Solution for the Towers of Hanoi 4 Ring Style Puzzle

WELCOME TO PUZZLES-ONLINE-NICHE

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.

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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.

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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

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

GRAY CODE : 0011

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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

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

GRAY CODE : 0110

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

GRAY CODE : 0111

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

GRAY CODE : 0101

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

GRAY CODE : 0100

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Step8: Move orange ring to the right

GRAY CODE : 1100

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

GRAY CODE :1101

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

GRAY CODE :1111

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

GRAY CODE :1110

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

GRAY CODE :1010

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

GRAY CODE :1011

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

GRAY CODE :1001

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

GRAY CODE :1000

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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

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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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