Miscellaneous: September 2015

I. Introduction

From [2]:

‘How do I solve the Rubik’s Cube? It took Erno Rubik (the inventor of the Rubik’s Cube) one month to learn how to do a Rubik’s Cube. Some people started thinking about how to complete the Rubik’s Cube back in the 80’s, and in 40 years have got little further than one side. If you want to learn how to solve the Rubik’s Cube, look no further, you have come to the right place! Getting help with solving the Rubik’s Cube is not cheating. There are 42 Quintillion possibilities, but only one correct solution. Hence without knowing how to solve a Rubik’s Cube it is nearly impossible. This six step guide will take you through everything you need to know when it comes to solving the Rubik’s Cube. It is really simple, you just have to follow the steps and you will be solving the Rubik’s Cube in less than two minutes (yes, that quickly!). This guide on how to do the Rubik’s Cube will take about 45 minutes to learn, but once you have you can impress all your friends with how you can solve one of life’s great mysteries: how to do a Rubik’s Cube.

From [5]:

Most people solve the cube layer by layer. This is a simple way for the human mind to approach the problem, but it is useless for speed cubing. No matter how good you are, you will use more than 100 moves. Going for speed, I use 55-60 moves on average. Going for few moves, I average 40-45.
The basic problem with the layer method is big, and obvious once you realize it. When you have completed the first layer, you can do nothing without breaking it up. So you break it, do something useful, then restore it. Break it, do something, restore it. Again and again. In a good solution you do something useful all the time. The first layer is in the way of the solution, not a part of it!

For everything about Rubik's cube, see [7]. For a 3x3x3 cube, there are about 43 quintillion possible configurations, which is about 43 billion billion.

II. Solutions

Beginner's solutions to a 3x3x3 cube take over 100 steps, see [12][18] or Appendix 1.

The fastest solutions take less steps (~ 50 steps), see [5] (Petrus method) and [13] (CFOP/Fridrich method).

A relatively complete list of available algorithms is [17].

Some tips on speeding up: [14].

III. Community

For Rubik's Cube World Records, see [8][9].

IV. Mathematics

For optimal solutions of Rubik's Cube, see [10]. The lower bound is 18. The value for upper bound in face turn is called the "God's number' [11], which was found to be 26 in 2007, 22 in 2008, and finally 20 in 2010 (found in 2010 by Tomas Rokicki, Herbert Kociemba, Morley Davidson, and John Dethridge). Alternatively if use quarter turn, the upper bound is 26, found in 2014 by Tomas Rokicki and Morley Davidson.

V. Purchase

A China company that produces Rubik's cube for a long time is Shengshou (圣手魔方).

To help improving speed, you can buy "speedcubes", which is faster to turn and twist. Check out [15][16].

References

[1] http://www.youcandothecube.com/secret-unlocked/solution-stage-one.aspx
[2] http://rubiks.com/blog/how-to-solve-the-rubiks-cube
[3] How to solve the Rubik’s Cube - beginner's method
[4] Rubik's Cube 3x3x3 Solution (PDF)
[5] Solving Rubik's Cube for speed
[6] Solving the Rubik's Revenge (4x4x4)
[7] wiki: Rubik's Cube
[8] Rubik's Cube World Records
[9] Rubik's Cube World Records - World Cube Association
[10] Optimal solutions for Rubik's Cube
[11] God's_algorithm
[12] Rubik Cube Algorithms List for 3x3x3 cube
[13] How to Speedsolve the Rubik's Cube (the CFOP/Fridrich method)
[14] How to get your times closer to zero
[15] Mega Comparison - What cube is best for you?
[16] Buying a Rubik's Cube – The Best Speedcubes out There
[17] Solutions to the Rubik's Cube 3x3x3
[18] How to Solve a Rubik's Cube, Guide for Beginners
[19] Stefan Pochmann's Cube Corner

[20] 三阶魔方盲拧视频教程
[21] 魔方吧·中国魔方俱乐部专业的中文魔方资讯平台

Appendix 1. Beginner's solution from Shengshou's manual:

Step 1. Bottom white cross
WR/WR -> WW/RR: F' U L' U'

Step 2. Bottom white
White at:
Left: F' U' F
Right: R U R'
Top: R U U R' U' --> R U R'

Step 3. Mid-layer
To Right: U R U' R', U' F' U F
To Left: U' F' U F, U R U' R'

Step 4. Top yellow cross
Center/Upper Left 3/middle 3
F R U R' U' F'

Step 5. Top yellow
Top has 0 Yellow Corner (yellow Left)/1(corner Left)/2 (yellow F)
R U R' U, R U U R'

Step 6. Top corner
R B' R F, F R' B R, F F R R

Step 7. Top edge
R U' R U, R U R U', R' U' R R

Appendix 2. Advanced Algorithm (Algorithm optimization from Beginner's Algorithm)

Step 1. Bottom white cross
Rotate left: F' U L' U'
or Rotate right: F U' R U

Step 7. Top edge (2 Look PLL Algorithms)

Counter-clockwise (Ua Perm): same as beginner's method
Clock-wise (Ub Perm): Reverse of Ua: R R U R, U R' U' R', U' R' U R'
Swap (H perm): M2 U M2 U, U M2 U M2
Z perm: M2 U, M2 U, M' U2, M2 U2, M' U2

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Friday, September 18, 2015

How to solve the Rubik’s Cube

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