Hanoi Pattern Description

"I first encountered the Towers of Hanoi puzzle when I was 8 years old. With an eager mind a attacked the puzzle and quickly discovered a pattern to its solution. This recursive solution is the one described in you web page discussion of this puzzle. At the same time I discovered another patten involved in moving the pieces, and since that time I have never seen any mention of this pattern in any discussion about this puzzle. This is not a difficult pattern, and I was wondering if I was just not reading the right articles. Although there is much more to it than this, here is the basic pattern that I discovered: Each piece in the puzzle moves in the same direction (clockwise or counterclockwise) throughout the entire solution of the puzzle. If you number the pieces (from smallest to largest or vice versa) all of the odd numbered pieces will move in one direction, and all the even numbered pieces will move in the opposite direction.
The frequency of the moves is also predictable. The smallest piece will move every other turn, the next smallest every fourth turn, the next smallest every eighth turn and so on. These facts together lead to a very simple solution to the puzzle. Pick a direction to move the smallest piece. Move this piece every other turn. On the alternate turns, there is only one move available to you, so no thinking is required.
This solution is much easier to work with (especially for larger stacks of disks), than the recursive solution, and yet I have never seen or heard any mention of it. My question is has anyone else ever seen this, or did I make an amazing discovery when I was a child?
I do have more information about patterns involved in this puzzle if anyone has any questions. For example, how do you determine which direction to move the smallest disk if you want to move the stack from tower A to tower C and not tower B. The answer depends on if the stack has an odd or even number of disks. You can experiment with the ideas I presented in here, but I would recommend working with a physical representation of the puzzle, not a computer version. My first exposure was with towers and disks made of wood. If I hadn't had hands on experience with this puzzle, I may have never noticed these patterns."
- see original post here.