Tower of Hanoi: Five Rings Solution 5.

Introduction

This tutorial provides a clear and concise guide on how to solve the Tower of Hanoi puzzle with five rings. The Tower of Hanoi is a classic problem involving three pegs and a number of rings that need to be moved from one peg to another, following specific rules. This guide will walk you through the optimal solution step-by-step.

Step 1: Understand the Rules of the Game

Before you start solving the Tower of Hanoi, it's important to understand the basic rules:

• You can only move one ring at a time.
• Each move consists of taking the upper ring from one of the stacks and placing it on top of another stack or on an empty peg.
• No ring may be placed on top of a smaller ring.

Step 2: Visualize the Setup

Set up your Tower of Hanoi with the following arrangement:

• Peg A (leftmost): Place all five rings in descending order of size, with the largest ring at the bottom.
• Peg B (middle): This peg will be used as a temporary holding area.
• Peg C (rightmost): This is the target peg where you will move all rings.

Step 3: Move the Rings

To move the five rings from Peg A to Peg C, follow these steps:

1. Move the top four rings from Peg A to Peg B:

   • Use Peg C as a temporary holding area.
   • This requires recursively moving smaller groups of rings.

2. Move the fifth (largest) ring from Peg A to Peg C.

3. Move the four rings from Peg B to Peg C:

   • Use Peg A as a temporary holding area.
   • Again, this involves recursive moves to ensure the smaller rings are stacked correctly.

Step 4: Recursive Strategy Breakdown

To clarify the recursive strategy for moving the rings, follow this pattern:

• To move n rings from source peg to target peg using auxiliary peg:
  1. Move the top n-1 rings from source to auxiliary peg using the target peg.
  2. Move the nth ring (largest) directly from source to target peg.
  3. Move the n-1 rings from auxiliary peg to target peg using the source peg.

Step 5: Implementing the Moves

For a practical application, here’s how to implement the moves:

• Example of moving 3 rings:
  • From A to B using C:
    • Move ring 1 from A to C.
    • Move ring 2 from A to B.
    • Move ring 1 from C to B.
    • Move ring 3 from A to C.
    • Move ring 1 from B to A.
    • Move ring 2 from B to C.
    • Move ring 1 from A to C.

Conclusion

In this tutorial, you learned how to solve the Tower of Hanoi puzzle with five rings using a systematic approach. By following the rules and employing a recursive strategy, you can transfer all rings from one peg to another efficiently. For further practice, try solving the puzzle with different numbers of rings or explore additional strategies. Happy puzzling!