It's a game. You want to make it so the other guy has no move. You can fuse any pair of stacks so long as the sizes are descending up. Once a stack is joined, it stays joined. Disks of (1,2,3): winning move is join (1,3). No further move is possible. If instead you fuse (1,2), then the second player can create (1,2,3) and win. I second bringing Alex Fink in; I also enjoyed getting to know him. -tom On Sun, Apr 11, 2010 at 4:20 PM, Dan Asimov <dasimov@earthlink.net> wrote:
Alex Fink wrote (forwarded):
<< Sticky Towers of Hanoi is played with the disks of an n-disk ToH set (the pegs can be disregarded). In the initial position all of the disks are separate. In a general position there will be stacks of fused disks, with top radius and bottom radius differing. A move is to pick up a stack S and set it on another stack whose top radius exceeds the bottom radius of S; this causes the two disks that come in contact to fuse.
I'm at least as perplexed as Fred here. Where it says "In a general position there will be stacks of fused disks" does that mean each stack is entirely fused, or just that it consists of a stack of fused stacks?
I don't see how the description of play can lead to anything but each stack being entirely fused, yet as Fred points out, that makes "solving" the puzzle all too obvious. (There is nothing about what constitutes a solution, so maybe that's where the confusion lies?) Perhaps Alex can clarify this?
--Dan
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