🗼 Tower of Hanoi Guide

🎯 Objective

Move the entire stack of disks from the left stick to the right stick, following the rules below. Middle stick is a helper stick you can use to temporarily place disks.

📋 Rules

• Move one disk at a time.
• Only the top disk of any stick can be moved.
• No disk can be placed above a smaller disk.

🧠 Core Idea (Why It Works)

The puzzle is solved by breaking it into smaller strategies. To move N disks from stick 1 to stick 3

1. Move the top N−1 disks from 1 to 2 (using stick 3 as assistance).
2. Move the largest disk (bottom one) from 1 to 3.
3. Move the N−1 disks from 2 to 3 (using stick 1 as helper).

This is the recursive strategy and ensures minimal moves.

🔢 Minimal Moves

The minimum moves that are required to solve Tower of Hanoi with N number of disks is 2^N − 1.

• 3 disks 7 moves
• 4 disks 15 moves
• 5 disks 31 moves
• 6 disks 63 moves

🛠️ How to Play (Step-by-Step)

For 3 Disks

1. Move disk 1 to stick 3
2. Move disk 2 to stick 2
3. Move disk 1 to stick (on top of disk 2)
4. Move disk 3 to stick 3
5. Move disk 1 to peg A
6. Move disk 2 to peg C
7. Move disk 1 to peg C

This sequence demonstrates the pattern you will reuse for larger puzzles.

💡 Strategies & Tips

• Always protect the largest disk: Aim to free and move the largest disk to the target peg as soon as it’s legal.
• Repeat the 3-step pattern: Move N−1 to helper, move largest to target, move N−1 to target.
• Track parity: For an even number of disks, first move to the middle peg; for an odd number, first move to the right peg (in many implementations).
• Think in chunks: Treat the top stack (N−1 disks) as a single unit you shuttle between helper and target.

🔄 Variations

• More pegs: Some versions add a fourth peg (Reve’s puzzle) which can reduce moves.
• Timed mode: Beat the puzzle under a time limit.
• Move counter challenges: Aim for the minimal-move solution.

🎮 Ready to Play?