The Rubik’s Cube
What they’re really about
Standard 3 x 3 Cube
• The 3x3 cube is the most common of all
Rubik’s cubes.
• The world record for the fastest ever solve is
7.08 seconds, by Erik Akkersdijk.
• The cube is solved using algorithms, rather
than “skill”, it is remembering that helps the
solution.
The Cube Algorithms
• The notation:
Up – U
Down – D
Right – R
Left – L
Front – F
Back – B
Vertical Middle – Y
Horizontal Middle – X
Vertical Horizontal – Z
A₋₁ = Anticlockwise turn 90⁰ (Where A = any letter
above)
Example: In this example,
RR ₋₁ = 1, so no change is made
Edge 3-Cycles
It is a necessity to know these to be able to
solve a Rubik’s cube. They usually involve
cyclic permutations of 3 edges. Repeating the
same cycle three times will return the cube to
the original state.
E.g: RU₋₁R₋₁YRUR₋₁Y₋₁
Represents: Cw Right, Acw Upper, Acw Right, Cw
Upper Middle, Cw Right, Cw Upper, Acw Right,
Acw Upper Middle.
Edge 3-Cycles
Or, in a picture form, represents the translation:
This is a common method of switching specific
pieces to specific places, as seen in the
diagram. (The edges are cycled)
Edge 3-Cycles
Another two cycles are:
1.
2.
RU₋₁R₋₁YYRUR₋₁YY
RU₋₁R₋₁Y₋₁RUR₋₁Y
2
1
Can you work out which cycle matches which diagram?
Corner Cycles
• A corner cycle is the process of moving two
corner pieces into different corners without
disrupting the state of the cube
• Although moving pieces for corner to corner
seems much simpler logically, mathematically,
it is a much more complex cycle.
• Similarly, repeating the cycle three times will
return the cube to the original state.
Corner Cycles
The first example of a Corner Cycle is:
FRF₋₁LFR₋₁F₋₁L₋₁
Can you translate this from Group Notation into
the separate turns required?
Note: Although there are several Corner Cycles,
it is possible to solve a Rubik’s cube knowing
only the one above.
Rubik’s Cube – World Domination
• Using the total 43,252,003,274,489,856,000
permutations of a cube (Different positions),
and then lining these permutations up, with
an average 57mm cube, there would be
enough cubes to cover the earth with 273
layers of Rubik’s cube.
• This is true even after the
57mm thickness of each
cube has been taken into
account !
The End
• Using the information in this presentation, you
should now be able to solve the basics of a
Rubik’s cube.
• Remember: It is a problem that requires the
memory of algorithms, not skill!