There are some poles, and on the first pole are some rings, each a different size. The sizes of the rings increases from the top to the bottom of the pole. The only allowable move is to take the top ring from any pole and place onto another pole. You cannot place a ring on top of another ring unless the other ring is exactly one size bigger. You can make as many moves as you like.
Your goal is to move all the rings onto the second pole, in the same order. What is the highest number of rings that can be moved when there are N poles? How can you move this many rings?
The Towers of Hanoi is a well known problem. Using 3 poles one can move any number of rings from one pole to another. The formula for the number of moves required for n rings is 2^n 1
The highest number of rings with N poles?
Easy:
If N=1 you can't move any
If N=2 you can only move 1
If N=3 you can move any amount
If N>3 you can move any amount without using the extra poles at all.
I'll assume you meant to ask what the minimum number of moves is as you add more poles. That is harder and I will work on it.

Posted by Jer
on 20050503 17:02:45 