Tower of Hanoi

Tower Of Hanoi

What is Tower of Hanoi ?

The Tower of Hanoi is a mathematical puzzle. It consists of three rods and a number of disks of different sizes, which can slide onto any rod:

The objective of the puzzle is to move the entire stack to another rod, obeying the following simple rules:

Only one disk can be moved at a time.

Each move consists of taking the upper disk from one of the stacks and placing it on top of another stack.

No disk may be placed on top of a smaller disk.

To create an solution algorithm, let's start with two disks:

- First, we move the smaller (top) disk to the middle rod.

- Then, we move the larger (bottom) disk to the destination rod.

- And finally, we move the smaller disk from the middle to the destination rod.

For a general algorithm we need to divide the stack into two parts - the largest disk (nth disk) is in one part and all other (n-1) disks are in the second part.

Our ultimate goal is to move disk n from source to destination and then put all other (n-1) disks onto it. So, we can break up the problem into smaller problems and come up with a general algorithm:

Step 1: Move n-1 disks from source to the middle.

Step 2: Move nth disk from source to destination.

Step 3: Move n-1 disks from the middle to destination.

With 3 disks, the puzzle can be solved in 7 moves.

The minimal number of moves required to solve a Tower of Hanoi puzzle is 2^n-1, where n is the number of disks.

Tower of Hanoi Visualization