The classic "Tower of Hanoi" problem involves moving discs of different sizes amongst three columns with the restrictions that large discs can’t be placed on small discs and discs can only be moved one at a time. The challenge is to move all the discs from one column to another. This activity requires students to solve this problem, recognise and use the recursive definition of an arithmetic sequence and explore alternative approaches to solving the problem. The TI-Nspire file contains a virtual Tower of Hanoi.
- Recognise and use the recursive definition of an arithmetic sequence;
- Use problem solving techniques to gain a deeper understanding of a problem;
- Use a spreadsheet to formulate a recursive definition.
Non-Linear functions, recursion, spreadsheets
About the Lesson
Students explore the relationship between the number of discs and moves required to solve the classic “Tower of Hanoi” problem. The TI-Nspire file contains an interactive virtual Tower of Hanoi (Programmed by Andy Kemp). The program automatically records the number of moves, allows the number of discs to be changed or the problem to be reset. Automatic counting allows students to keep focus on the moves and patterns.