# Rubik's Cube/Reference Summary

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+---------------------------------------------------------------------------------------------+ | HOW TO FIND YOUR VERY OWN PERSONAL WAYS TO SOLVE RUBIK'S CUBE | | (Preliminary April 20, 2007 version) | | by Mr. Ray Calvin Baker | | FREE Public Domain Educational Material | | | | Chapter Ten - - - - - - - - - - Reference Summary of Useful Operations | | | | In a "group", (and mathematical group theory is a part of finite discrete mathematics | | relevant to the solution of Rubik's Cube and many other puzzles) every operation has an | | inverse operation which undoes what that operation does. The most important operation in a | | group is the identity operation -- it does nothing at all! A Cube fresh from the factory | | represents the identity operation. Scrambling the Cube is another operation. Applying the | | inverse of that scrambling operation is your goal. It restores the Cube to its pristine | | condition, as if nothing at all had been done. | | | | Here is a reference summary of the most useful moves, as scribbled on my work sheets. | | | |---------------------------------------------------------------------------------------------| | | | INTERCHANGE THREE CORNER CUBIES | | | | _ a _ (h) _ a _ (*) _ g _ (*) _ g _ (h) | | b _ T _ c * _ T _ * * _ T _ * b _ T _ c | | | F d R | | F d R | "Fv R^ F^ Rv T2" | F a R | | F a R | | | e _ | _ f * _ | _ * ---------------> * _ | _ * e _ | _ f | | g g d d | | | |---------------------------------------------------------------------------------------------| | | | INTERCHANGE TWO CORNER CUBIES | | | | 1st: "Fv R^ F^ Rv T2" | | _ a _ (h) _ * _ (*) 2nd: "L^" _ * _ (*) _ a _ (h) | | b _ T _ c * _ T _ * 3rd: "Fv R^ F^ Rv T2" * _ T _ * b _ T _ c | | | F d R | | F d R | 4th: "Fv R^ F^ Rv T2" | F g R | | F g R | | | e _ | _ f * _ | _ * 5th: "Lv" * _ | _ * e _ | _ f | | g g 6th: "Rv Tv R^" d d | | ---------------> | | | |---------------------------------------------------------------------------------------------| | | | CHANGE ORIENTATION OF TWO CORNER CUBIES _ * _ Corner | | * _ 1 _ * cubie | | 1st: "Fv R^ Fv R^ Fv R^" | 3 * 2 | before... | | 0 0 0 0 0 2nd: "Fv R^ Fv R^ Fv R^" 0 + - 0 0 * _ | _ * | | 0 0 0 0 0 3rd: "Fv" 0 0 0 0 0 _ * _ * _ * _ | | [F] [k] 4th: "Fv R^ Fv R^ Fv R^" [F] [K] * _ 2 _ * * _ 3 _ * | | 5th: "F^" | 1 * 3 | | 2 * 1 | | | ------------------> * _ | _ * * _ | _ * | | * * | | ...after "+". ...after "-". | | | |---------------------------------------------------------------------------------------------| | | | INTERCHANGE THREE EDGE CUBIES | | | | +--+ +--+ +--+ +--+ +--+ +--+ +--+ +--+ | | | | |#3| | | |#2| Down-slice: "2R^ Rv" | | |#1| | | |#3| | | +--+--+--+--+--+--+--+--+--+ TOP twice: "T2" +--+--+--+--+--+--+--+--+--+ | | | | L| | F| | R| | K| | Up-slice: "2Rv R^" | | L| | F| | R| | K| | | | +--+--+--+--+--+--+--+--+--+ TOP twice: "T2" +--+--+--+--+--+--+--+--+--+ | | | | | | | | |#1| -------> | | | | | | |#2| | | +--+ +--+ +--+ +--+ +--+ +--+ +--+ +--+ | | | |---------------------------------------------------------------------------------------------| | | | CHANGE ORIENTATION OF TWO EDGE CUBIES | | | | Down-slice: "2R^ Rv" (Only the orientation of | | Turn TOP: "Tv" marked edge cubies | | Down-slice: "2R^ Rv" is changed -- "flipped",) | | +--+ +--+ +--+ +--+ Turn TOP: "Tv" +--+ +--+ +--+ +--+ | | | | |#3| | | |#2| Down-slice: "2R^ Rv" | | |#3| | | |#2| | | +--+--+--+--+--+--+--+--+--+ TOP twice "T2" +--+--+--+--+--+--+--+--+--+ | | | | L| | F| | R| | K| | Up-slice: "2Rv R^" | | L| | F| | R| | K| | | | +--+--+--+--+--+--+--+--+--+ Turn TOP: "Tv" +--+--+--+--+--+--+--+--+--+ | | | | | | | | | | Up-slice: "2Rv R^" | | | | | | | | | | +--+ +--+ +--+ +--+ Turn TOP: "Tv" +--+ +--+ +--+ +--+ | | Up-slice: "2Rv R^" (Rubik's Maneuver does not change | | TOP twice: "T2" position of any cubie.) | | | |---------------------------------------------------------------------------------------------| | | | Don't forget that you can use the ideas in Chapter Six, "Customize Your Moves -- | | Commutation", to "customize" these fundamental operations for those situations where the | | Cube you are working with doesn't quite agree with the diagrams! | | | | I hope this book has helped you to solve the Cube. But, even more, I hope it has | | encouraged you to seek and find more efficient methods -- YOUR VERY OWN PERSONAL WAYS | | TO SOLVE RUBIK'S CUBE. | | | | By the way, if you ever get tired of plain colors on all six sides of your Cube, you can | | look for "Pretty Patterns" to make your Cube look more decorative. Try | | "2R2 R2 2F2 F2 2T2 T2" for a start. Douglas Hofstadter invented an entire alphabet, | | so you can even make your Cube spell out messages (or at least your initials). | | | | Now you should be ready to write Chapter Eleven, "MY VERY OWN PERSONAL WAY TO SOLVE RUBIK'S | | CUBE"! Then we can all say, | | " The end. ". | | | +---------------------------------------------------------------------------------------------+