Tower of Hanoi
A classic mathematical puzzle. Move all disks to the target tower!
Tower of Hanoi
Moves: 0 / Min: 7
Click a tower to select the top disk, then click another tower to move it
How to Play:
- Move all disks from the Source tower to the Target tower
- Only one disk can be moved at a time
- A larger disk cannot be placed on a smaller disk
- Use the Auxiliary tower as a helper
What is Tower of Hanoi?
Tower of Hanoi is a classic mathematical puzzle invented by French mathematician Édouard Lucas in 1883. The game consists of three towers and a number of disks of different sizes. The objective is to move the entire stack from the source tower to the target tower, following specific rules.
Tower of Hanoi Rules
- Only one disk can be moved at a time
- Each move consists of taking the upper disk from one tower and placing it on top of another tower
- No disk may be placed on top of a smaller disk
Tower of Hanoi Strategy
The optimal solution for n disks requires exactly 2^n - 1 moves. Here's the recursive strategy:
- Step 1: Move the top n-1 disks from Source to Auxiliary tower
- Step 2: Move the largest disk from Source to Target tower
- Step 3: Move the n-1 disks from Auxiliary to Target tower
Minimum Moves by Disk Count
| Disks | Minimum Moves |
|---|---|
| 3 | 7 |
| 4 | 15 |
| 5 | 31 |
| 6 | 63 |
| 7 | 127 |
Educational Benefits
- Recursive Thinking: Understanding the recursive algorithm behind the solution
- Problem Solving: Developing strategic planning skills
- Mathematical Thinking: Learning about exponential growth and algorithms
- Patience: Building persistence and attention to detail
History of Tower of Hanoi
The puzzle was invented by Édouard Lucas in 1883. There's a legend about Vietnamese monks solving a Tower of Hanoi puzzle with 64 golden disks. According to the legend, when the monks complete the puzzle, the world will end. With 64 disks, this would take 2^64 - 1 moves, which would take billions of years even at one move per second!
Frequently Asked Questions
What is the minimum number of moves?
For n disks, the minimum is 2^n - 1 moves. For example, 3 disks require 7 moves, 4 disks require 15 moves, and 5 disks require 31 moves.
Is Tower of Hanoi good for brain training?
Yes! Tower of Hanoi helps develop logical thinking, problem-solving skills, and understanding of recursive algorithms. It's used in computer science education to teach recursion.
Can I solve it in more than the minimum moves?
Absolutely! The minimum moves represent the optimal solution. Beginners often take more moves as they learn the strategy. Practice helps achieve the optimal solution.