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

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

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

1. 1. SOLVING LAST LAYER OF RUBIK CUBE 3x3x3<br />WITH MINIMUM NUMBER OF FORMULA.<br />FOCUS<br /><ul><li>How to solve the cube without involving the rotation of B, CC and SS.
2. 2. Last Layer solution for beginners
3. 3. To make learners understand without difficulty.</li></ul>1. 0PERMUTATION / MOVEMENT OVERVIEW. <br />83566058420I use the Red Face as Front Face - the surface alwaysfacing you while making rotation/permutation.<br />100266513208011874513017517272038100107759538100U U’ ( Ui ). R R’ ( Ri).10687058870952590808870951695451320801000125121285L L’ ( Li ).28829082994511169658299451676401352551000125124460171450311151000125273052209801270001125220155575F F’ ( Fi ).B B’ ( Bi ).9925058343901733558343909950453175017716531750D D’ ( Di ).10598168629661739908629659855204127516446541275M M’ ( Mi ).10775958350252203458350251000125996951689109969510001259969516954510922011899902476525097933655S S’ ( Si ).E E’ ( Ei ).11944359017003544919017001689109969510001259969510775956350022034563500 ( DE) ( D’E’ ).1143635806450306705806450<br />2.0 Exercise <br />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.<br /> <br />16624306985Position : <br /> Front <br />Determine your Front (F) face and do the following permuation.<br />2.1 Exercise 1 <br />58185058191551060358191543935658191536810958191529686258191522561558191515436858191583121581915<br /> a) <br />510603514795543935651479553681095147955296862514795522561551479551543685147955831215147955<br />b)<br />43935659906036810959906029686259906022561559906015436859906083121599060<br />c) <br />510603516446543935651644653681095164465296862516446515436851644658312151644652256155164465<br /> <br /> d)<br />2968625127022561551155701543685115570831215115570<br />58185051143051060351143043935651143036810951143029686251143022561551143015436851143083121511430<br />f) <br />2.2 Exercise 2 <br /> (B, D, E and S faces are excluded )<br />48685456223042748206223036810956223030873706223024936456223018999206223013061956223071247062230<br /> a) <br />30873707239036810957239024936457239018999207239013061957239071247072390<br />b) <br />48685457556542748207556536810957556530873707556524936457556518999207556513061957556571247075565<br />c) <br />60559958191554622708191548685458191542748208191536810958191530873708191524936458191518999208191513061958191571247081915<br /> d) <br />2.3 Exercise 3 <br /> (B, D, E and S faces are excluded )<br />(a)F U R Ui Ri Fi<br />(b)F R U Ri Ui Fi<br />(c)R U Ri U R UU Ri <br />(d)Li U R Ui L UU Ri U R UU Ri <br />(e)FF U L Ri FF Li R U FF<br />(f)U R Ui Ri Ui Fi U F<br /> (g) U R Ui Ri [ E D ] Li U L<br /> <br />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).<br />3. 0 SOLUTION TIPS FOR FIRST LAYER.<br /> I will not give you the specific formula to solve the first layer ( D ) but the following tips <br /> may useful for you. ( We focus on third layer )<br />72136066675<br /> 3.1Define your base colour; white for example. <br />72136069215<br /> 3.2Match one of edges; lets say green and white<br />72136081280<br /> 3.3 Match the center piece of E (green) with the correct edge ( green-white).<br />That means we lock the E to put the all center pieces of E in correct <br />position. <br />72136027940448881529845<br /> 3.4 Make “PLUS” white of the base.<br />The other side of this cube look like this.<br />72136040005<br /> 3.5Permutate the corner of base (green-red-white).<br />79756042545<br /> 3.6 Permutate all of the corners to put them in exact positions.<br />4. 0 SIMPLE SOLUTION TIPS OF SECOND LAYER.<br />The following tips may useful for you to solve the second layer;<br /> <br />1. Red face as F ( Front ) <br />2. Green face as F ( Front ) <br />In this stage, I suggest you to use ( DE ) and ( D’E’ ) instead of F and F’<br /><ul><li>ProblemAim /TargetSolution387985698501.184785136525 Use RED as F ( facing you )197802558420136842558420323855842070104056515 U R U’ R’5397515049519780251504951368425150495697865150495 (D’E’) L’ U LSummary:U R U’ R’ (D’E’) L’ U L3879851143002. 184785107950Use GREEN as F ( facing you )18732506356502406351261110-381075565-3810 U’ F’ U F7302511430019780251143001368425114300705485114300 (DE) R U’ R’Summary:U’ F’ U F (DE) R U’ R’</li></ul>Notes : If you are confusing on my diagram, please refer to ( 1.0 ) above.<br />5.0 SOLVING THIRD LAYER<br />After completing second layer you may get various thirds layer patterns. <br />I categorize them as 1/9, 3/9, 4/9, and 9/9<br />In this stage, I provide you Formula instead of graphics illustration. <br />5.1 Stage 1 Category 1/9 State 1<br />Expected top layer patterns outcomes. , , , , , , , Each illustration above have basic pattern of 1/9 Category as the shown diagram below;1276358255 Target23183853683028003527305 becomes Concept & Cube Position129540121285 Red is must be F , always facing you )Formula F U R U’ R’ F’PermutationUse the above formula until you get the Stage 2 Category 3/9 V or 3/9 INotes<br />5.2 Stage 1 Category 3/9 State 2<br />Expected top layer patterns outcomes., , , , , , , , , , , , Each illustration above have basic pattern of 3/9 Category as the shown diagram below;13208088265 Target / Focus335661011874514668533020230886025400 becomes orConcept & Cube Position20383515875 Red is must be F , always facing you )Formula F U R U’ R’ F’PermutationUse the above formula; F U R U’ R’ F’ and repeat this formula until you get the Stage 3 Category 4/9 PlusNotes 1. You may use the above formula for many times.2. But sometimes, unexpectedly, you will get the Stage 4 Category FISH.<br />5.3 Stage 2 Category 3/9 State 3<br />Expected top layer patterns outcomes. , , , , , , , , , Each illustration above have basic pattern of 3/9 Category as the shown diagram below;7048519685 Target33185108699522326601536706096012700 becomes or Concept & Cube Position70485151765 Red is must be F , always facing you )Formula F R U R’ U’ F’ PermutationUse the above formula; F R U R’ U’ F’ and repeat this formula until you get the Stage 3 Category 4/9 PlusNotesAnd at this stage, you may get the Stage 4 Category FISH. It’s wonderful!<br />5.4 Stage 2 Category 4/9 Plus<br />Expected top layer patterns outcomes Type 1 : , Target 21336012319021748751231903251835113665 becomes orConcept & Cube Position 2185035109220375285109220 i) turn to 384810317521850353175ii ) turn toRed is always F , always facing you )3451860124460Important : 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’ Permutation1. You can repeat the formula above until you get the Target Stage 4 Category 6/9 as2070735146050You will get this pattern in any incorrect position.212788520955So,Adjust it like this pattern and keep usingR U R’ U R UU R’ to reach the final categoryof 9/9.Notes<br />5.5 Stage 2 Category 8/9 <br />Expected top layer patterns outcomes , , Target 1889760140970356235140970i) becomes 3606801619251880235-3175ii) becomes 1880235135255356235135255iii) becomesConcept & Cube Position Remember, Red is always F , always facing you )35623512128529184601308101613536135572 i) ii) iii)29908513144515373351314452851785131445Formula R U R’ U R UU R’ PermutationRepeat the formula above until you get the Stage 4 Category 9/9 Notes<br />5.6 Stage 2 Category 6/9 FISH<br />Expected top layer patterns outcomes 14420858826537528569215 i) ii)Target 2223135135255489585126365 i) becomes 223266013271551816010795 ii) becomes Concept & Cube Position 280035109219 Red is always F , always facing you )Formula R U R’ U R UU R’ Permutation1003935102235 When this permutated using formula of295656023495 R U R’ U R UU R’ , you will get . So, adjust the cube position as shown below; 1061085117475156210-5080 Or which Red Face is F, and use3509010134620 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). <br />5.7 Stage 3 Category 9/9 Corners <br />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 PositionBased 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’ PermutationFor (A ) you will use the formula twice, butFor (B) you just use the formula once.NotesAnd at this stage, you may solve the Rubik cube. It’s fantastic!<br />5.8 Stage 4 (Final Stage) Category 9/9 Edges<br />ProblemSolution / Permutation Clockwise (+ve)52895688266 i)52895579375 ii) Y(+ve) Formula : FF U L R’ FF L’ R U FFi) Use Y (+ve) formula twice.ii) Use Y (+ve) formula once. Anti-Clockwise (-ve)586105135255 i) 621030124460 ii) Y (-ve) Formula : FF U’ L R’ FF L’ R U’ FFi) Use Y (-ve) formula twice.ii) Use Y (-ve) formula once.59436034925MUM Formula ; M2 U M2 U2 M2 U M2 57658060960MUM Formula ; M2 U M2 U M’ U2 M2 U2 M’ U2 <br /> <br />6. SUMMARY <br />6.1 Summary - The Aim Chart / Summary <br />20072351460510140955080368363514605<br /> Stage 1 or but<br /> F U R U’ R’ F’ F R U R’ U’ F’<br /> <br />254063581915202819010287015214608191589281082550 <br /> Stage 2 <br /> <br />1721485146050 R U R’ U R UU R’ <br />13404851174753293110146050<br />Stage 3<br /> <br /> L’ U R U’ L UU R’ U R UU R’ <br />423355314923427787601327151292860133985 <br /> <br /> <br /> FF U’ L R’ FF L’ R U’ FF<br />27787605715420490165474129286045720<br /> Stage 4 <br /> FF U L R’ FF L’ R U FF<br />422179786043 <br />12928600<br /> <br />4202747152718 MM U MM UU MM U MM <br />1264285118110<br /> <br /> M2 U M2 U M’ U2 M2 U2 M’ U2 <br />323596020320129286020320 <br /> FINISH <br /> <br /> <br />6.2 Summary - List of Practical Minimum Formula (solution for 3rd Layer).<br />BriefsFormulae / StepsDiagrams1. FURF U R U’ R’ F’2429510123190195453012319014795501231901004570123190529590123190501651149352. FRUF R U R’ U’ F’2429510121285195453012128514795501212851004570121285529590121285501651155703. FISH (F)R U R’ U R UU R’ 19545301187451479550118745100457011874552959011874554610118745998855666755238756667548895666754. LRL’ U R U’ L U R’29044901333524295101333519500858255147955013335100457013335529590133355016582555. LRF Combinationof 4 & 3L’ U R U’ L UUR’ U R UU R’ 230632052451018313405245101475105524510100012552451052514552451048895527050278003069850242379569850194881569850147383569850998855698505238756985050165673106. Y (+ve) 7. Y (-ve)Clockwise:FF U L R’ FF L’ R U FFAnti Clockwise:FF U’ L R’ FF L’ R U’ FFClockwise:21863053746518300703746513563603048088011037465405130374654889537465 488951549401355090154940523875154940998855154940Anti Clockwise:21863051219201830070121920135509012192048895121920405130121920881380114935 1355090850901000125781055238758509048895850908. H 9. D M2 U M2 U2 M2 U M2 M2 U M2 U M’ U2 M2 U2 M’ U2 <br /> Notes : i) L’ U R U’ L UU R’ U R UU R’ - used frequently. <br /> ii) Brief Column above – it’s my idea to make “Life Easier”.<br /> By, JURIM_SARAMBUNG @PUWORK2010<br />