# Metalwork - Projects - The Towers of Hanoi

There are two different models shown here. The first is basic and suitable for the classroom as it is made of Acrylic mainly. The second is more like a model you might put in your living room and competent Lathe skills are necessary.

The project is pretty easy to make, however drilling Acrylic as always can be problematic if not done correctly. The shapes shown here are squares but of course any regular shape will do. Care also needs to be taken when tapping and threading as if not the pillars may not be vertical afterwards.

### The Legend

In Vietnam there is a temple which contains a large room with three time-worn posts in it surrounded by 64 golden disks. The Monks of Hanoi have been moving these disks, in accordance with the rules of the puzzle, since the beginning of time. When the last move of the puzzle is completed, the world will end.

If the legend were true, and if the priests were able to move disks at a rate of one per second, using the smallest number of moves, it would take roughly 600 billion years to complete the puzzle. (So no need to worry just yet then ! ). With 64 disks it would take 18,446,744,073,709,551,615 moves to finish the puzzle.

### The Rules of the Puzzle

The objective of the puzzle is to move the entire stack of disks to another Pillar, obeying the following rules:

• Only one disk may be moved at a time.
• No disk may be placed on top of a smaller disk.

A challenge is to see how few moves you take to complete the puzzle. The more disks you have the more likely a mistake, sadly.

### The Maths

Depending on the number of disks you use, there is a minimum to the amount of moves you can complete the puzzle in.

The mathematical formula is 2n - 1, where n is the number of disks you use. Here are a few examples :

3 Disks => 23 - 1 = (2 x 2 x 2) - 1 = 7
4 Disks => 24 - 1 = (2 x 2 x 2 x 2) - 1 = 15
5 Disks => 25 - 1 = (2 x 2 x 2 x 2 x 2) - 1 = 31
6 Disks => 26 - 1 = (2 x 2 x 2 x 2 x 2 x 2) - 1 = 63
8 Disks => 28 - 1 = (2 x 2 x 2 x 2 x 2 x 2x2 x2) - 1 = 255
10 Disks => 210 - 1 = (2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2) - 1 = 1023

You may notice that adding 1 disk to the puzzle means doubling the number of moves and still needing 1 more move !

### Parts List - The Towers of Hanoi I

Parts 7 to 10 are 4 optional disks that can be manufactured by the better students.

 Part No. Part Name Required Material & Description 1 Base 1 Acrylic 2 Pillar 3 Brass 3 Disk 1 1 Acrylic 4 Disk 2 1 Acrylic 5 Disk 3 1 Acrylic 6 Disk 4 1 Acrylic 7 Disk 5 1 Acrylic 8 Disk 6 1 Acrylic 9 Disk 7 1 Acrylic 10 Disk 8 1 Acrylic 11 Support 2 Aluminium

### Zip Files

Download All : Solidworks Part, Solidworks Drawing, PDF of Drawing and 3D images for The Towers of Hanoi I

### Parts List - The Towers of Hanoi II

 Part No. Part Name Required Material & Description 1 Base 1 Wood 2 Disk 1 1 Brass 3 Disk 2 1 Brass 4 Disk 3 1 Brass 5 Disk 4 1 Brass 6 Disk 5 1 Brass 7 Disk 6 1 Brass 8 Disk 7 1 Brass 9 Disk 8 1 Brass 10 Disk 9 1 Brass 11 Disk 10 1 Brass 12 Pillar 3 Brass

### As Supplied

 Part No. Part Name Required Material and Description 13 M6 Thin Hex Nut 3 Brass or Steel 14 ID 6 Flat Washer 3 Brass or Steel

### Student Handout

Towers of Hanoi II Handout

### Zip Files

Download All : Solidworks Part, Solidworks Drawing, PDF of Drawing and 3D images for The Towers of Hanoi II