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The Rubik’s Cube What they’re really about

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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.

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The Cube Algorithms The notation:Up – UDown – D Right – RLeft – L Front – FBack – 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

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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.

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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)

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Edge 3-Cycles Another two cycles are: 1.RU₋₁R₋₁YYRUR₋₁YY 2.RU₋₁R₋₁Y₋₁RUR₋₁Y Can you work out which cycle matches which diagram? 12

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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.

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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.

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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 !

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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!

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Higher Dimensions. x Let's say we use a pencil to mark a point on paper. x is this point. We pick a direction and move the pencil along this direction.

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