Tower of Hanoi - Play Online Game

Master the classic Tower of Hanoi puzzle game online. Learn recursive algorithms, solve mathematical puzzles step-by-step, and discover the ancient wisdom from India through interactive gameplay.

๐ŸŽฎ Play Tower of Hanoi๐Ÿง  Learn Algorithms๐ŸŽฏ Solve Puzzles
0
Moves
7
Optimal
Source
Auxiliary
Target

๐Ÿš€How to Solve Tower of Hanoi - Step by Step Guide

1๏ธโƒฃ

Choose Game Mode

Select "Learn Mode" to watch the solution or "Play Mode" to solve the Tower of Hanoi puzzle yourself

2๏ธโƒฃ

Set Difficulty

Start with 3 disks and gradually challenge yourself with more complex Tower of Hanoi problems

3๏ธโƒฃ

Master the Rules

Learn the three fundamental Tower of Hanoi rules and movement constraints

4๏ธโƒฃ

Explore Algorithms

Discover recursive thinking and divide-and-conquer strategies behind the solution

๐Ÿ’ก Learning Strategy

We recommend starting with Learn Mode to observe the complete Tower of Hanoi solution process. Understanding the basic strategy before entering Play Mode will help you master recursive thinking through practice.

๐Ÿ“‹Tower of Hanoi Rules - Complete Gameplay Guide

Rule 1One disk per moveRule 2Only move the top diskโœ“ OKโœ— NoRule 3Big on small not allowedโœ“ OKโœ— WrongGame Rules

1.Move only one disk at a timeโญ

Each operation can only move one disk. Multiple disks cannot be moved simultaneously.

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2.Only move the top disk from each rodโญโญ

Only the disk at the top of each rod can be moved. Disks underneath must wait until the disks above them are moved away.

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3.Never place a larger disk on a smaller diskโญโญโญ

When moving disks, you cannot place a larger disk on top of a smaller one. The order must always be maintained with larger disks below smaller ones.

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๐ŸŽฏ Objective

Move all disks from the source rod to the target rod while maintaining the same stacking order (largest disk at bottom, smallest at top).

๐Ÿง How to Solve Tower of Hanoi - Recursive Algorithm Tutorial

3-Disk Hanoi SolutionMinimum 7 stepsStep 1Small disk โ†’ TargetStep 2Mid disk โ†’ AuxiliaryRecursive Idea1Move n-1 disks to auxiliarySolve subproblem recursively2Move largest disk to targetBase case: direct move3Move n-1 disks to targetComplete with recursionComplexity:Time: O(2โฟ) | Space: O(n) | Min Moves: 2โฟ - 1Applications:Recursion, Divide & Conquer, Modeling๐Ÿ’กInsight

๐ŸŽฏProblem-Solving Approach

  • โ€ข Analyze the goal: move all disks to target rod
  • โ€ข Identify constraints: follow the three basic rules
  • โ€ข Find patterns: solution approach for smaller problems
  • โ€ข Scale up gradually: from simple to complex cases

โšกKey Insights

  • โ€ข To move n disks, first move the top n-1 disks
  • โ€ข Large disk movement depends on smaller disks "clearing the way"
  • โ€ข Each subproblem has the same structure as the original
  • โ€ข The roles of the three rods change dynamically

๐Ÿ“ŠComplexity Analysis

  • โ€ข Time complexity: O(2โฟ)
  • โ€ข Space complexity: O(n)
  • โ€ข Minimum moves: 2โฟ - 1
  • โ€ข Recursion depth: n

๐Ÿ“šTower of Hanoi - Ancient Legend & Mathematical Origins

The Tower of Hanoi, also known as the Towers of Hanoi or Lucas' Tower, is a mathematical puzzle that originated from an ancient Indian legend. According to the tale, in the great temple of Benares, there stands a brass plate with three diamond needles.

๐Ÿ›๏ธ The Ancient Legend

When the Hindu god Brahma created the world, he placed 64 golden disks on one of the needles, arranged from largest at the bottom to smallest at the top. Day and night, monks work tirelessly to move these disks according to the immutable laws of Brahma.

โฐ The Prophecy

Legend says that when all 64 disks are moved from Brahma's needle to another, the world will end in a thunderclap, and the temple, along with all creation, will crumble to dust.

๐Ÿ”ข Mathematical Beauty

If the monks moved one disk per second, completing the 64-disk Tower of Hanoi would take approximately 584 billion years! This demonstrates the incredible power of exponential growth in mathematical puzzles.

Legend of HanoiAncient Indian Wisdom

โ“Tower of Hanoi FAQ - Common Questions

What is the Tower of Hanoi minimum moves formula?

The minimum number of moves for n disks is 2โฟ - 1.

  • โ€ข 3 disks: 2ยณ - 1 = 7 moves
  • โ€ข 4 disks: 2โด - 1 = 15 moves
  • โ€ข 10 disks: 2ยนโฐ - 1 = 1,023 moves

How do I solve the 10-disk Tower of Hanoi?

Use the recursive strategy: move 9 disks to auxiliary rod, move the largest disk to target, then move 9 disks to target. Our learning mode demonstrates the complete 10-disk solution step by step.

Is Tower of Hanoi good for learning recursion?

Yes! Tower of Hanoi is one of the best examples for understanding recursive algorithms and divide-and-conquer strategies. It demonstrates how complex problems can be broken down into simpler subproblems.

What programming language is best for Tower of Hanoi?

Any language with recursion support works well. Python and JavaScript are popular for beginners due to clean syntax. Our tutorial includes examples in multiple programming languages.

Can I solve Tower of Hanoi iteratively?

Yes! While recursion is more intuitive, iterative solutions using stacks are possible and can be more memory-efficient for large numbers of disks.

What's the time complexity of Tower of Hanoi?

The time complexity is O(2โฟ) where n is the number of disks. This exponential growth demonstrates why the legendary 64-disk version would take billions of years to complete.

๐ŸŽ“Educational Value - Cognitive Development & Real-World Applications

Educational Value๐Ÿง  Core SkillsLogicโ€ข Problem Analysisโ€ข Pattern Seekingโ€ข Step ReasoningMathโ€ข Recursion Conceptโ€ข Exponential Growthโ€ข OptimizationComputationโ€ข Algorithm Designโ€ข Decompositionโ€ข Pattern Recognition๐Ÿ‘ฅ For Whom?๐ŸŽ“KidsLogic Training๐Ÿ“šStudentsRecursive Thinking๐Ÿ”ฌCollegeAlgorithm Analysis๐Ÿ’ปProgrammersRecursion Practice๐ŸŽฏ Use CasesIn Class:Teaching recursion & algorithm design.For Competitions:Math/coding contest training.

๐Ÿง Cognitive Skills Development

Logical Thinking

  • โ€ข Cause-and-effect analysis
  • โ€ข Conditional reasoning abilities
  • โ€ข Step-by-step planning skills

Abstract Thinking

  • โ€ข Pattern recognition capabilities
  • โ€ข Deep conceptual understanding
  • โ€ข Analogical reasoning skills

Systems Thinking

  • โ€ข Whole-part relationships
  • โ€ข Hierarchical understanding
  • โ€ข Structured analysis approach

Creative Problem-Solving

  • โ€ข Problem transformation skills
  • โ€ข Strategy optimization thinking
  • โ€ข Transfer learning abilities

๐ŸŒReal-World Applications

Computer Science

Recursive algorithm design, data structure understanding, algorithm complexity analysis, divide-and-conquer strategy applications

Mathematics Education

Mathematical induction comprehension, exponential function properties, combinatorics concepts, discrete mathematics applications

Logic Training

Reasoning ability enhancement, problem decomposition techniques, strategic planning capabilities, decision-making skill development

Innovation Education

Creative thinking stimulation, multiple solution exploration, interdisciplinary knowledge integration

๐ŸŽ“ Master Algorithms Through Interactive Learning

Tower of Hanoi is more than just a puzzle gameโ€”it's your gateway to understanding recursive algorithms and computational thinking. Build systematic problem-solving skills through this timeless mathematical challenge.

๐ŸŒŸ Free to Play๐Ÿ“ฑ Mobile Friendly๐ŸŽฏ Educational Focus๐Ÿ”„ Regular Updates