Selected Topics on the Rubik’s Cube

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.

The Rubik’s Cube in Pop Culture

They cube – so should you!

They cube – so should you! • See this guy do a complete solve on youtube! (1:20)

Solution Methods – Little Memorization • 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 – Little to Lots of Memorization • 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 • 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!

2011 World ChampionshipsOctober 14-16, 2011 • 3x3x3 Results • Winners and World Records

Solving Variations • Craziness – Yuhui Xu (China) October 4, 2011 • Multi-craziness – Chester Lian (Malaysia) Marcell Endrey (Hungary) • One-handed – Feliks Zemdegs (Australia) Piotr Tomczyk (Poland) • 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

Selected Topics on the Rubik’s Cube