Tower of Hanoi
This problem is in two parts. The first part provides some building blocks which will help you to solve the final challenge. These can be attempted in any order. Of course, you are welcome to go straight to the Final Challenge without looking at the building blocks!
In this problem, you will be working on a famous mathematical puzzle called The Tower of Hanoi. There are three pegs, and on the first peg is a stack of discs of different sizes, arranged in order of descending size. The object of the game is to move all of the discs to another peg. However, only one disc can be moved at a time, and a disc cannot be placed on top of a smaller disc.
A video showing the most efficient way of moving the discs from one end to the other is available here
Click on a question below to get started:
Question A
i) One disc?
ii) Two discs?
iii) Three discs?
iv) Four discs?
Do you notice anything interesting about the way the number of moves increases?
Can you explain any patterns you find?
Question B
The Tower of Hanoi puzzle can be completed in 15 moves with four discs. Can you use this to work out how many moves would be needed with five discs?
In general, can you describe a way of working out how many moves are needed when one extra disc is added?
Final Challenge
Extension
Printable NRICH Roadshow resource.
You may also like
Adding All Nine
Make a set of numbers that use all the digits from 1 to 9, once and once only. Add them up. The result is divisible by 9. Add each of the digits in the new number. What is their sum? Now try some other possibilities for yourself!
Summing Consecutive Numbers
15 = 7 + 8 and 10 = 1 + 2 + 3 + 4. Can you say which numbers can be expressed as the sum of two or more consecutive integers?