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## Selected Topics on the Rubik’s Cube

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**Selected Topics on the Rubik’s Cube**Ian Winokur Greenfield Community College winokuri@gcc.mass.edu Picture from Math Horizons, November 2010**Outline**• History of the cube • The cube in pop culture • Two solving methods • Some demonstration solves • Counting the number of possible scrambles • Videos that look fake but aren’t**History of the Rubik’s Cube**• Invented in 1974 by Erno Rubik, a Hungarian architect and professor. • The cube made its international debut in London, Paris, Nuremburg, and New York in 1980. • It’s popularity faded for a while but there has been a rebirth largely as a result of the internet.**They cube – so should you!**• See this guy do a complete solve on youtube! (1:20)**Solution Methods**• What’s an algorithm? • Basic commutator method: • Do something. We’ll call this A. • Then do something else. We’ll call this B. • Then undo the first something. This is A inverse. • Then undo the second something. This is B inverse. • Eg. Put on your socks, then put on your shoes,…**Solution Methods**• Lots of good beginner methods out there – youtube Tyson Mao or google Jasmine Lee. • Fridrich Method – the overwhelming favorite amongst speedcubers. • CFOP – manyalgorithmsrequired(41 + 57 + 21) • A virtual example solve (or two) • Me live!**How many different states of the cube?**• Virtual cube**Corners**• Orient them: 3*3*3*3*3*3*3*3 • Permute them: 8*7*6*5*4*3*2*1 • Multiply everything above: 3^8 * 8!**Edges**• Orient them: 2*2*2*2*2*2*2*2*2*2*2*2 • Permute them: 12*11*10*9*8*7*6*5*4*3*2*1 • Multiply everything above: 2^12 * 12!**Putting it all together**• Multiply all of the corner numbers by all of the edge numbers: 3^8 * 8! * 2^12 * 12! • Lots of good math reasons to divide by 12 • 3^8 * 8! * 2^12 * 12! / 12 = …**Number of Rubik’s Cube Scrambles**43,252,003,274,489,856,000**How big is 43 quintillion?**• Let’s calculate how many cubes it would take to cover the surface of the Earth: • The Rubik’s Cube measures 5.7 centimeters on a side so the area of one face is 5.7^2 or 32.49 square centimeters**How big is 43 quintillion?**• Radius of Earth = 6378.1 kilometers • Convert this to centimeters by multiplying by 100,000: • Radius of Earth = 637,810,000 centimeters • Surface area of a sphere = • Surface area of Earth =**How big is 43 quintillion?**• Summary: • The area of one face of the cube is • Surface area of Earth is • To find the number of cubes needed to cover the surface of the Earth, …**How big is 43 quintillion?**• Number of cubes to cover the Earth: 157,261,558,849,369,000 • Number of different cube scrambles: 43,252,003,274,489,900,000 • To find how many Earths we can cover with all those cubes…**Single Solve World Record Progression**• Erik Akkersdijk – 2008 (Netherlands) • Feliks Zemdegs – 2010 (Australia) • Feliks – later that same day • Feliks – 2010 • Feliks – 2011 • Feliks –2011 – slow motion • Feliks –2011**Facts about Feliks**• Feliks Zemdegs – Australian speedcuber • 15 years old • Complete domination on the 3x3x3**Bigger Cubes and Other Twisty Puzzles**• Cubes of size 2x2x2 through 7x7x7 are being mass produced and sold. • Google ‘Jaap’ for a nice site if you have a twisty puzzle you want to solve. • Feliks is the best or near the best in all of the cubes pictured!**Solving Variations**• Craziness – Gabriel Alejandro Orozco Casillas (Mexico) • Multi-craziness – Chester Lian (Malaysia) • One-handed - Feliks • None-handed – Anssi Vanhala (Finland)**Questions?**• This PowerPoint (with links) is available at http://www.fentonphysics.com/smashday/ Ian Winokur Greenfield Community College winokuri@gcc.mass.edu