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Breaking an Old Code -And Beating It to Pieces
Breaking an Old Code -And beating it to pieces Daniel Vu - 1 - Table of Contents About the Author................................................ - 4 - Notation ............................................................... - 5 - Time for Some Cube Math........................................................................... Error! Bookmark not defined. Layer By Layer Method................................... - 10 - Step One- Cross .................................................................................................................................. - 10 - Step Two- Solving the White Corners ................................................................................................. - 11 - Step Three- Solving the Middle Layer................................................................................................. - 11 - Step Four- Orient the Yellow Edges.................................................................................................... - 12 - Step Five- Corner Orientation ............................................................................................................ - 12 - Step Six- Corner Permutation ............................................................................................................. - 13 - Step Seven- Edge Permutation............................................................................................................ - 14 - The Petrus Method........................................... - 17 - Step One- Creating the 2x2x2 Block .................................................................................................. -
How to Solve the Rubik's Cube 03/11/2007 05:07 PM
How to Solve the Rubik's Cube 03/11/2007 05:07 PM Rubik's Revolution Rubik's Cubes & Puzzles Rubik Cube Boston's Wig Store Everything you wanted to know Rubiks Cube 4x4, Keychain & Huge selection of Rubik Cube Great selection & service Serving about the all new electronic Twist In Stock Now-Free Shipping items. the Boston area Rubik’s cube Over $75 eBay.com www.mayswigs.com www.rubiksrevolution.com AwesomeAvenue.biz Ads by Goooooogle Advertise on this site How to Solve the Rubik's Cube This page is featured under Recreation:Games:Puzzles:Rubik's Cube:Solutions in Yahoo! My Home Page | My Blog | My NHL Shootout Stats 2006-2007 There are three translations of this page: Danish (Dansk) (Word Document), Japanese (日本語) (HTML) and Portuguese (Português) (HTML). If you want to translate this page, go ahead. Send me an email when you are done and I will add your translation to this list. So you have a Rubik's Cube, and you've played with it and stared at it and taken it apart...need I go on any further? The following are two complete, fool-proof solutions to solving the cube from absolutely any legal position. Credit goes not to me, but to David Singmaster, who wrote a book in 1980, Notes on Rubik's Magic Cube, which explains pretty much all of what you need to know, plus more. Singmaster wrote about all of these moves except the move for Step 2, which I discovered independently (along with many other people, no doubt). I've updated this page to include a second solution to the cube. -
Rubik's Cube Solutions
Rubik’s Cube Solutions Rubik’s Cube Solution – Useful Links http://www.geocities.com/jaapsch/puzzles/theory.htm http://www.ryanheise.com/cube/ http://peter.stillhq.com/jasmine/rubikscubesolution.html http://en.wikibooks.org/wiki/How_to_solve_the_Rubik's_Cube http://www.rubiks.com/World/~/media/Files/Solution_book_LOW_RES.ashx http://helm.lu/cube/MarshallPhilipp/index.htm Rubik’s Cube in a Scrambled State Rubik’s Cube in a Solved State – CubeTwister Front: Red, Right: Yellow, Up: Blue Back: Orange, Down: Green, Left: White Cube Colors: Red opposed to Orange, Yellow opposed to White, Blue opposed to Green Rubik’s Cube Solutions 06.12.2008 http://www.mementoslangues.fr/ Rubik’s Cube Commutators and Conjugates Introduction A Commutator is an algorithm of the form X Y X' Y', and a conjugate is an algorithm of the form X Y X', where X and Y denote arbitrary algorithms on a puzzle, and X', Y' denote their respective inverses. They are formal versions of the simple, intuitive idea of "do something to set up another task which does something useful, and undo the setup." Commutators can be used to generate algorithms that only modify specific portions of a cube, and are intuitively derivable. Many puzzle solutions are heavily or fully based on commutators. Commutator and Conjugate Notation [X, Y] is a commonly used notation to represent the sequence X Y X' Y'. [X: Y] is a well-accepted representation of the conjugate X Y X'. Since commutators and conjugates are often nested together, Lucas Garron has proposed the following system for compact notation: Brackets denote an entire algorithm, and within these, the comma delimits a commutator, and a colon or a semicolon a conjugate. -
Rubik's Cube Study
Rubik’s Cube Study Hwa Chong Institution (High School) Project Work 2020 - Category 8 (Mathematics) Written Report Group 8-21 1A1 - Alastair Chua Wei Jie (1) - Leader 1P2 - John Pan Zhenda (11) - Member 1P2 - Li Junle Tristen (16) - Member 1 Contents 1.0 Introduction 3 1.1 Rationale 3 1.2 Research Questions 3 2.0 Mechanics 3 2.0.1 Orientation of Colours 4 2.1 Notations 4 2.2 Intended Methodology 5 3.0 Literature Review 5 3.0.1 History of Rubik’s Cube 6 3.1 Background 7 4.0 Findings 8 4.1 Factors Affecting Speedcubing 8 4.2 Discovery of God’s Number 9 4.3 Formation of Algorithms 11 5.0 Conclusions 12 6.0 Possibility of Project Extension 13 7.0 References 13 2 1.0 Introduction The Rubik’s Cube has been a very well-known toy for several years, challenging for most, but a piece of cake for the intelligent few. As of January 2009, 350 million cubes had been sold worldwide, thus widely regarded as the world’s best selling toy. It is a 3D combination puzzle invented in 1974, by Ernö Rubik. 1.1 Rationale The Rubik’s Cube is not only a three-dimensional puzzle to toy with for fun, but also a source of mathematical concepts and calculations. Through this project, we intend to learn more about the mechanics of the Rubik’s Cube, and get more in-depth knowledge about how it works and the mathematics behind it. We also aim to discover more about the different types of cubes, including studying their mechanisms and algorithms. -
The Interpretation of Sustainability Criteria Using Game Theory Models (Sustainable Project Development with Rubik’S Cube Solution)
The Interpretation of Sustainability Criteria using Game Theory Models (Sustainable Project Development with Rubik’s Cube Solution) The Interpretation of Sustainability Criteria using Game Theory Models (Sustainable Project Development with Rubik’s Cube Solution) DR. CSABA FOGARASSY Budapest, 2014 Reviewers: Prof. István Szűcs DSc., Prof. Sándor Molnár PhD. L’Harmattan France 7 rue de l’Ecole Polytechnique 75005 Paris T.: 33.1.40.46.79.20 L’Harmattan Italia SRL Via Bava, 37 10124 Torino–Italia T./F.: 011.817.13.88 © Fogarassy Csaba, 2014 © L’Harmattan Kiadó, 2014 ISBN 978-963-236-789-7 Responsible publiser: Ádám Gyenes L’Harmattan Liberary Párbeszéd könyvesbolt 1053 Budapest, Kossuth L. u. 14–16. 1085 Budapest, Horánszky u. 20. Phone: +36-1-267-5979 www.konyveslap.hu [email protected] www.harmattan.hu Cover: RICHÁRD NAGY – CO&CO Ltd. Printing: Robinco Ltd. Executive director: Péter Kecskeméthy I dedicate this book to the memory of my cousin, IT specialist and physicist Tamás Fogarassy (1968-2013) Table of contents ABSTRACT. 11 1. INTERPRETATION OF SUSTAINABILITY WITH BASIC GAME THEORY MODELS AND RUBIK’S CUBE SYMBOLISM. 14 1.1. SUSTAINABILITY DILEMMAS, AND QUESTIONS OF TOLERANCE. 14 . 14 1.1.2. Ecologic economy versus enviro-economy �������������������������������������������������������������������������������������������17 1.1.1. Definition of strong and weak sustainability 1.1.3. Relations between total economic value and sustainable economic value . 17 1.2. THEORY OF NON-COOPERATIVE GAMES . 19 1.2.1. Search for points of equilibrium in non-cooperative games ����������������������������������������������������������20 . 23 ����26 1.2.2. Theoretical correspondences of finite games 1.2.3.1. Games with a single point of equilibrium . -
Karisma Bayu Cipta Wijaya-150210101014.Pdf
DigitalDigital RepositoryRepository UniversitasUniversitas JemberJember PENGEMBANGAN ALGORITMA PENYELESAIAN RUBIK STANDAR DALAM BENTUK GRAF BERARAH SKRIPSI Oleh Karisma Bayu Cipta Wijaya NIM 150210101014 PROGRAM STUDI PENDIDIKAN MATEMATIKA JURUSAN PENDIDIKAN MIPA FAKULTAS KEGURUAN DAN ILMU PENDIDIKAN UNIVERSITAS JEMBER 2019 DigitalDigital RepositoryRepository UniversitasUniversitas JemberJember HALAMAN JUDUL PENGEMBANGAN ALGORITMA PENYELESAIAN RUBIK STANDAR DALAM BENTUK GRAF BERARAH SKRIPSI diajukan guna melengkapi tugas akhir dan memenuhi salah satu syarat untuk menyelesaikan Program Studi Pendidikan Matematika (S1) dan mencapai gelar Sarjana Pendidikan Oleh: Karisma Bayu Cipta Wijaya NIM 150210101014 PROGRAM STUDI PENDIDIKAN MATEMATIKA JURUSAN PENDIDIKAN MIPA FAKULTAS KEGURUAN DAN ILMU PENDIDIKAN UNIVERSITAS JEMBER 2019 ii DigitalDigital RepositoryRepository UniversitasUniversitas JemberJember HALAMAN PERSEMBAHAN Puji syukur kehadirat Allah SWT atas segala rahmat dan karunia-Nya, sehingga skripsi ini dapat terselesaikan. Skripsi ini saya persembahkan kepada: 1. Kedua orangtua saya yang tercinta, terima kasih untuk dukungan, motivasi, doa serta kasih sayang yang tidak pernah pudar; 2. Kakak dan adikku, serta keluarga besar bapak dan ibuku, terima kasih atas motivasi dan doa untuk saya selama ini; 3. Bapak dan Ibu Dosen Pendidikan Matematika yang telah membagikan ilmu dan pengalamannya; 4. Bapak dan Ibu Guru SDN Kepatihan 1 Jember, SMPN 2 Jember, dan SMAN 2 Jember yang telah mencurahkan ilmu, bimbingan, dan kasih sayangnya dengan tulus ikhlas; 5. Almamaterku tercinta Universitas Jember, khususnya Program Studi Pendidikan Matematika, Fakultas Keguruan dan Ilmu Pendidikan (FKIP). 6. Sahabat-sahabatku (Ida Ulan Asih, Kevin Dwi Wicaksono, Inggil Ismiharto, M. Taufik Hidayat, Lendi Ike Hermawan, Dodi Pratama, Kukuh Sahrianto, Yuris Mimbadri, Dwita Sari Oktavia, Rosalia Indah, Moch Yusup Ade, Keluarga Besar Logaritma, Keluarga Besar Paranada dan teman-teman yang selalu mendukung saya). -
Rubik's Cube - Wikipedia, the Free Encyclopedia 5/11/11 6:47 PM Rubik's Cube from Wikipedia, the Free Encyclopedia
Rubik's Cube - Wikipedia, the free encyclopedia 5/11/11 6:47 PM Rubik's Cube From Wikipedia, the free encyclopedia The Rubik's Cube is a 3-D mechanical puzzle invented in Rubik's Cube 1974[1] by Hungarian sculptor and professor of architecture Ernő Rubik. Originally called the "Magic Cube",[2] the puzzle was licensed by Rubik to be sold by Ideal Toy Corp. in 1980[3] and won the German Game of the Year special award for Best Puzzle that year. As of January 2009, 350 million cubes have sold worldwide[4][5] making it the world's top-selling puzzle game.[6][7] It is widely considered to be the world's best-selling toy.[8] In a classic Rubik's Cube, each of the six faces is covered by nine stickers, among six solid colours (traditionally white, red, blue, orange, green, and yellow).[9] A pivot mechanism enables each face to turn independently, thus mixing up the Other names Magic Cube colours. For the puzzle to be solved, each face must be a Type Puzzle solid colour. Similar puzzles have now been produced with various numbers of stickers, not all of them by Rubik. The Inventor Ernő Rubik original 3×3×3 version celebrated its thirtieth anniversary in Company Ideal Toy Corporation 2010.[10] Country Hungary Availability 1974–present Contents Official website (http://www.rubiks.com/) 1 Conception and development 1.1 Prior attempts 1.2 Rubik's invention 1.3 Patent disputes 2 Mechanics 3 Mathematics 3.1 Permutations 3.2 Centre faces 3.3 Algorithms 4 Solutions 4.1 Move notation 4.2 Optimal solutions 5 Competitions and records 5.1 Speedcubing competitions 5.2 Records 6 Variations 6.1 Custom-built puzzles 6.2 Rubik's Cube software 7 Popular culture 8 See also 9 Notes http://en.wikipedia.org/wiki/Rubik's_Cube Page 1 of 13 Rubik's Cube - Wikipedia, the free encyclopedia 5/11/11 6:47 PM 10 References 11 External links Conception and development Prior attempts In March 1970, Larry Nichols invented a 2×2×2 "Puzzle with Pieces Rotatable in Groups" and filed a Canadian patent application for it. -
Resolución Del Cubo De Rubik
Resolución del cubo de Rubik Ignacio Alonso Muñoz Maxi Arévalo Garbayo Víctor Collado Negro Ingeniero de Telecomunicación Ingeniero de Telecomunicación Ingeniero de Telecomunicación Universidad Carlos III de Madrid Universidad Carlos III de Madrid Universidad Carlos III de Madrid Avda. Universidad, 30. 28911, Madrid Avda. Universidad, 30. 28911, Madrid Avda. Universidad, 30. 28911, Madrid +34 646120451 +34 660972878 +34 625095620 [email protected] [email protected] 100038943alumnos.uc3m.es RESUMEN 2. HISTORIA Este artículo trata sobre el invento del escultor y arquitecto Ern 2.1 Invento Rubik, el mundialmente conocido Cubo de Rubik. En el comentaremos El famoso cubo de Rubik fue inventado en la larga historia de este famoso “juguete”, además de tratar de explicar el año 1974 por un profesor de los diferentes algoritmos de resolución. Arquitectura de la Universidad de Budapest, en Hungría, llamado Erno Categorías y Descriptores del Tema Rubik, quien lo bautizó originalmente F.2.m [Theory of Computation]: Analysis Of Algorithms And como el Cubo Mágico. Después de Problem Complexity – Miscellaneous. terminar sus estudios, se quedó en la academia para dar clases de Diseño de Interiores. Como maestro, Erno Rubik Términos Generales prefería comunicar sus ideas utilizando Algoritmos, Lenguajes, Programación. modelos reales, hechos de papel, cartón, Figura 1. madera o plástico, desafiando a sus Erno Rubik Palabras Clave estudiantes a experimentar mediante la Cubo de Rubik, Esquina, Arista, Centro, Ern Rubik, Jessica Fridrich, manipulación de formas claramente construidas y fáciles de interpretar. Lars Petrus. Esto le permitió darse cuenta que aún los elementos más simples, manipulados inteligentemente, daban una abundancia de múltiples 1. -
Preface Preface Preface
CubeRoot Preface Preface Preface The Rubiks cube is a Combination puzzle in the shape of a cube that is cut two times along each of three axes. It is invented in 1974 by Ernő Rubik, which is the best-selling toy in history. Since 2003, WCA (World Cube Association), the official ruling and organizing entity for speedsolving Rubiks Cube and other puzzles, has organized competitions worldwide and recognize world records. From around 2007 the cubing community has seen the development of speedcubes made in China like Qiyi, GAN, Moyu, Yuxin. This puzzle consists of 6 faces, each with 9 colored facets. From another aspect, it has 6 fixed centers, 12 edges, 8 corners, and a total of 43,252,003,274,489,856,000 positions. A solved cube has all facets on each face with the same color. The cube move F,, BU , DLR ,, rotates the front, back, upper, down, left, right face 90 degree turn clockwise, respectively. A letter followed by a prime () symbol denotes a 90 degree turn counterclockwise. A letter followed by a 2 denotes a double turn of that face. CFOP method (Cross – F2L – OLL – PLL), the most commonly used speedsolving method for 3x3, heavily relies on algorithms, pattern recognition and muscle memory compared to more intuitive methods such as Roux, ZZ or Petrus method. It was first developed in the early 1980s combining innovations by a number of cubers. Jessica Fridrich popularized it by publishing it online in 1997. Its average number of moves is 56. Gods Number is either used to refer to the diameter of the group of the puzzle (the furthest distance two states can be from each other) or to the furthest distance any position can be from solved. -
Jessica Fridrich
Rubik's cube 11/25/11 10:51 AM My speed cubing page This is a copy of Ernö Rubik's signature as it appears in my notebook. He signed it at the World Championship in Budapest in 1982 This system for advanced cubers and is not appropriate for a beginner. It is intended for those of you who can already solve the cube in a few minutes and want to get really fast. If you are a complete beginner, please, visit Jasmine's Beginner Solution. My system for solving Rubik's cube Unique features The first two layers (additional useful hints and examples of how I solve the first two layers) The last layer 20 years of speed cubing (a short historical narrative) Watch me solving the cube Hints for speed cubing Customizing algorithms Multiple algorithms Finger shortcuts Move algorithms to your subconsciousness No delays between algorithms Faster twisting does not have to mean shorter times Preparing the cube for record times Hard work What are the limits of speed cubing? Collections of various algorithms (by Mirek Goljan, mgoljan (AT) binghamton. edu) Swapping two edges and two corners http://ws2.binghamton.edu/fridrich/cube.html Page 1 of 2 Rubik's cube 11/25/11 10:51 AM Swaping two and two edges Twisting and moving corners and edges in one layer (by Mirek Goljan, mgoljan (AT) binghamton. edu) Pretty patterns by Mirek Goljan, mgoljan (AT) binghamton. edu Richard Carr is THE expert on solving large cubes with a list of his record times. Richard can solve the cube blindfolded and willingly shares with us his method. -
Syllabus Draft
5 SPEEDCUBING: HISTORY, THEORY, AND PRACTICE Syllabus, Fall 2009 Instructor: Lucas Garron Email: - Class Meeting Time: Undetermined (tentatively, late afternoon/evening, 2 hours) Office Hours: Cube Club Meetings and by appointment COURSE DESCRIPTION Speedcubing is the modern sport revolving around solving the Rubik's Cube quickly. In this course, we will cove the history of the cube and what led to its current status. We will also look at the current cubing community, as well as topics like basic math theory about the cube. Students will learn to solve a cube, and will be introduced to concepts and resources that can help them improve their speedsolving skill. GRADING This course is only offered for one unit, Pass/No Credit. In order to receive a passing grade in the course, each student will be expected to: • Attend and participate in class (no more than two unexcused absences). • Complete the readings/homework, and discuss them in class. • Complete ONE of the following and give a short presentation about it to the class: ◦ A research project on a person associated with the cube. ◦ A short research paper on an aspect of the Cube (approved topic). ◦ Learn a significantly advanced system for the Rubik's cube (will be reviewed for effort). Examples: Blindfolded Solving, Petrus, Heise, Roux, ... ◦ A multimedia/programming project for the Cube. ◦ A self-proposed project that involves specific research or work. Note: Students will learn to solve a Rubik's Cube, but solving a cube is not a requirement for passing the course. Students are also encouraged to attend cube club meetings and participate in the Stanford Fall Competition. -
The Ultimate Solution to Rubik's Cube
RUBIK's CUBE: THE ULTIMATE SOLUTION 02/10/2007 11:53 AM THE ULTIMATE SOLUTION TO RUBIK'S CUBE A unique solution using only two series Requires only 65 moves to solve a scrambled Rubik's Cube This site also contains solutions to 2x2x2 cubes 3x3x3 cubes with images 4x4x4 cubes 5x5x5 cubes dodecahedron The Ultimate Solution to Rubik's Cube The Edge Piece Series The Corner Piece Series Step One: The Cross Step Two: Center Section Edge Pieces Step Three: Top Edge Pieces Step Four: Five Corner Pieces Step Five: The End Game http://helm.lu/cube/MarshallPhilipp/ Page 1 of 2 RUBIK's CUBE: THE ULTIMATE SOLUTION 02/10/2007 11:53 AM The Ultimate Solution to Rubik's Pocket Cube The Ultimate Solution to Rubik's Cube with Oriented Images The Ultimate Solution to Rubik's Revenge The Ultimate Solution to The Professor Cube The Ultimate Solution to Megaminx Other Puzzles A Comparison of Various Methods If you have mastered The Ultimate Solution to Rubik's Cube and also solved scrambled versions of the other cubes given above, then perhaps you are ready for a still more challenging puzzle. In theory one can design a true four dimensional analog of Rubik's Cube (3x3x3x3). While one cannot make a working model of this puzzle in the real world, one can project its image into three dimensions which can then be displayed, manipulated and solved using standard 3D computer graphics You can find MAGIC CUBE 4D on the web. It was designed and constructed over a period of several years by Daniel Green and Don Hatch with later help from E.