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 Towers of Hanoi variation (Posted on 2005-05-03)
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?

 See The Solution Submitted by Tristan Rating: 4.0000 (4 votes)

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 solution (I think) | Comment 1 of 14
If I'm solving the puzzle correctly, then the number of rings is related to triangular numbers--  1/2 * (nē+n)

If you have one additional pole, then you can only move 1 ring.

If you have 2 additional poles, then you can move the top ring to pole 1, the second ring to pole 2, the top ring on top of ring 2, then move the bottom ring to pole 1, the top ring to the original pole, the second ring on top of the bottom ring, and the top one fits back on the top. 2 additional poles = 3 rings.

Using the same algorithm, you find that the number of rings which can be moved is goverend by the number of additional poles plugged into the formula written above.
 Posted by Erik O. on 2005-05-03 15:00:31

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