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 – LFront – F Back – BVertical Middle – YHorizontal Middle – XVertical 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-CyclesIt 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. RU₋₁R₋₁YYRUR₋₁YY2. RU₋₁R₋₁Y₋₁RUR₋₁Y

Can you work out which cycle matches which diagram?

12

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!