Selected Topics on the Rubik’s Cube

Ian WinokurGreenfield 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

The Rubik’s Cube in Pop Culture

The Rubik’s Cube in Pop Culture

The Rubik’s Cube in Pop Culture

The Rubik’s Cube in Pop Culture

The Rubik’s Cube in Pop Culture

The Rubik’s Cube in Pop Culture

They cube – so should you!

They cube – so should you!

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 – many algorithms required (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 =

24 r2000,810,6374

2cm0,000047,016,005,109,428,

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, …

2cm0,000047,016,005,109,428,

2cm 2.493

cubes 0008,849,369,157,261,552

cm 32.49

2cm0,000047,016,005,109,428,

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…

Earths 341.71hcubes/Eart 0008,849,369,157,261,55

cubes00,000,274,489,943,252,003

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!

Results from 2011 World Championships

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 athttp://www.fentonphysics.com/smashday/

Ian WinokurGreenfield Community Collegewinokuri@gcc.mass.edu