how to solve a 3x3 Rubik's cube

3x3 Rubik's Cube

It is widely considered to be the world's best selling toy. I tried the Rubik's cube for the first time in 2nd semester in college (IIT Ropar), in 2011. I was very happy when I solved it for the first time.

My best time:

One-handed : 4 min 15 sec
Two-handed : 1 min 21 sec

Do you want to solve Rubik's cube ??? Have tried but not solved completely?? Here's the solution to your problem. To know about the mathematics behind it see my posts Rubik's Cube Group and One move-sequence solves the Rubik's Cube!!

Move notation:
U (Up): the side above or on top of the front side
D (Down): the side opposite the top, underneath the Cube
L (Left): the side directly to the left of the front
R (Right): the side directly to the right of the front
F (Front): the side currently facing the solver

Note: When a prime symbol ( ′ ) follows a letter, it denotes a face turn counter-clockwise, while a letter without a prime symbol denotes a clockwise turn

Generally,

White is opposite to Yellow
Blue is opposite to Green
Red is opposite to Orange

Assumption: white centre piece is on top while yellow centre piece is in the bottom.

Algorithm:

Step 1: Make a cross on the upper face with middle pieces consisting of colours of the opposite centre piece.

Step 2: Now make a '+' sign on the face opp. to the face containing cross. It can be done by matching "front colour of the middle piece of upper face" with its "corresponding centre colour on the front face" and then rotate front face by 180 degree. Note that cube should be hold such that cross is on upper face. Since, there are four middle pieces, this procedure is repeated at most 4 times, one for each middle piece consisting yellow colour.

Step 3: Complete Layer

Now, hold the cube with '+' sign containing face in the bottom. We have to correctly place the corners and our job for step 3 will be done. So, choose any corner piece of upper face containing a yellow colour (it should not face upward If it faces upward then correct it). See the other two colours contained in the that piece, say colour X and colour Y. Move the upper layer using U or U' to place the corner between centre pieces X and Y and face the yellow piece.

If the corner piece is on the upper right corner do : U R U' R'

If the corner piece is on the upper right corner do : U' L' U L

Finally, after 3rd step it will look like this after rotating :

Step 4: Complete the Middle Layer : Hold the cube as shown in Fig. above. Find the middle not containing white colour. Now match that piece to the centre piece to form a straight 3-colour middle edge. Hold the cube such that the 3-colour straight edge is on the right face.

If the centre piece corresponding to the bottom colour is on the BACK side, do :

R' D' R' D' R' D R D R D

If the centre piece corresponding to the bottom colour is on the FRONT side. do :

R D R D R D' R' D' R' D'

Finally, after step 4 it will look like this :

Step 5 : Cross on the top layer :

Hold the cube with yellow layer downside and white centre piece on the top layer.

There are 3 case on the upper side :

at most one adjacent piece is white to centre white piece.
inverted L of white colours on the top left corner.
a straight line of white colours parallel to us.

Repeat following algorithm till we get a '+' sign of white colours:

F R U R' U' F'

Step 6 : Matching top middle pieces :

Rotate the top layer until at least two middle pieces of top layer gets matched with corresponding centre pieces. You're lucky if all the 4 gets matched. If not,one of the two cases may occur

i) hold the cube with one matched middle piece on the right side and one on the back side.

ii) hold the cube with one matched middle piece on the front side and one on the back side.

Repeat the following algorithm until all the four middle pieces gets matched.

R U R' U R U U R'

Note that you should check after every repetition by rotating the top layer whether all the 4 got matched or not.

Step 7 : Placing the top layer corners in right place not necessary in the correct order.:

Check: If any corner is matched already, place it on the front right corner else doesn't matter which piece is on the front right corner.

Follow the algorithm :

U R U' L' U R' U' L

Repeat the algorithm and check alternately until all the four corner pieces are in the right places.

Step 8: Solving the corners correctly::

With unsolved layer on upper side, rotate the layer to move an unsolved corner piece in the front right corner and follow the algorithm until the corner piece gets solved. And continue to follow the procedure until all the corners gets solved. Note that you should not rotate the cube during the whole procedure i.e. don't change the front face every time.

R' D' R D

Finally,....!!!!!!!!!!!!