Hanoin Tornit

Hanoin Tornit is a variation on the Tower of Hanoi puzzle, published as a type-in game in the March 1984 issue of the Finnish magazine MikroBitti.

Hanoin Tornit is a little different from the usual Tower of Hanoi puzzle. It's got an additional restriction: the discs may only be moved to adjacent stacks. This makes the solution much more drawn out; thankfully, the game only has four discs.

As usual with these early games, there's no sound nor animation. Unusually, it is possible to ask the game to show you the correct solution, a good addition. There is only one solution, though, up to reversible mistakes, so there's not much else to do, once you've seen it.

Since this review is working out to be quite short, let's see how many steps it takes to solve this variation. To solve the puzzle with n discs:

1. Solve the (n-1)-disc puzzle with all but the largest disc.
2. Move the largest disc to the center.
3. Solve the (n-1)-disc puzzle in reverse.
4. Move the largest disc to the right.
5. Finally, solve the (n-1)-disc puzzle again.

Adding these moves up, that means that if Hanoin(n) is the number of moves required to solve the n disc puzzle in this variation, then Hanoin(n) = 3*Hanoin(n-1) + 2. Clearly, it takes 2 moves to solve the 1-disc puzzle. So, applying a little math, we find H(4) = 80, quite a few more moves than the 15 required by the traditional Tower of Hanoi puzzle. In general, Hanoin(n) = 3^n - 1, while Hanoi(n) = 2^n - 1--quite a huge difference. In fact, solving Hanoin Tornit requires you to move the discs through every possible position--it couldn't possibly take any longer to solve.

Since the math was more fun than the game, I'd recommend against playing this one.