Minimum formula for 3 x3x3 rubik cube solution - last layer permutation

How solve Rubik Cube 3X3X3 using minimum formula especially for the last layer.

1. SOLVING LAST LAYER OF RUBIK CUBE 3x3x3
WITH MINIMUM NUMBER OF FORMULA .

FOCUS

1. How to solve the cube without involving the rotation of B, CC and SS.
2. Last Layer solution for beginners
3. To make learners understand without difficulty .

1. 0 PERMUTATION / MOVEMENT OVERVIEW.




































I use the Red Face as Front Face - the surface always
facing you while making rotation/permutation.
U U’ ( Ui )
.
R R’ ( Ri)
.
L L’ ( Li )
.
F F’ ( Fi )
.
B B’ ( Bi )
.
D D’ ( Di )
.
M M’ ( Mi )
.
S S’ ( Si )
.
E E’ ( Ei )
.
( DE) ( D’E’ )
.

2. 2.0 Exercise
These exercises help you to remember the symbols and directions of cube
permutations. The exercises intend to focus on basic formula without
involving the faces of B, D, E and S. It is difficult for intermediate player to
rotate the sides of B, D, E and S.


Position :





Front

Determine your Front (F) face and do the following permuation.

2.1 Exercise 1



a)




b)




c)




d)









f)

3. 2.2 Exercise 2
(B, D, E and S faces are excluded )



a)



b)



c)



d)





2.3 Exercise 3
(B, D, E and S faces are excluded )


(a) F U R Ui Ri Fi


(b) F R U Ri Ui Fi


(c) R U Ri U R UU Ri


(d) Li U R Ui L UU Ri U R UU Ri


(e) FF U L Ri FF Li R U FF


(f) U R Ui Ri Ui Fi U F


(g) U R Ui Ri [ E D ] Li U L


In fact, formula of (f) and (g) generate the same outcome for second layer. When you
use the formula of (f) above you will experience using (g) automatically. Soon, you
will familiar with formula (g) because it faster the (f).

4. 3. 0 SOLUTION TIPS FOR FIRST LAY ER.

I will not give you the specific formula to solve the first layer ( D ) but the following tips
may useful for you. ( We focus on third layer )


3.1 Define your base colour; white for example.




3.2 Match one of edges; lets say green and white




3.3 Match the center piece of E (green) with the correct edge ( green-white).
That means we lock the E to put the all center pieces of E in correct
position.



3.4 Make “PLUS” white of the base.
The other side of this cube look like this.



3.5 Permutate the corner of base (green-red-white).




3.6 Permutate all of the corners to put them in exact positions.

5. 4. 0 SIMPLE SOLUTION TIPS OF SECOND LAYER.

The following tips may useful for you to solve the second layer;

1. Red face as F ( Front )
2. Green face as F ( Front )

In this stage, I suggest you to use ( DE ) and ( D’E’ ) instead of F and F’


Problem

Aim /Target

Solution


1.





Use RED as F ( facing you )




U R U’ R’




(D’E’) L’ U L


Summary:
U R U’ R’ (D’E’) L’ U L



2.








Use GREEN as F ( facing you )





U’ F’ U F





(DE) R U’ R’


Summary:
U’ F’ U F (DE) R U’ R’



Notes : If you are confusing on my diagram, please refer to ( 1.0 ) above.

6. 5.0 SOLVING THIRD LAYER

After completing second layer you may get various thirds layer patterns.
I categorize them as 1/9, 3/9, 4/9, and 9/9
In this stage, I provide you Formula instead of graphics illustration.


5.1 Stage 1 Category 1/9 State 1



Expected top layer
patterns outcomes.


, , , , ,
, ,

Each illustration above have basic pattern of 1/9
Category as the shown diagram below;







Target



becomes



Concept & Cube
Position






Red is must be F , always facing you )


Formula

F U R U’ R’ F’


Permutation


Use the above formula until you get the

Stage 2 Category 3/9 V or 3/9 I


Notes

7. 5.2 Stage 1 Category 3/9 State 2




Expected top layer
patterns outcomes.


, , , , , ,
, , , , , ,



Each illustration above have basic pattern of 3/9
Category as the shown diagram below;







Target / Focus



becomes or





Concept & Cube
Position







Red is must be F , always facing you )


Formula

F U R U’ R’ F’


Permutation


Use the above formula;
F U R U’ R’ F’ and repeat this formula until
you get the Stage 3 Category 4/9 Plus


Notes


1. You may use the above formula for many times.

2. But sometimes, unexpectedly, you will get the
Stage 4 Category FISH.

8. 5.3 Stage 2 Category 3/9 State 3




Expected top layer
patterns outcomes.


, , , , , ,
, , ,


Each illustration above have basic pattern of 3/9
Category as the shown diagram below;







Target



becomes or




Concept & Cube
Position







Red is must be F , always facing you )


Formula

F R U R’ U’ F’


Permutation


Use the above formula;
F R U R’ U’ F’ and repeat this formula until
you get the Stage 3 Category 4/9 Plus


Notes


And at this stage, you may get the Stage 4 Category
FISH. It’s wonderful!

9. 5.4 Stage 2 Category 4/9 Plus




Expected top layer
patterns outcomes



Type 1 :

,



Target



becomes or




Concept & Cube
Position



i) turn to




ii ) turn to


Red is always F , always facing you )

Important : At least one of
match Colours
always facing at
you left hand side
when you hold th cube.


Formula

R U R’ U R UU R’


Permutation


1. You can repeat the formula above until you get the
Target Stage 4 Category 6/9 as


You will get this pattern in any incorrect
position.

So,
Adjust it like this pattern and keep using


R U R’ U R UU R’ to reach the final category
of 9/9.


Notes

10. 5.5 Stage 2 Category 8/9


Expected top layer
patterns outcomes

, ,


Target



i) becomes



ii) becomes



iii) becomes





Concept & Cube
Position


Remember, Red is always F , always facing you )


i) ii) iii)










Formula

R U R’ U R UU R’


Permutation


Repeat the formula above until you get the Stage 4
Category 9/9


Notes

11. 5.6 Stage 2 Category 6/9 FISH




Expected top layer
patterns outcomes



i) ii)


Target



i) becomes



ii) becomes




Concept & Cube
Position






Red is always F , always facing you )


Formula

R U R’ U R UU R’



Permutation



When this permutated using formula of


R U R’ U R UU R’ , you will get .


So, adjust the cube position as shown below;


Or which Red Face is F, and use



R U R’ U R UU R’ again to gain



Notes


If you get different patterns as shown in (i) and (ii)
but they are still 6/9 then simply use that formula
( R U R’ U R UU R’ ) again and again until you
Come to pattern of (i) or (ii).

12. 5.7 Stage 3 Category 9/9 Corners




Expected top layer
patterns outcomes.


Sometimes you will get;
( Make Green face as F , always facing you )

( A ) ( B )

or





Target


To make,





Concept & Cube
Position


Based on illustration above, you must use the Green face
as F, surface that always facing you instead of red
face.


Formula

L’ U R U’ L UU R’ U R UU R’


Permutation


For (A ) you will use the formula twice, but
For (B) you just use the formula once.


Notes


And at this stage, you may solve the Rubik cube.
It’s fantastic!

13. 5.8 Stage 4 (Final Stage) Category 9/9 Edges


Problem

Solution / Permutation


Clockwise (+ve)



i)




ii)




Y(+ve) Formula : FF U L R’ FF L’ R U FF



i) Use Y (+ve) formula twice.




ii) Use Y (+ve) formula once.


Anti-Clockwise (-ve)



i)




ii)



Y (-ve) Formula : FF U’ L R’ FF L’ R U’ FF



i) Use Y (-ve) formula twice.




ii) Use Y (-ve) formula once.










MUM Formula ;

M2 U M2 U2 M2 U M2










MUM Formula ;

M2 U M2 U M’ U2 M2 U2 M’ U2

14. 6. SUMMARY

6.1 Summary - The Aim Chart / Summary


Stage 1 or but

F U R U’ R’ F’ F R U R’ U’ F’




Stage 2

R U R’ U R UU R’






Stage 3


L’ U R U’ L UU R’ U R UU R’






FF U’ L R’ FF L’ R U’ FF


Stage 4


FF U L R’ FF L’ R U FF




MM U MM UU MM U MM




M2 U M2 U M’ U2 M2 U2 M’ U2




FINISH

15. 6.2 Summary - List of Practical Minimum Formula (solution for 3
rd
Layer).


Briefs

Formulae / Steps

Diagrams


1. FUR


F U R U’ R’ F’





2. FRU


F R U R’ U’ F’





3. FISH (F)


R U R’ U R UU R’







4. LR


L’ U R U’ L U R’





5. LRF

Combination
of 4 & 3



L’ U R U’ L UU

R’ U R UU R’



6. Y (+ve)






7. Y (-ve)

Clockwise:

FF U L R’ FF
L’ R U FF



Anti Clockwise:

FF U’ L R’ FF
L’ R U’ FF


Clockwise:






Anti Clockwise:







8. H

9. D


M2 U M2 U2 M2 U M2

M2 U M2 U M’ U2 M2 U2 M’ U2

Notes : i) L’ U R U’ L UU R’ U R UU R’ - used frequently.
ii) Brief Column above – it’s my idea to make “Life Easier”.
By, JURIM_SARAMBUNG @PUWORK2010