The Towers of Hanoi Puzzle

[System Requirements|Using Hanoi.lbr|Minimum number of moves|Feedback

Hanoi.lbr main window

No doubt you've seen the Towers of Hanoi puzzle in some shape or form. The object of the puzzle is to move the disks from the starting peg to one of the other two pegs. The rules are simple:

You can only move one disk at a time
When moving a disk, you can only place it on top of a smaller disk

System Requirements & Installation

You must use Omnis7 version 3.5.x in order to run Hanoi since it calls procedures by name.

Using Hanoi.lbr

When you start a new game, Hanoi.lbr asks you how many disks to set up on the first peg. You can have as little as 3 or as many as 7 disks.

Click and hold the mouse on the disk you want to move. When the mouse cursor changes to a hand, you can drag the disk to another peg. The pegs appear momentarily outlined when a disk is in the drop position. You can drop the disk anywhere on the peg. If the drop is a legal move, the disk is automatically positioned on top of the other disks on that peg. If the move is illegal, the disk returns to its original position.

Dragging a disk

The status bar displays the number of moves you have made so far. Want to know the minimum number of moves?

A congratulatory message pops up when you solve the game. You can also give up by closing the main window.

The Towers of Hanoi menu has three options:

New Game starts a new game
Color Scheme has a few options which let you set the color scheme of the disk & pegs. Note that the Flat setting only works on the Macintosh (the disks and pegs are actually pushbuttons). The color options reflect my peculiar tastes. Add your own color schemes if you like!
Help presents you with a brief set of instructions on solving the puzzle. The Hints pane will make up to the first 7 moves for you if you are having trouble starting the puzzle.

Computing the Minimum Number of Moves

The minimum number of moves required to solve the puzzle for n disks is given by the recurrance relation: $T$ _n = T_n-1 + 1 + T_n-1

The values can also be computed as $T$ _n = 2ⁿ - 1

For example, when n = 3, you must first move the top 2 disks to an intermediate peg (T_n-1), then move the 3rd disk to the target peg, and finally move the 2 smaller disks on top of the 3rd disk (T_n-1). The following table shows the minimum number of moves for 1 to 7 disks:

Disks	Moves
1	1
2	3
3	7
4	15
5	31
6	63
7	127

Feedback

I hope you find Hanoi.lbr to be entertaining. You may be wondering what compelled me to write it... I was reading a Delphi programming book one evening. One of the examples was a Delphi implementation of the Towers of Hanoi puzzle. I thought "why can't that be done in Omnis?" So I set out to develop an Omnis version of this famous puzzle.

Hanoi.lbr also makes a fun example of using drag-and-drop in Omnis.

Feel free to send any comments, suggestions or bug reports to me at brianos@ziplink.net.

Disclaimers

This is a freeware utility. I do not warranty Hanoi in any way, and am not liable for any damages that may occur in its use. Use Hanoi at your own risk. Look both ways before crossing the street. By downloading and using Hanoi.lbr you acknowledge your agreement to these terms.