Quote:
Originally Posted by prizna
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I have the Tower of Hanoi down to a science...on my physical, 7-level tower, I can complete it in minimal steps in two minutes.
The number of steps required, if anyone is curious is 2^n - 1, where n is the number of levels.
Here's the trick: Any time a piece is moved to an empty peg, the next goal is to stack all smaller pieces on top of that piece. You might say "Well, isn't that the goal of the entire puzzle?" Sure, but it's also the goal of every single intermediate step, making it a recursive process.
Imagine a four-level tower. First, I move the top piece, creating a tower of 1. Then I move piece 2 to the empty peg and put piece 1 on top of it, creating a tower of 2. Then I move piece 3 to the empty peg...my goal now is to get a tower of 3 so that I have an empty peg for piece 4.
Here's a method I use to speed things up. Let's say I have a tower of x pieces that I'm trying to transfer onto the next largest base (example: I have a 4-level tower that I'm trying to transfer onto the next largest piece to make a 5-level tower). If x is odd, I move the top, smallest piece of my tower directly onto the new base. If x is even, I move the smallest piece onto the peg that the new base *isn't* on. The place where most people make mistakes, I'd imagine, is right at the beginning of these minitower constructions, because if you make this one false move, your tower won't be transferred to the base, it will be transferred to the other peg.
Anyway, I'm done with my crazy Tower of Hanoi raves.