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Tower of Hanoi

Classic Mathematical Puzzle

Move all disks from the first tower to the last tower. Only one disk can be moved at a time, and no larger disk can be placed on a smaller disk.

Configuration

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Rules:

• Move one disk at a time

• Only the top disk can be moved

• No larger disk on smaller disk

About Tower of Hanoi

The Tower of Hanoi is a classic mathematical puzzle invented by French mathematician Édouard Lucas in 1883.

Objective:

Move all disks from the first tower to the last tower

Formula:

Minimum moves = 2ⁿ - 1

where n is the number of disks

Features

  • Interactive disk movement
  • 1-8 disks support
  • Move counter
  • Undo functionality
  • Optimal solution display
  • Auto-solve animation
  • Visual feedback
  • Completion detection

Minimum Moves

3 disks:7 moves
4 disks:15 moves
5 disks:31 moves
6 disks:63 moves
8 disks:255 moves

Tips

  • Start with 3 disks to learn
  • Plan moves ahead
  • Use the middle tower strategically
  • Undo if you make a mistake
  • Try to match optimal moves
  • Watch auto-solve to learn patterns

Mathematical Properties

Key Facts:

Recursive Solution: The puzzle can be solved using recursion

Exponential Growth: Moves double with each additional disk (plus 1)

Binary Connection: Related to binary counting and Gray code

64 Disks Legend: Would take 585 billion years to complete!

Applications

  • Teaching recursion in computer science
  • Algorithm complexity demonstration
  • Problem-solving skills development
  • Mathematical thinking exercises
  • Backup rotation strategies (computing)
  • Psychological research on planning
  • Educational puzzles and games
  • Brain training and cognitive exercises