# 'Find the hidden sequence in this game that makes it such a great puzzle'

The Tower of Hanoi game is a great puzzle that everyone can have a go at! How can we move three different sized discs from one side to the other, without ever putting a bigger disc on top of a smaller one and in as few moves as possible? How do we know we have used as few moves as possible? What if there were four discs to start with? What about five or six? Can we predict how many moves it would take to move ten discs? If we knew how to do it, what is the biggest number of discs we could move from one side to the other in our lifetimes? This activity is about the search for answers to these questions. In doing so, the aim is to collect data, look for patterns, make conjectures, test them and go on to make a generalisation about how the number of moves needed is related to the number of discs!

Watch this student solve the puzzle with 3 discs. Pay attention to when they hesitate!

### Resources

The task is easily introduced and explained. 'Investigate the number of moves it takes to move different numbers of discs from one side to the other'. There is a worksheet available to help students get started  Tower of Hanoi. There are also some teacher notes  Tower of Hanoi to help make this a rich experience.

The puzzle can be solved by hand if real versions are avaialble, otherwise there is this virtual manipulative from 'Mazeworks' Tower of Hanoi. (See our free page on  virtual manipulatives for algebra) Read more about the  Tower of Hanoi on wikipedia.

#### 10 Disks

Watch the virtual manipulative solve the problem starting with 10 disks! Try and guess the number of moves.

### Description

• Explain the rules of the game.
• Everybody should try playing the game and share their solutions for 'the least number of moves'.
• Students collect data for different numbers of disks and make predictions/conjectures about what might happen next.
• Students test their conjectures and try to arrive at a generalisation for the relationship between the number of discs and the number of moves it takes to shift them from one side to the other.
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