feb 15 2004 
I agree wholeheartedly with your request for an Undo button. Starting
over every time you make a mistake is just ridiculous in some situations. It's
not so bad if you're working with 3 or even 4 discs, but beyond that... I just
did the puzzle with 8 discs and was yearning for that Undo button. I know the
pattern and have done it many times before, but I made one simple mistake late
in the game and had no recourse but to keep going, ending up with this
screen:
http://www.mste.uiuc.edu/courses/ci336sp04/folders/mmckelve/images/hanoi.jpg
If I made this mistake even though I had experience with the puzzle, how is a
student who is just learning about it ever going to manage to move all the discs
in the minimum number of moves? Especially if s/he doesn't yet know the
pattern, and needs to try different things out to test developing theories...
I'd say the Undo button would be one of the most important additions that could
be made to this applet.
Also, should discussion of the 2^n1 and 2*x(n1)+1 patterns come into play
in the applet, or should that be left up to the teacher to implement in his/her
own way in the classroom? These are very important patterns to recognize,
especially the 2*x(n1)+1 pattern. It shows how each number of discs can be
solved simply by solving for n1 discs (but ending up on the middle peg), then
moving the nth disc to the last peg, then solving for n1 discs again. Hence,
x(n1) + 1 + x(n1) = 2*x(n1)+1. It's a recursive pattern that a
gradeschooler might be able to grasp, because there's such a tangible
demonstration of it right there in front of him/her. I guess it's sufficient to
leave it off the applet, because there are good support pages provided, but it
really wouldn't hurt to have the minimum # of moves a student has found for each
# of pegs displayed at the bottom of the applet...
Michael
 
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