# Solution for the Towers of Hanoi 4 Ring Style Puzzle

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There you have see it the solution to the puzzle..Joking , Of course I will now perform a step-by-step analysis of what we see here, keep on reading.

As I hinted earlier the Solution for the Towers of Hanoi follows an interesting mathematical process based off Gray's code(reflected binary code), more on that following our solution.

The solution for the puzzle may seem complicated at first glance at, but above is a graphical color-coded solution for the 4 -ring style.

Still look complicated?

Allow me to take the mystery out of this puzzle.The solution follows a similar pattern like the 5-ring mechanical , or Chinese style ring puzzle( click here to review).

In the puzzle we follow a mathematical principle based on the Gray Binary code ( or reflected code).

To put this in it's simplest terms the formula basically states we can only move one item at a time, or in any given system only one item can change at any given time.

To apply this to the current puzzle, follow the diagram below.

It consists of three rods, and a number of disks of different sizes which can slide onto any rod. The puzzle starts with the disks in a neat stack in ascending order of size on one rod, the smallest at the top, thus making a conical shape.

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

(A). Only one disk may be moved at a time.

(B). Each move consists of taking the upper disk from one of the rods* and sliding it onto another rod, on top of the other disks that may already be present on that rod*.

(C). No disk may be placed on top of a smaller disk.

* For the simplification of the solution I have removed the rods in the diagram below.

This in no way hinders the answer to the puzzle.

Step1: Move red ring to the 1st available position( as shown). This is the only possible position using the rules of the game.

GRAY CODE : 0001

Step2: Move yellow ring to the 1st available position.( Remember rule C- no larger disk can be atop a smaller disk)

GRAY CODE : 0011

Step3: Move red ring to the next available position( as shown ). Here we see red is smaller and the only possible move at this time.

GRAY CODE : 0010

Step4: Move blue ring to the 1st available position( as shown).The third , or blue ring now comes into play..

GRAY CODE : 0110

Step5: Move red ring to the right wrap-around ( as shown)

GRAY CODE : 0111

Step6: Move yellow ring to the right wrap-around ( as shown)

GRAY CODE : 0101

Step7: Move red ring to the right ( as shown)

GRAY CODE : 0100

Step8: Move orange ring to the right

GRAY CODE : 1100

Step9: Move red ring to the right ( as shown)

GRAY CODE :1101

Step10: Move yellow ring to the right ( as shown)

GRAY CODE :1111

Step11: Move red ring to the right again using wrap-around feature ( as shown)

GRAY CODE :1110

Step12: Move blue ring to the right atop orange ( as shown)

GRAY CODE :1010

Step13: Move red ring to the right ( as shown)

GRAY CODE :1011

Step14: Move yellow ring to the right ( as shown)

GRAY CODE :1001

Step15: Move red ring to the right ( as shown)

GRAY CODE :1000

Solution for the Towers of Hanoi Style Puzzle has been completed!!!

Note: I have included the annotation for the Gray code in each step above,

to indicate The one-move one ring change concept (mathematical approach) to the model.

If you study the pattern above more closely we see from line to line only one digit place changes:

Step1: GRAY CODE :0001

Step2: GRAY CODE :0011

Step3: GRAY CODE :0010

Step4: GRAY CODE :0110

Step5: GRAY CODE :0111

Step6: GRAY CODE :0101

Step7: GRAY CODE :0100

Step8: GRAY CODE :1100

Step9: GRAY CODE :1101

Step10: GRAY CODE :1111

Step11: GRAY CODE :1110

Step12: GRAY CODE :1010

Step13: GRAY CODE :1011

Step14: GRAY CODE :1001

Step15: GRAY CODE :1000

If you would like more information on the mathematical theory behind the solution please fill out the form below.

I will be glad to send you a detailed analysis, or even discuss the theory of Gray's code (the reflected binary code) as it applies to the Towers of Hanoi and other ring puzzle solutions.

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