Rubik's Cube and Others from Puzzle Master 6/27/10 3:37 PM

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002-Contents.Pdf
CubeRoot Contents Contents Contents Purple denotes upcoming contents. 1 Preface 2 Signatures of Top Cubers in the World 3 Quotes 4 Photo Albums 5 Getting Started 5.1 Cube History 5.2 WCA Events 5.3 WCA Notation 5.4 WCA Competition Tutorial 5.5 Tips to Cubers 6 Rubik's Cube 6.1 Beginner 6.1.1 LBL Method (Layer-By-Layer) 6.1.2 Finger and Toe Tricks 6.1.3 Optimizing LBL Method 6.1.4 4LLL Algorithms 6.2 Intermediate 进阶 6.2.1 Triggers 6.2.2 How to Get Faster 6.2.3 Practice Tips 6.2.4 CN (Color Neutrality) 6.2.5 Lookahead 6.2.6 CFOP Algorithms 6.2.7 Solve Critiques 3x3 - 12.20 Ao5 6.2.8 Solve Critiques 3x3 - 13.99 Ao5 6.2.9 Cross Algorithms 6.2.10 Xcross Examples 6.2.11 F2L Algorithms 6.2.12 F2L Techniques 6.2.13 Multi-Angle F2L Algorithms 6.2.14 Non-Standard F2L Algorithms 6.2.15 OLL Algorithms, Finger Tricks and Recognition 6.2.16 PLL Algorithms and Finger Tricks 6.2.17 CP Look Ahead 6.2.18 Two-Sided PLL Recognition 6.2.19 Pre-AUF CubeRoot Contents Contents 7 Speedcubing Advice 7.1 How To Get Faster 7.2 Competition Performance 7.3 Cube Maintenance 8 Speedcubing Thoughts 8.1 Speedcubing Limit 8.2 2018 Plans, Goals and Predictions 8.3 2019 Plans, Goals and Predictions 8.4 Interviewing Feliks Zemdegs on 3.47 3x3 WR Single 9 Advanced - Last Slot and Last Layer 9.1 COLL Algorithms 9.2 CxLL Recognition 9.3 Useful OLLCP Algorithms 9.4 WV Algorithms 9.5 Easy VLS Algorithms 9.6 BLE Algorithms 9.7 Easy CLS Algorithms 9.8 Easy EOLS Algorithms 9.9 VHLS Algorithms 9.10 Easy OLS Algorithms 9.11 ZBLL Algorithms 9.12 ELL Algorithms 9.13 Useful 1LLL Algorithms
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Mathematics of the Rubik's cube Associate Professor W. D. Joyner Spring Semester, 1996{7 2 \By and large it is uniformly true that in mathematics that there is a time lapse between a mathematical discovery and the moment it becomes useful; and that this lapse can be anything from 30 to 100 years, in some cases even more; and that the whole system seems to function without any direction, without any reference to usefulness, and without any desire to do things which are useful." John von Neumann COLLECTED WORKS, VI, p. 489 For more mathematical quotes, see the ﬁrst page of each chapter below, [M], [S] or the www page at http://math.furman.edu/~mwoodard/mquot. html 3 \There are some things which cannot be learned quickly, and time, which is all we have, must be paid heavily for their acquiring. They are the very simplest things, and because it takes a man's life to know them the little new that each man gets from life is very costly and the only heritage he has to leave." Ernest Hemingway (From A. E. Hotchner, PAPA HEMMINGWAY, Random House, NY, 1966) 4 Contents 0 Introduction 13 1 Logic and sets 15 1.1 Logic................................ 15 1.1.1 Expressing an everyday sentence symbolically..... 18 1.2 Sets................................ 19 2 Functions, matrices, relations and counting 23 2.1 Functions............................. 23 2.2 Functions on vectors....................... 28 2.2.1 History........................... 28 2.2.2 3 × 3 matrices....................... 29 2.2.3 Matrix multiplication, inverses.............. 30 2.2.4 Muliplication and inverses...............
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General Information Project Details
MATH 304 FINAL TERM PROJECT General Information There will be no written final exam in Math 304, instead each student will be responsible for researching and producing a final project. You are to work in groups consisting of a maximum of 5 students. Short presentations will be held during the final weeks of classes. The ultimate goal is for you to have a truly enjoyable time working on your course term project. I want you to produce something that you will be proud to show your friends and family about what you’ve learned by taking this course. The expectation is that every student will wholeheartedly participate in their chosen project, and come away with some specialized knowledge for the area chosen to investigate. I expect you to let your imagination flourish and to use your familiarity with contemporary technology and both high- and pop-culture to create a product that you will be proud of for years to come. Project Details Your project should have a story/application/context that is explainable to an audience of your classmates, and include a connection to content covered in this course. The mathematical part of your poster must include an interpretation of the mathematical symbols used within your story, and a statement of a theoretical or computational result. In short, be sure your project has (i) math, and (ii) is connected to the course in some way. Here are some examples of possible topics: 1. Analyze another twisty puzzle (not the 15-puzzle, Oval Track, Hungarian Rings, or Rubik’s cube). Come up with a solvability criteria (i.e.
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Permutation Puzzles a Mathematical Perspective
Permutation Puzzles A Mathematical Perspective Jamie Mulholland Copyright c 2021 Jamie Mulholland SELF PUBLISHED http://www.sfu.ca/~jtmulhol/permutationpuzzles Licensed under the Creative Commons Attribution-NonCommercial-ShareAlike 4.0 License (the “License”). You may not use this document except in compliance with the License. You may obtain a copy of the License at http://creativecommons.org/licenses/by-nc-sa/4.0/. Unless required by applicable law or agreed to in writing, software distributed under the License is dis- tributed on an “AS IS” BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. See the License for the specific language governing permissions and limitations under the License. First printing, May 2011 Contents I Part One: Foundations 1 Permutation Puzzles ........................................... 11 1.1 Introduction 11 1.2 A Collection of Puzzles 12 1.3 Which brings us to the Definition of a Permutation Puzzle 22 1.4 Exercises 22 2 A Bit of Set Theory ............................................ 25 2.1 Introduction 25 2.2 Sets and Subsets 25 2.3 Laws of Set Theory 26 2.4 Examples Using SageMath 28 2.5 Exercises 30 II Part Two: Permutations 3 Permutations ................................................. 33 3.1 Permutation: Preliminary Definition 33 3.2 Permutation: Mathematical Definition 35 3.3 Composing Permutations 38 3.4 Associativity of Permutation Composition 41 3.5 Inverses of Permutations 42 3.6 The Symmetric Group Sn 45 3.7 Rules for Exponents 46 3.8 Order of a Permutation 47 3.9 Exercises 48 4 Permutations: Cycle Notation ................................. 51 4.1 Permutations: Cycle Notation 51 4.2 Products of Permutations: Revisited 54 4.3 Properties of Cycle Form 55 4.4 Order of a Permutation: Revisited 55 4.5 Inverse of a Permutation: Revisited 57 4.6 Summary of Permutations 58 4.7 Working with Permutations in SageMath 59 4.8 Exercises 59 5 From Puzzles To Permutations .................................
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Adventures in Group Theory: Rubik's Cube, Merlin's Machine, and Other
Adventures in Group Theory: Rubik’s Cube, Merlin’s Machine, and Other Mathematical Toys David Joyner 5-15-2008 In mathematics you don’t understand things. You just get used to them. Johann von Neumann v Contents Preface ................................................... ................ix Acknowledgements ................................................... xiii Where to begin ................................................... .xvii Chapter 1: Elementary my dear Watson ................................1 Chapter 2: And you do addition? .......................................13 Chapter 3: Bell ringing and other permutations ......................37 Chapter 4: A procession of permutation puzzles ......................61 Chapter 5: What’s commutative and purple? .........................83 Chapter 6: Welcome to the machine ..................................123 Chapter 7: ‘God’s algorithm’ and graphs .............................143 Chapter 8: Symmetry and the Platonic solids .......................155 Chapter 9: The illegal cube group ....................................167 Chapter 10: Words which move .......................................199 Chapter 11: The (legal) Rubik’s Cube group ........................219 Chapter 12: Squares, two faces, and other subgroups ...............233 Chapter 13: Other Rubik-like puzzle groups .........................251 Chapter 14: Crossing the rubicon .....................................269 Chapter 15: Some solution strategies .................................285 Chapter 16: Coda: questions and other directions
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Platonic Solids and Rubik's Cubes*
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A Variation on the Rubik's Cube
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Polish Speedcubing Tour LLS Lublin 2020 Jan 4 - 5, 2020
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Wca-Regulations-And-Guidelines.Pdf
WCA Regulations and Guidelines WCA Regulations Committee WCA Regulations Version: January 1, 2014 Notes WCA Regulations and Guidelines The WCA Regulations contains the full set of Regulations that apply to all official competitions sanctioned by the World Cube Association. The WCA Regulations are also supplemented by the WCA Guidelines. The Regulations should be considered a complete document, but the Guidelines contain additional clarifications and ex- planations. Wording To make the Regulations and Guidelines easier to read we use \he" where the reader should read \she or he". Uses of the words \must", \must not", \should", \should not" and \may" match RFC 2119. Information on the Internet Website of World Cube Association: www.worldcubeassociation.org Original source of the WCA regulations: www.worldcubeassociation.org/regulations WCA Regulations in PDF format Source Development of the WCA Regulations and Guidelines is public on GitHub. Contact For questions and feedback, please contact the WCA Regulations Committee (WRC). Contents Note: Because Article and Regulation numbers are not reassigned when Regulations are deleted, there may be gaps in numbering. 1 Article 1: Officials WCA REGULATIONS Article 1: Officials • 1a) A competition must include a WCA Delegate and an organisation team (consisting of one or more individuals) with the following officials: judges, scramblers and score takers. • 1b) The organisation team of a competition is responsible for logistics before, during, and after the competition. • 1c) The WCA Delegate may delegate responsibilities to other members of the organisation team, but is ultimately accountable for how these responsibilities are carried out. The WCA Delegate for a competition is responsible for: { 1c1) Reporting to the WCA Board regarding adherence to WCA Regulations during the competition, the overall course of the competition, and any incidents.
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Polish Speedcubing Tour Rzeszów 2019 Oct 5 - 6, 2019
Polish Speedcubing Tour Rzeszów 2019 Oct 5 - 6, 2019 II Liceum Ogólnokształcące im. płk. Leopolda Lisa-Kuli w Rzeszowie Księdza Józefa Jałowego 22, 35-010 Rzeszów (50.041041, 21.994628) Rzeszów, Poland Events Event Round Format Time limit Proceed First round Ao5 10:00.00 Top 25 Second round Ao5 10:00.00 Top 10 Final Ao5 10:00.00 First round Ao5 1:00.00 Top 20 Second round Ao5 1:00.00 Top 6 Final Ao5 1:00.00 Bo2 / Ao5 First round 3:00.00 Top 10 Cutoff: 1:00.00 Second round Ao5 3:00.00 Top 6 Final Ao5 3:00.00 Bo2 / Ao5 First round 4:00.00 Top 10 Cutoff: 1:45.00 Second round Ao5 4:00.00 Top 6 Final Ao5 4:00.00 Bo1 / Mo3 First round 7:00.00 Top 6 Cutoff: 3:15.00 Final Mo3 7:00.00 Bo1 / Mo3 First round 9:00.00 Top 6 Cutoff: 4:15.00 Final Mo3 9:00.00 First round Bo3 10:00.00 cumulative Top 8 Final Bo3 10:00.00 cumulative Bo2 / Ao5 First round 2:00.00 Top 8 Cutoff: 30.00 Final Ao5 2:00.00 Bo2 / Ao5 First round 2:00.00 Top 6 Cutoff: 20.00 Final Ao5 2:00.00 Bo2 / Ao5 First round 3:00.00 Top 8 Cutoff: 1:30.00 Final Ao5 3:00.00 Event Round Format Time limit Proceed First round Ao5 1:00.00 Top 20 Second round Ao5 1:00.00 Top 6 Final Ao5 1:00.00 First round Ao5 1:00.00 Top 20 Second round Ao5 1:00.00 Top 6 Final Ao5 1:00.00 Bo2 / Ao5 First round 2:00.00 Top 10 Cutoff: 35.00 Second round Ao5 2:00.00 Top 6 Final Ao5 2:00.00 Bo2 / Ao5 First round 4:00.00 Top 4 Cutoff: 2:00.00 Final Ao5 4:00.00 Schedule for Saturday (October 05, 2019) Start End Activity Format Time limit Proceed 09:00 AM 09:25 AM Registration 09:00 AM 09:25 AM Tutorial for
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Wca-Regulations-And-Guidelines.Pdf
WCA Regulations and Guidelines WCA Regulations Committee WCA Regulations Version: May 1, 2021 [official:7845f8d] Notes WCA Regulations and Guidelines The WCA Regulations contain the full set of Regulations that apply to all oﬃcial competitions sanctioned by the World Cube Association. The WCA Regulations are also supplemented by the WCA Guidelines. The Regulations should be considered a complete document, but the Guidelines contain additional clarifications and explanations. Wording Uses of the words "must", "must not", "should", "should not" and "may" match RFC 2119. Information on the Internet Website of World Cube Association: www.worldcubeassociation.org Original source of the WCA Regulations: www.worldcubeassociation.org/regulations WCA Regulations in PDF format Source Development of the WCA Regulations and Guidelines is public on GitHub and the discussion is public on the WCA Forum. Contact For questions and feedback, please contact the WCA Regulations Committee (WRC). Contents Note: Because Article and Regulation numbers are not reassigned when Regulations are deleted, there may be gaps in numbering. Article 1: Officials 1a) A competition must include a WCA Delegate and an organization team (consisting of one or more individuals) with the following officials: judges, scramblers and score takers. 1b) The organization team of a competition is responsible for logistics before, during, and after the competition. 1c) The WCA Delegate is responsible for ensuring that the competition adheres to the WCA Regulations and any applicable WCA policies or requirements. The WCA Delegate may appoint other members of the organization team to carry out specific responsibilities on their behalf, but is ultimately accountable for how these responsibilities are carried out.
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