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?

My answers follow a pattern of

2^(N-1) - 1

So for N= 1, 2, 3, 4, 5, 6 poles I can move

0, 1, 3, 7, 15, 31 . . .

Which is also equal to: when a pole is added, twice as many rings can be moved plus one.  

Edited on May 3, 2005, 6:20 pm

Posted by Leming on 2005-05-03 18:20:21