Pupils investigate the classic Towers of Hanoi problem showing that the number of moves required to complete the classic version of the game is closely related to powers of 2.

It is preferable for pupils to be given a physical version of the Towers of Hanoi game, but if this is not possible they could be directed to the website below to experiment playing the game:

https://www.mathsisfun.com/games/towerofhanoi.html

Powers of 2 and 3, and ideally a basic knowledge of binary.

Perhaps introduce pupils to this in the lesson before this investigation.

1. Briely explain the rules to pupils, ideally by using a physical version of the game to demonstrate foul moves, but do not solve the problem in front of pupils.

2. Distribute a copy of the pupil sheet to each pupil, or pair if preferred and allow pupils to work through at their own pace. Emphasise to pupils that they need to write a rule at the bottom of the first page, and check their formula with you.