Rubik

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Rubiks Cube 101

• By Andy Camann

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How the Cube Works

• Taken apart, one can see that the cube consists
  of 6 centers, 8 corners, and 12 edges
• The centers are fixed on a central mechanism, so
  they dont move relative to each other
• The color of a center determines what color that
  face will be when the cube is completed

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Number of Configurations

• Simply put, there are
• configurations on the cube
• 43,252,003,274,489,856,000

(12! 212)(8! 38) 2 3 3
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43,252,003,274,489,856,000

• If one were to make one move every second, it
  would take 1,370,000,000,000 (1.37 trillion)
  years to reach every case, assuming no repeats
• That amount of time spans the age of the universe
  ten times
• If this person began to twist from the moment the
  dinos died out (65 MYA), he/she would have
  reached only 4.7 of all the cases
• If a cube existed for every configuration, and
  all were lined up next to each other, they would
  circle the earth five times
• That is 124,508 miles, or about half the distance
  from Earth to the moon

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What You Will Learn

• The method you will learn consists of 6 major
  steps, and each step is broken down into smaller
  steps
• 1. Top edges
• 2. Three Top Layer corners
• At this point, we have all but one top layer
  cubie solved
• 3. Three Middle Edges
• Now we (almost) have 2 layers done. Flip over the
  cube so the last layer (LL) is on top.
• 4. Solve the remaining corner and edge
• Now we have 2 layers (of three) solved.
• 5. Orient Last Layer (OLL)
• Edges first, then corners
• 6. Permute Last Layer (PLL)
• Again, edges first, then corners

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The Solution, Step by Step

• 1. Top Edges 4. Finish 2 Layers
• 2. Top Corners 5. Orient LL
• 3. Middle Edges 6. Permute LL

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Notation

• Everyone needs to know the notation used for
  cubing
• For example, what do these mean
• F (R U R U) F
• (R2 U)(R U R U)(R U)(R U R)
• x((R U)(R U))(D R Ds)(R U R)z((l R)U)
• (M U)4 (M U)4
• E M E M
• These are algorithms. Each letter represents a
  move to be carried out in sequence, and
  represents a face of the cube.
• There are 6 faces, named (F)ront, (B)ack, (U)p,
  (B)own, (R)ight, (L)eft. There are also 3 slices,
  named (M)iddle, (E)quator, (S)ide

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More Notation

• A lone letter means to turn that face 90º
  clockwise (CW) as if you were looking down at
  that face
• A letter followed by an apostrophe ( ) means to
  turn that face 90º counter-clockwise (CCW) as if
  you were looking down on that face
• A letter followed by a 2 means to turn that face
  180º

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Notation U and D
U U U2
D D D2
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Notation F and B
F F F2
B B B2
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Notation R and L
R R R2
L L L2
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Top Edges

• Also called the cross
• We will use orange as our top face
• This is the first step towards completing
• the top layer
• Complete one edge at a time
• Experienced cubers usually solve the cross
• consistently in 6 moves, lt 2 seconds
• Reasonable average is 15 moves, 10 seconds with
  some practice

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Cross - Details

• Oriented vs. non-oriented edge
• Your first goal is to locate an edge that makes
  up the cross
• This means that it has orange as one of its two
  stickers
• Remember that the center of a face determines
  what color it will be

lt-- Bad edge Good edge --gt
lt-- Bad cross Good cross --gt
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In case of a bad cross

• do the following
• Rotate the top layer until at least two of the
  edges are in place (you will always be able to
  get two)
• Match your cube with one of the following cases
• Execute the sequence to place the edges that are
  out of place

These two edges need to switch places
These two edges need to switch places
L R U2 L R
R U R U R
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Corners

• Solving the corners completes the top layer
• This step is easier than the cross since there
  are fewer possibilities

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Solving a Corner

• The only thing to keep in mind is you cant mess
  up the cross
• To make progress, you must temporarily disturb
  what you have already solved, then restore it
• Hopefully, when you restore a few solved pieces,
  progress gets made
• To solve a corner, find one that belongs in the
  top layer
• Move it directly beneath where it belongs

Corner belongs here Move corner to here
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Finding a Corner

• Remember that the centers dont move
• So the corner (which has three stickers) depends
  on the color of three centers
• So, the corner that belongs in this spot must be
  orange, green, and white
• This is the process used to figure out where a
  piece belongs
• Use it to figure out where any piece belongs

This must be orange This must be green
This must be white
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Three Possibilities

• Once you have a corner in the right spot in the
  bottom layer, you must determine its
  orientation.
• F D F R D R R
  D R F D2 F

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The Other Corners

• Follow this step for the other three corners
• When 3 corners are done, it should look like
  this

Its important to have the T on each face
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Middle Layer

• Flip over the cube so the top layer becomes the
  bottom layer

Hold cube so the edge will end up here, in FR
Make sure the empty corner is below the edge you
want to solve

• Find an edge that belongs in the middle layer

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Inserting an Edge

• There are two flips of an edge
• Thus there are two cases for inserting an edge

U F U F R U R

• Follow these steps until three of the middle
  edges are solved

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The Other 2 Edges

• Always hold the cube so the edge that you wish to
  solve will end up in FR
• This means you will have to change the
  orientation of the cube in your hands
• You will also need to rotate the bottom layer so
  the empty corner is just below where the edge is
  to be placed

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Top Layer

• At this point, 2/3 of the cube is done
• Last Layer Strategy
• 1. Orient Edges
• 2. Orient Corners
• 3. Permute Edges
• 4. Permute Corners

After orientation After permutation
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Orient Edges

• Three cases

A F U R U R F B F R U R U F
A U2 B
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Orient Corners

• Seven cases

R B L B R B L B R2 D R U2 R D R U2 R
L B R B L B R B
L U R U L U R R U L U R
U L
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Orient Corners
R U2 R2 U R2 U R2 U2 R R U R U R U
R U R U2 R
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Permute Edges

• Rotate the top layer until you have one of the
  following cases for edge permutation
• These two cases show that only one edge is
  permuted.
• It is possible that you wont encounter either of
  these cases in any particular solve. There is one
  other case

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Permutation

• You must learn at least one of the first two
  cases
• Breaking down each sequence into groups of fewer
  moves makes it easier to learn long sequences
• These two sequences are broken into groups
  (indicated by parentheses) that make learning
  them easier.

(R2 U) (F B) R2 (F B) (U R2) (R2 U) (F B) R2
(F B) (U R2)
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The Other Case

• In case you want to learn an extra sequence, here
  is the solution

(R B R B)(F R)(B F)(R B R)(F2 U)
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Permute Corners

• There are four possibilities for corner
  permutation
• Do not rotate the top layer like you did for
  edges (that would mess up the edges!)
• Here are the possibilities

Case 1 Case 2 Case 3 Case 4
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The Final Step

• You only need to learn one of these cases (either
  c1 or c2)
• They have similar solutions

R F R D2 R F R D2 R2 R B R F2 R B R F2
R2
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You Are Done!

• You now know the way to avoid nearly all of the
  43 quintillion combos of a cube
• Now you need to learn how to become faster by
  learning the following
• Finger tricks/triggers
• Lubing your cube
• Solve from bottom -gt top
• Learn all 57 orientations!
• Learn all 21 permutations!