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Nests and trees both?

It's not clear to me how you can have both nests and trees, and still use "standard" Tower of Hanoi rules. Don't those rules require that the sizes of pieces in a stack always get smaller as they build upwards? — Rootbeer (Tom) (U | T | C) 15:20, 19 Sep 2005 (GMT)

  • My idea was only to have the stacks 'start' as nests and then 'evolve' into trees. Per ToH rules (only same size or smaller), the pieces should naturally evolve out of it given enough moves. Only the initial setup breaks these rules.Veled 13:37, 20 Sep 2005 (GMT)

Number of moves

Has anyone tried to work out the minimum number of moves needed, and how it scales with te number of nests started with? I just managed to confirm to myself that it's possible when starting with just 3 nests (in 35 moves). I've also tested that 4 nests of different colours can be made to trees of the same colour quite easily, so it could also work with a Treehouse set. --Lardarse 08:48, 22 March 2008 (EDT)

As you seem to have noticed, having more nests doesn't make much difference (if you have 3 stacks with a large piece on top, you can just unstack a nest onto them then restack it as a tree, meaning that all but 3 nests can be turned into trees without affecting any other pieces). Having different colours might be interesting. I'm currently pondering ways of tweaking the standard Hanoi rules to allow 5/6 colours on three "rods". — Cheshire Swift 23:18, 28 April 2009 (UTC)

Simple version

What if you start with two trees of different colors, on the ends of a 1 by 3 board, and have them trade places? (Clarification: You can place a piece on top of one with the same size.)