STUDENT CLASSROOM ACTIVITY - TOWER OF HANOI

The Tower of Hanoi is a 'stacking tower' game. According to the story, a group of Buddhist monks believed that by finding the answer to this problem, they would discover the date that the world would end.

According to the rules of the game, to snwer the qusetion, the monks had to move 100 disks form one location to another. The amount of time taken to move the disks is the same amount of time left before the world will end. According to the game story, by finding out how long it will take to move the disks, the monks could discover the date when the world would end.

GETTING STARTED

Record the date and the title 'Towers of Hanoi' on a clean page in your journal (write your name at the top of the page if you are sharing or not using your own journal).

There are two rules about how the disks can be moved:

1. Only move one disk at a time (you can only move the top disk from a stack/tower)
2. Only place smaller disks on top of a larger disk (you cannot put a large disk on top of a smaller disk)

Using the above rules, what is the smallest number of moves you can make;

1. to move 3 disks - write down your prediction and draw a circle around it.
2. to move 4 disks - write down your prediction and draw a circle around it.
3. to move 5 disks - write down your prediction and draw a circle around it.

Write down the total number of moves you found using your solution and draw a square around it. Share and compare your solution and justification with others in your group.

EXTENDED ACTIVITIES

If there were 100 disks, when would the game story predict that the world would end?

• Write down your prediction of the number of moves it will take.
• Draw a circle around the number of moves that you predict

How do you think you can find out how long it will take to move 100 disks?

Share and compare your solution and justification with others in your group.

• Write down the total amount of time you found using your solution and draw a square around it.
• Write down your justifications/proof, so that you can share and explain your solution to other students.

Can you discover a general formula that would help you find the total number of moves?

• Write down your justifications/proof, so that you can share and explain it to other students.

IN YOUR JOURNAL - WHEN YOU HAVE FINISHED

• Think about what you have done today and write down anything interesting, new or surprising that you learnt.

• Did you change your mind about anything?
  • What did you used to think?
  • What do you think now?