Lupin’s Approach of Solving Rubik’s CubeBy Michael Bon Jaime (April 6, 2008)

Introduction:

To start let me introduce my self and how I come up with this method. At first I really don’t have an idea of solving Rubik’s cube what I only know is the name of the cube. One day I see a man solving the cube, I think he solved it around five minutes. Then in the store I see the same cube, I ask “how much is that?” and the vendor said “oh, the Rubik’s cube? Its 15pesos”, and then I buy it.

At first I can only solve the first layer, and then in two days I can solve it up to two layers. But I found it hard to solve the first layer and the second layer consecutively because I don’t yet have any patterns. So I come up with the idea of solving my first pair of six and then make a 2×2×3 Rubik’s figure using it. And then finishing the second layer, I made two patterns that help me a lot to solve the cube. And so I solved the Rubik’s cube up to two layers in four days. Then the last layer, that time I try and try many rotations but I can’t solve the last layer without scrambling my first and second layer that’s why I try it in a different way. Looking at the last layer as a BS-Mathematics student I realize that the cube’s last layer combinations/permutations are not that so many. So I disassemble my cube into pieces and bring back each piece in its original position. Then I made some rotations that will rearrange the last layer without rearranging the first and two layers. From that I made two patterns (I called it fish move and flip move) and with those two patterns I can then solve the last layer.

It took me around seven days two complete my patterns (4 patterns) just two solve the Rubik’s Cube. And now after months of experimenting I improve my solution that I called “Lupin’s Approach”. In the same months while improving my solution I found out that there are many solutions of Rubik’s Cube exist and are post in the internet. I also found out that there are many cubers (that’s what they called their selves) who can solve the cube in just a few second. And now that I improve the “Lupin’s Approach” I believe that this solution can someday bits them.

Preliminary Concepts

Properties of the Cube

Knowing the Rubik’s cube properties is very important. In some way this properties becomes a big help to the cubers.

Rubik’s Cube

Have 8 corners, 12 edges and 6 centers that are all unique.

Used notations:

R- right, L- left, F- front, B- back, U-up and D- down. Those letters are used to represent the clockwise rotation of a given area and their clockwise direction are in code by a prime (‘) where the clockwise rotation of right is R’. The X and Y represents the rotation of the whole cube and I just base it to the X-axis and Y-axis of a Cartesian plane where X means right, X’ is left, Y is up and Y’ is down. Small letters are also use to represent the rotation of both the center and a given area. I also sometimes used letter H to represent the center Rotation.

Lupin’s Approach

Step 1: The first pair of six.Step 2: Making 2×2×3Step 3: Finishing first and second layer (includes special cases)Step 4: Last layer (part 1)Step 5: Last layer (part 2)

Lupin’s Approach

To start choose your first pair of six.

The First step is turn this into this

And then turn this into this

This step can be learned by practicing and no patterns are required.

The second step is to turn this into this

Actually this step is very logical and there is no need for explanation but here are some tips how to solve this.

Always remember that two face of the cube is available to move without rearranging your 1×2×3 in first step.

It is easier if you will first put the edge color to color, see the illustration below.

Moves: L B L

U’ R U

L2

Note: By practicing this step, you can finish both step 1 and 2 in 15 moves or less.

The third step is to turn this into this

My third step has two parts the first part is for mastery so I suggest that you should skip that part first, and then master it later.

Before proceeding to my patterns I will first show you how to flip an edge, because sometimes it is necessary to flip an edge specially the white-red edge (remember: it is not always white-red, it is only because I start with red-yellow, it always depend in you).

Flipping white-red

F R F’ u2

Orienting a square

Smile!r’ U’ R’ U R U’ R’ U r

r’ U’ R U R’ U’ R U r

r’ U’ R U’ r H’ B’ R’ B L

U2 R’ U2 R’ U2 R2 U2

F R B’ R’ F’ B

F B’ R B R’ F’

U R2 U’ L’ B’ R2 B L

r U R’ U’ B’ R2 B r’

F R’ l F’ R’ F R’ F’ R’ F

U’ R U R U’ R U R’ F R F’

F R F’ U2 R U R’ U2

U’ R’ U H U R U’ r’

F R’ F’ U’ R2 U

U R2 U2 R2 U F R F’

B’ R B R2 F R F’ R U’ R’ U

B’ R’ B F R’ F’ U’ R2 U

L U2 R’ U2 R U2 L’

U’ R U R U R’ U2 R U

F’ U F2 R2 F U2 R2 U

U’ R U R’ U R’ U2 R U

U R U2 R’ U

R U R’ U2 R U

L’ B’ R’ B L B’ F R’ F’ B

U R2 U’ R U R2 U2 R’ U

U R’ U’ R U’ R’ U2 F’ U’ F

B L’ U’ L B’

U R’ U2 R2 U F R2 F’

U’ R U2 R2 U’ F R F’

U R2 U’ F R F’

F’ U2 F R U’ R’ U2

U’ R’ U2 R’ U2 R2 U F R2 F’

U R’ U’ R’ U R U’ R F R’ F’

B’ R B R’ U’ R’ U

B’ R B R B’ R’ B U’ R2 U

R U R U2 R2 U

R2 U R’ U’ R U’ R’ U

R2 B’ R2 B R U’ R’

R’ U R2 U’ R F R F’

R’ B’ R B F R’ F’

B’ F R’ F’ B

Finishing Second Layer

Smile!F2(R2 F’ R’ F) (R’ F’) (R2 F’)

(F R2) (F R) (F’ R) (F R2) F2

U2 R’ U2 R’ U2 R2 U2

R U R U’ R U’ R2 U

R’ U’ R’ U R2 U’ R’ U

F R’ F’ l F’ R2 F R2 F’ R F

F R’ l F’ R’ F R’ F’ R’ F

(U’ R U) (R U’) (R U R’) (F R F’)

(F R’ F’) (U’ R2 U)

(R U’) (R’ U) (R’ F R F’)

(R’ F) (R F’ R) (U’ R’ U)

(U R) (U R) (U R’ U’) (R’ U’)

(U’ R’ U) (R U’ R’) U

(U’ R U) (R’ U’ R U’)

U’ R2 U R U’ R’ U

R’ U’ R U R U’ R U R’ U’ R’ U

R’ F’ R’ F’ R’ F’ R F R F

R’ U’ R2 U F R2 F’

R2 F l’ F R2 F’ U’

R2 F2 R2 F’ R’ F R’ U2

R U’ R2 U l’ U R U’

U’ R U R2 F R F’

R U R U R U R’ U’ R’ U’

R2 U’ l U’ R2 U F

R U’ R U R’ U’ R U’

R2 U2 R2 U’ R U’ R U2

F R’ F’ R2 F’ R’ U

R’ F R2 F’ R U’ R’ U

F’ R’ F’ R’ F’ R F R F

F l’ U’ R U R’ U’

l' U l’ U R2 U’ B’

F R2 F’ R’ F R F’

R’ F R’ F’ R F R F’

F’ U F U’

U’ R2 U R’ U’ R U’

R2 U’ R’ U R U’ R2 U

R U’ R’ U

R’ F R U’ R F R ’F’

U’ R’ U R2 F R F’

F R2 F’ R’ F R2 F’

R U’ R’ U2 F’ U’ F

U’ R2 U R U’ R2 U

U’ R’ U R’ U’ R’ U

F R2 F’ R U R’ U’

R’ F R F’ R2 F R U’ R’ F R2 F’

Note: It is not necessary that you fully follow step 3, this is just a guide, and of course you can start with step 3 by finishing the green-white and then do the F2L on the blue-white.

Last layerPart 1

(R U2) (R’ U’ R U’ R’)

(L’ U2) (L U L’ U L)

(R2 D) (R’ U2) (R D’) (R’ U2 R’)

(R’ F’ L F) (R F’ L’ F)

(F R’ F’) (L F R F’ L’)

(R U2) (R’ U’ R U R’ U’ R) (U’ R’)

(R U2 R2 U’) (R2 U’) (R2 U2 R)

F (U R U’ R’) F’

F’ (U’ L’ U L) F

(L F’ L’ F) U (F R U’ R’ F’)

(R’ F R F’) U’ (F’ L’ U L F)

F (R U R’ U’) F’

(R U R’ U’) (R’ F R F’)

(F R’ F’) (R U R U’ R’)

(R U2) (R2 F R F’) (R U2) R’

(B’ R2) (F R F’) (R’ F R F’) (R B)

U B (L’ B’ L) U2 (B2 R B R’) B

F (R’ F2) (L F2) (R F2) (L’ F)

(F (R U R’ U’ R U R’U’)) F’

R’ (F’ U’ F U F’ U’ F U) R

U (F’ L F2) (R’ F2) (L’ F2) (R F’)

(F (R U R’ U’)) (F’ L (F R’ F’) L’ (F R F’))

(U R’) U2 (R2 U) (R’ U) (R U2) (B’ R’ B)

(U’ R U) (R’ U R U’) (B U’ B’ R’)

F (U R U’ R’ U R U’ R’) F’

L (F R’ F R) (F2 L’)

R’ (F’ L F’ L’) (F2 R)

(U R’) (F’ U’ F U) (F’ L) (F’ L’ F2 R)

(U’ L) (F U F’ U’) (F R’) (F L F2 L’)

(R B2) (L’ B’ L) (B’ R’)

(L’ B2) (R B R’) (B L)

((R’ U’) (R’ F R) (F’ U R))

(X) (R U R’ U) (X’) (R’ F’ L) (F H’)

(H’ F R’ F’) (H F R F’)

(F R’ F’) (H’ F) (R F’ H)

(X2) (L’ U L U2) (L’ U’) (X) (L’ U L) (X) (U R)

(X2) (R U’ R U2) (R U) (X’) (R U R’) (X’) U’ L’

F (L’ F’) (L2 U) (L U L’ U’ L) F2

F (R' F) (R2 U') (R' U' R U R') F2

(R U R’) (U R U’ R’ U’) (Y) (R U R U’)

(X) (R’ U’ R) (U’ R’ U R) U (l’ U’ R’ U)

(X) (R U R’) (X’) (R’ F) (R U’) (R’ F’ R)

(X’) (L’ U’ L) (X) (L F’) (L’ U) (L F L’)

(l’ U l U l’ U’ l) (X) (R U’ R’)

(r U’ r’ U’ r U r’) (X’) (L’ U L)

(r U’ r’ U’ r U r’) (X’) (L’ U’ L U L’ U L)

(l’ U l U l’ U’ l) (X) (R U R’ U’ R U R’)

(R U2) (R2 F R F') U2) (R' F R F’)

(F R' F' R) U2 (F R' F' R2) U2 R'

(R U2) B' (R' U' R U) (X’) (R2 U2) (R' F')

(L F’ L’ F U) (F U’ R U R’ U’) F’

F (U R U’ R’ U) (F’ U’) (F’ L F L’)

(F R U R’ U’) (X) (R’ F’) (U’ L’ U L F)

(F L’ U’ L U’) (X’) (L F) (R U R U’ R’ F’)

Last layerPart 2

(R' U R' U') (R' U' R' U) (R U R2)

(R2 U') (R' U' R U) (R U) (R U' R)

(H2 U) (H2 U2) (H2 U) H2

U (F R’ F’ r R) (U’ R’ L U’ R U L2)

(F’ L) (F’ R2) (F L’) (F’ R2) F2

F2 R2 (F L F’ R2) (F L’ F)

B (L’ B’) (R B L) (B’ R2) (F’ L F) (R F’ L’ F)

(L’ U R U’ L) U2 (R’ U R) (U2 R’)

(L U’ R’ U) (L’ U2) (R U’ R’ U2) R

U’ (L’ U R’) U2 (L U’ R) (L’ U R’) U2 (L U’ R)

U (R U’ L) U2 (R’ U L’) (R U’ L) U2 (R’ U L’)

(R’ U R U’ R2) (X) (R’ U’ R) (X’) U (R F R’ F’ R2) U’

(R U R’ U’) (R’ F R2 U’) (R’ U’ R U R’ F’)

U (R U2 R’ U2) (R B’) (R’ U’ R) U (R B R2)

U’ (L’ U2 L U2) (L’ B) (L U L’) U’ (L’ B’ L2)

U’ (B’ R B R’) (U’ R’ U) (R2 U R’ U’) (R’ F R F’)

(X) ((L’ U) (R U’) (L U L’) (U R’ U’) (L U2) (R U2 R’))

(L2 u’) (L U’ L) (U L’) (u L2) (X) (R U’ R’)

(R2 u) (R’ U R’) (U’ R) (u’ R2) (X’) (L’ U L)

(L’ U’ L) F2 D (R’ U R U’ R) (u’ R2)

(R U R’) F2 D’ (L U’ L’ U L’) (u L2)

Note: There are many algorithms/patterns that are just right, left cosets or inverse of the other algorithms. That will lessen your algorithms to memorize.

If you really want to get faster try to always think ahead. Presence of mind is very important in improving your speed. And of course noting bits practice, so if you have that what they called “tyaga” (in the Philippines), dude you can rock!

This method is still on progress and seeking for a tangible development. If you have questions, comments or other convincing algorithms or patterns that can help to improve this method my e-mail address is WizardVon@yahoo.com or WizardVon@math.com.

Lupin’s Approach is a kind of method which is seeking to have a consistent speed even in the worst scenario. That means one can have a consistent speed but cannot be speeder than his speed. For example, if you average 13 seconds, then even in the worst scenario you will still have a time of 13 – 14 seconds, but in the best scenario you will just have a time of 11 – 12 seconds. Unlike Fridrich method that when you average 13 seconds, you may got 9 – 10 seconds but still can have 15 - 16 seconds.

Beginners Solution

Lupin’s approach is not appropriate for beginners so if you are a beginner you must first follow these steps.

Even if you where a beginner you can still do steps 1 and 2 by practice. So we will start with finishing the first two layers. After solving 2×2×3 you will now flip the edges (watch video).

After you flip the 3 edges you will now position the 2 corners.

R U’ R U R U’ R2 U

R’ U’ R’ U R2 U’ R’ U

U2 R’ U2 R’ U2 R2 U2

R U’ R U R U’ R2 U

R’ U’ R’ U R2 U’ R’ U

U2 R’ U2 R’ U2 R2 U2

The next step is the last layer. You must first flip the edges to make a cross.

F U R U’ R’ F’

F R U R’ U’ F’

After making a cross you will apply the following algorithms to their respective figure.

Figure:

Fish 1 (R U2) (R’ U’ R U’ R’)

Fish 2 (L’ U2) (L U L’ U L)

Tank 1 (R2 D) (R’ U2) (R D’) (R’ U2 R’)

Tank 2 (R’ F’ L F) (R F’ L’ F)

Two Holes (F R’ F’) (L F R F’ L’)

Cross 1 (R U2) (R’ U’ R U R’ U’ R) (U’ R’)

Cross 2 (R U2 R2 U’) (R2 U’) (R2 U2 R)

Then you will arrange the corners to its respective position. The algorithm of changing corner is L’ U R U’ L U R’ (this will only change the two corners in the right) after you apply that algorithm you will form a fish 2 figure. Then on the same position you will apply the algorithm for that.(See video)

When all the corners are in their right position you will now rotate the edges the algorithms are: (See Video)

F2 U R’ L F2 L’ R U F2

F2 U’ R’ L F2 L’ R U’ F2

And that’s how you solve the rubik’s cube.