Wednesday, July 14, 2010

Solve Rubik's cube without any external help

* Even if you don't have a Rubik's cube, you can use a Java virtual Rubik's cube HERE

What I am giving here won't be the fastest way to solve a Rubik's cube, you won't need to understand the whole mechanics but neither will you have to refer to anything or need external help after this help of mine of course! This is for those who can solve a bit of the cube, not whole or those who can do it by following a lot of algorithms from somewhere. With this, you will be able to solve the whole cube and only remembering a few easy algorithms.




Rubik's cube remains one of the most interesting and yet simple puzzles ever made. It caught the imagination of the world and still remains one of the elusive ones. Dealing with a Rubik's cube can be very frustrating and so a majority of people don't even try it.

A little more about it- The Rubik's Cube is a 3-D mechanical puzzle invented in 1974 by Hungarian sculptor and professor of architecture Ernő Rubik. Originally called the "Magic Cube", the puzzle was licensed by Rubik to be sold by Ideal Toys in 1980 and won the German Game of the Year special award for Best Puzzle that year. As of January 2009, 350 million cubes have sold worldwide making it the world's top-selling puzzle game. It is widely considered to be the world's best-selling toy.

In a classic Rubik's Cube, each of the six faces is covered by nine stickers, among six solid colours (traditionally white, red, blue, orange, green, and yellow). A pivot mechanism enables each face to turn independently, thus mixing up the colours. For the puzzle to be solved, each face must be a solid colour. Similar puzzles have now been produced with various numbers of stickers, not all of them by Rubik. The original 3×3×3 version celebrates its thirtieth anniversary in 2010.

It was also shown in one of the most popular movies- The Pursuit of Happyness. In the 2006 movie The Pursuit of Happyness, Chris Gardner (character played by Will Smith) impresses his future employer by solving a Rubik's Cube. Will Smith accomplished the same trick thirteen years prior in an episode of The Fresh Prince of Bel-Air to impress a college recruiter. And apparently Will Smith can solve it in real life too and there is also a video showing him do that in 55 seconds.

In Bollywood movies too, it has been shown-

- In the 2010 Bollywood movie My Name is Khan, Rizwan Khan played by Bollywood legend shahrukh khan is seen solving Rubik's Cube.
- In the 2010 Bollywood movie 3 Idiots, Rancho (character played by Aamir Khan) is seen roaming around in the College holding a Rubik's cube.

- In the 2010 Bollywood movie Karthik Calling Karthik, Karthik (character played by Farhan Akhtar) is seen solving the Rubik's Cube by his split personality.


As you might have seen, generally anywhere in the movies or ads or Tv shows, whenever they want to show someone as intelligent, they show him solving the Rubik's cube. But it is not so much about intelligence as it is about simple algorithms. Now onto the actual, main part. What I am going to tell you is how to solve a Rubik's cube without any external help. As it is, it is difficult to solve even after getting all the help. Most people would be happy if they can just solve the Rubik's cube without doing things like changing the stickers or dismantling it, and then there are others who are into speedcubing with the world record for solving the fastest being 7.08 seconds!

So what I am giving here is something in between. It won't be the fastest way, you won't need to understand the whole mechanics but neither will you have to refer to anything or need external help after this help of mine of course! This is for those who can solve a bit of the cube, not whole or those who can do it by following a lot of algorithms from somewhere. With this, you will be able to solve the whole cube and only remembering a few easy algorithms.

Here is how to do it -

Terms you need to know   


Here you can see that each side of the cube has a different name:


Front (F), Back (B), Right (R), Left (L), Up (U), Down (D).
These sides are named because of their orientation to you, not because of their color. If you turn the cube upside down, the UP becomes DOWN, and the DOWN becomes UP, so the sides don't retain their names. DOWN is whatever side is pointing to your feet, and UP is always pointing up.


There are only 3 types of turns that are useful: clockwise, counterclockwise ( ' ) and half turn ( 2) . The symbols in parenthesis will be what I use to differentiate between different types of turns.



For example:




R would mean to make a CLOCKWISE quarter turn of the RIGHT face:  See figure


 ( & F would mean to make a CLOCKWISE quarter turn of the FRONT face,
L would mean to make a CLOCKWISE quarter turn of the LEFT face & so on)





F' would mean to make a COUNTERCLOCKWISE quarter turn of the FRONT face:
See Figure


(& U' would mean to make a COUNTERCLOCKWISE quarter turn of the UPPER face,

L' would mean to make a COUNTERCLOCKWISE quarter turn of the LEFT face & so on)



U2 would mean turning the upper face twice (half turn) ( clockwise or counterclockwise doesn't matter because the end result will be the same- turning 180 degrees)



 Step 1 - Solving the topmost layer.
             I am assuming you already know the basics which would mean you know how to do the first layer at least because it is not that difficult. You can take any coloured layer prefer the side which has maximum number of correct faces. Now here you have to keep in mind that whatever colour top layer you select, you should ensure that the top layer of all faces is maintained properly. In short, it should look like this.


As you can see, while doing the top layer which is green, you also maintain the other sides too- Red and Yellow visible here. If you are wondering how the centres of all the sides are in place too ( Red, Yellow visible), that is one thing good about this cube. If they are not already in place after doing the first layer, just turn the middle layer around till one side matches and all sides centre would match.

Step 2 - Solving the middle layer

Now comes the part which is quite easy and fast to do if you know a very simple algorithm.



As you can see the red of the bottom layer needs to go either to the left or right side in the 2nd layer. Assuming yellow is the colour below red of the last layer, then it would need to go to the right so that yellow of the second layer is done too.

The Algorithm for each case is-

To the Left - DL   D'L'   D'F'   DF
To the Right - D'R'  DR    DF    D'F'

As you can see, it is a very easy to remember algorithm.

In this way you can complete the whole 2nd layer. In case there is no part in place like this above example, you can do any of the 2 algorithms above anywhere and you will see that you will again get a part in the last layer that needs to be taken to either to the left or right in 2nd layer (like in this example).

Step 3 - Solving the last layer  (Making a correct cross)-

Now there can be 2 situations with the last remaining layer as given below and the simple algorithms to be done as per the situation. If there is none of the 2 situations shown below, do any of the 2 algorithms given below anywhere and you should get it.




After doing either of the algorithm given above as per the situation, there would be a cross formed. If the cross is properly formed which means matching all the sides, then it's fine (as in the figure below, blue cross formed with red and green sides matching too.)



If the cross is formed, but it does not match all sides, turn it around such that only one of the sides matches. As in our example, let's say a cross is formed and only the red sides matches, the green shown above and 2 other sides too don't match, then keeping the correct side in front of you ( in this case, the red side) perform the following algorithm

R U2 R' U' R U' R'

This should get the cross of the last layer properly oriented.



Step 4 - Getting the 4 corners of the last layer in right place -

This step is to get the 4 last corners in the right place, but not necessarily rotated correctly. For example:




As you can see all the 4 corners are in correct place though not properly facing. Ex- In the top right corner of the Face visible, you can see 3 colours- Red, blue and green. And those are the 3 coloured faces around that corner. Although the green is where blue should be and blue is where red should be. That is called proper orientation or correct facing. That will be the last step. Here you only need to have 4 corners in correct place.

If not, to put them in proper place, 2 algorithms-

 

If you need to turn them around as given in the pic above (left) to get them in right place, use that algorithm given. Otherwise use the one on right.
If none of the situations match your cube, do any of the algorithms till you get one of the above situations and do the applicable algorithm again

Step 5 - Last step

Here you only need to correctly orient the corners which will complete your cube.
This is just an extension of the algorithm to orient the cross.

 R    U2     R'     U'     R      U'     R'               L'    U2      L      U      L'   U   L
(Same algorithm as orienting the cross)      (Just the opposite of the first part)




As shown in pic above, 2 corners are done and only 2 need to be done. If the situation is as above, just turn it so that the Red face is on the right side (where green is now) and do the algorithm given.
You might have to do the algorithm twice and it should be done.

Congratulations! Now you are among 5.8 % people of the world who can solve the Rubik's cube (According to one statistic).

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