1. Selected Topics on the Rubik’s Cube
Ian Winokur
Greenfield Community College
Picture from Math Horizons, November 2010

2. 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

3. 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.

4. The Rubik’s Cube in Pop Culture

5. The Rubik’s Cube in Pop Culture

6. The Rubik’s Cube in Pop Culture

7. The Rubik’s Cube in Pop Culture

8. The Rubik’s Cube in Pop Culture

9. The Rubik’s Cube in Pop Culture

10. The Rubik’s Cube in Pop Culture

11. They cube – so should you!

12. They cube – so should you!

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

14. 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,…

15. 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 – many algorithms required ( )
A virtual example solve (or two)
Me live!

16. How many different states of the cube?
Virtual cube

17. 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!

18. 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!

19. 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 = …

20. Number of Rubik’s Cube Scrambles
43,252,003,274,489,856,000

21. 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 square centimeters

22. 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 =

23. 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, …

24. 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…

25. Single Solve World Record Progression
Feliks Zemdegs – 2010 (Australia)
Feliks – later that same day
Feliks – 2010
Feliks – 2011
Feliks –2011 – slow motion
Feliks –2011

26. Facts about Feliks Feliks Zemdegs – Australian speedcuber 15 years old
Complete domination on the 3x3x3

27. 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!

28. 2011 World Championships October 14-16, 2011
3x3x3 Results
Winners and World Records

29. 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)

30. Questions? This PowerPoint (with links) is available at
Ian Winokur
Greenfield Community College