My Take on the Rubik’s Cube

It was invented by Hungarian sculptor and professor of architecture Ernő Rubik in 1974. It is a puzzle disguised as a toy. It is simple to play with but difficult to solve. Its popularity has not diminished as the new generation of the mass also finds the Cube intriguing and a brain teaser. The Cube is made of 26 interlocking same-sized small cubes arranged in 3 layers with 9 small cubes each (the mid layer has only 8 cubes). The 3 layers can be subdivided into 9 movable levels each can be turned freely and independently in 360 degrees without breaking the whole Cube apart (how it is put together is a marvel worthy of another story). The Cube has 6 sides each with a different color; normally in white, yellow, green, blue, orange, and red. Each small cube can be moved as followed:

1) Small cube at the center of each side can be moved to the similar position on the other 5 sides,

2) Small cube next to the center cube can be moved to any position next to the center cube on the same side as well as next to the center cube on the other 5 sides,

3) Small cube at the corner of each side can be moved to any corner position on the same side as well as those on the other 5 sides.

So, after the Cube is randomly turned and scrambled with each side consisting of a mixture of colors, it becomes a challenge to restore the Cube to its original and only one possible same-colored position. Without a coordinated sequence of précised movements, solving the puzzle of Rubik’s Cube will remain to be a pipedream.

Since the Rubik’s Cube introduction to the market, numerous solutions to the puzzle had come out. There were even competitions that were held regularly around the world to show the fastest time to solve the puzzle. For the past 30 years, I have been working on the Rubik’s Cube in my spare times on and off. Only till recently, I am able to put together a repeatable sequence of movements that will solve the Cube’s puzzle. It may not break the speed record, but it demonstrates how to use systematic methods to reach the solution to a complex problem.

Basic Move #1 - This move shows how to relocate the small white cube between the corners on the bottom level to the top level where it belongs.

Basic Move #2 - This move also shows how to relocate the small white cube on the bottom level facing in a different direction to the top level where it belongs.

Basic Move #3 - This move shows how to relocate the small white right-corner cube on the bottom level to the top level where it belongs.

Basic Move #4 - This move shows how to relocate the small white left-corner cube on the bottom level to the top level where it belongs.

Basic Move #5 - This move shows how to relocate the small white right-corner cube on the bottom level facing in a different direction to the top level where it belongs.

Basic Move #6 - This move shows how to relocate the 3 small cubes (orange, green, and yellow) on the bottom level to their correct positions without disturbing cubes in the other 2 levels.

Basic Move #7 - This move is similar to #6 with the exception that the 3 small cubes on the bottom level need to be moved to the left instead of right.

Basic Move #8 - This move is used together with #9 to alter the cube’s positions on the bottom level only, with the aim of getting the 4 corners with all the same correct colors.

Basic Move #9 - This move is used together with #8 to alter the cube’s positions on the bottom level only, with the aim of getting the 4 corners with all the same correct colors.

Solving the Puzzle

With the above 9 basic moves, we are ready to tackle the Cube’s puzzle. We start by scrambling the Cube as randomly as possible to the effect that each side consists of diverse color combinations (1). Then:

1) Use moves #3 - #5 to arrange the 4 corners on the top level with the same color (2 - white in this case),


2) Move the middle level so that the center small cube is the same color as the 2 small cubes at the corner of the top level (3),

3) Now, the challenge is to arrange the 4 corner cubes on the bottom level with the same color without disturbing the small cubes on the top level (4). Execute moves #8 and then #9 once.

If the top 2 corner cubes have the same color (5 - red in this case), move the bottom level such that they align on the side with the red center cube (6). Now, there are only 2 corners that are not the right color.


4) Execute moves #8 and then #9 once.

a) If the 4 corners are the same color (7 – blue in this case), then go to step 6.

b) If the color pattern is as shown in (8), then use move #5 to get to (9) Next, move the 2 same colored corner cubes (red in this case) on bottom level such that they align on the side with the red center cube (10). Go to step 5.

If neither a) or b) occurs, repeat step 4.


5) Execute moves #8 and then #9 once. If the bottom 4 corner cubes are not the same color, repeat step 5 till (11) is achieved.

6) Now, with all corners on each side having the same color, starting with the white side as the top level, use moves #1 and #2 to make all 9 cubes the same white color (13). Use moves #6 and 7 to make the mid level with the correct color one cube at a time (12). This may require moving the levels in order to align the colored cube into position (14-16).


7) With the top and bottom levels all having the correct and same colors, working on the bottom level becomes much easier. Since moves #6 and 7 change positions of the cubes only adjacent to the center cube on the bottom level only, several moves later, the mission is accomplished (17-18).

Key Idea

The most difficult part in solving this puzzle is to make all 4 corners on each side with the same correct colors. Then moves #6 and #7 can be used repeatedly to move each cube between the corners to its desired position without disturbing those cubes that we do not want to change. Moves #3 to #5 will set the 4 corners on the first or top level to the same color. Then, we need to work on only the 4 corners on the third or bottom level. Moves #8 and then #9 will not set them into the correct colors right away. What those 2 moves do is to go through the limited possible patterns (not more than 6) till the right one shows up.

Insight

Rubik’s Cube is no easy puzzle to solve for the average Joe. For a rare few who possess the mental capability to process patterns in 3 dimensions, the puzzle is a walk in the park and a showcase to their naturally-born special talent. But, by breaking the complex problem into its simpler components, the average people are also able to unravel the mystery and take a peek into the seemingly improbable and the unimaginable. No doubt, the advance of our civilization relies on the contributions of a few, but it is the mass that provides the fuel to allow it to blossom and last..

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