Tower of Hanoi

Tower of Hanoi is fun and creative mathematical puzzle, which consist of 3 pegs and a number of disks (See example below).

* Figure 1*. Tower of Hannoi. This figure illustrates

example of Tower of Hannoi with 8 disks.

Who invented?

One of the French mathematician, Edouard Lucas, invented this puzzle in 1883.

What is the goal of the game?

The goal of this puzzle is to move all the discs from the left peg to the right peg. As you can see from the above picture, the discs on the left peg are all different sizes and arranged with the largest on the bottom and the smallest on the top. You should have exact arragne when you finish moving disks on the right peg. Try to move all the discs using as small as possible number of movement.

What kind of rule?

- You need to move one disk at a time.
- Larger disk cannot be on top of the smaller disk.

How do I play?

Click and drag to move a disc. You can choose a number of discs that you want to play by pressing + or - on the right side of the winidow. Higher number discs may indicate more difficult to solve the puzzle. Try to solve the puzzle using smaller number at first if it is difficult. If you need help, you can press Solution button to watch how the computer solve the puzzle. If you want to restart the puzzle, you can press Restart button to play it again.

*Figure 2*. Tower of Hannoi game. This figure illustrates

image of Tower of Hannoi Retrieved from

http://www.mazeworks.com/hanoi/index.htm.

Game?

You can play from this website: http://www.mazeworks.com/hanoi/index.htm

What to look for in this game other than playing?

- What are the minimum number of moves for each of different number of disks?
- What kind of pattern can we find with the number of disks and the minimum number of moves? For example, what are the minimum number of moves for 1, 2, 3, and 4 disks? If it is different than your friends, then check with computer by clicking solution button.
- How many minimum number of moves will be required if there are 10, 50, or 100 disks on the left peg?
- Based on your observation of pattern, will this pattern continue even if there are infinite number of disks on the left peg?

Example of the Tower of Hanoi puzzle?

You can see this example how another player solved the Tower of Hanoi puzzle.

References:

Herzog, D. *Tower of Hannoi*. Retrieved from http://www.mazeworks.com/hanoi/index.htm.

Mathsnet. (2007, April 21). Tower of Hannoi. Message posted to http://www.youtube.com/watch?v=aGlt2G-DC8c.

Tower of Hannoi. (n.d.). Retrieved from the Wikipedia: http://en.wikipedia.org/wiki/Tower_of_Hanoi.

Tower of Hannoi. (n.d.). Retrieved from the NCTM resource: http://illuminations.nctm.org/ActivityDetail.aspx?id=40.

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