Introduction
The Towers of Hanoi is a classic mathematical puzzle that involves three pegs (or rods) and a number of disks of different sizes which can slide onto any peg.
🧩 The Setup:
- You start with all the disks stacked in ascending order on one peg (largest at the bottom, smallest at the top).
- The goal is to move the entire stack to another peg, obeying the following rules:
📜 The Rules:
- Only one disk can be moved at a time.
- Each move involves taking the top disk from one stack and placing it on another peg.
- No disk may be placed on top of a smaller disk.
🧠 Purpose and Significance:
- The puzzle is often used to teach recursion in computer science.
- It also appears in algorithm design and problem-solving strategy courses.
🧮 Mathematical Insight:
- The minimum number of moves required to solve the puzzle is 2n−1, where n is the number of disks.
- So, for 3 disks: 23−1=7 moves minimum.
🏛️ Fun Fact (Legend):
There’s a legend that in a temple in India, priests are working on a giant Towers of Hanoi with 64 disks. Once they finish, the world will end!
At 1 move per second, it would take: 264−1=18,446,744,073,709,551,615 moves
Video
What is the objective of the Towers of Hanoi puzzle?
The goal is to move an entire stack of disks from the source peg to the destination peg, following the three rules: move one disk at a time, never place a larger disk on a smaller one, and use the third peg as needed.
How many pegs and disks are there in the standard Tower of Hanoi puzzle?
The standard puzzle involves three pegs and a variable number of disks. While toy versions often have around 3 to 9 disks, the mathematical problem can be considered with any number of disks.
What is the minimum number of moves required to solve the Tower of Hanoi puzzle?
The minimum number of moves required to solve the Tower of Hanoi puzzle with n disks is 2n−1