Adventures in Group Theory

Adventures in Group Theory: Rubik’s Cube, Merlin’s Machine, and Other Mathematical Toys David Joyner  5-15-2008

Published on Jan 15, 2016

The vast majority of people who tackle the Rubik’s cube never succeed in solving it without looking up somebody else’s solution. In this video the Mathologer reveals a simple insight that will enable all those of you who can solve the first layer to design your own full solution for the Rubik’s cube, as well as for many other highly symmetric twisty puzzles.
For more details about this really very fundamental idea behind many twisty puzzle solutions have a look at this article by the Mathologer from a couple of years ago
Googling “commutator, Rubik’s cube” will also produce links to a lot of very good articles on this topic.
For a few footnotes you may also want to check out this video on Mathologer 2:
The Rubik’s cube animations in this video were produced using the program CubeTwister by Werner Randelshofer:

Rubik’s Cube is a 3-D combination puzzle invented in 1974[1][2] by Hungarian sculptor and professor of architecture Ernő Rubik. Originally called the Magic Cube,[3] the puzzle was licensed by Rubik to be sold by Ideal Toy Corp. in 1980[4] via businessman Tibor Laczi and Seven Towns founder Tom Kremer,[5] and won the German Game of the Year special award for Best Puzzle that year. As of January 2009, 350 million cubes had been sold worldwide[6][7] making it the world’s top-selling puzzle game.[8][9] It is widely considered to be the world’s best-selling toy.[10]

In a classic Rubik’s Cube, each of the six faces is covered by nine stickers, each of one of six solid colours: white, red, blue, orange, green, and yellow. In currently sold models, white is opposite yellow, blue is opposite green, and orange is opposite red, and the red, white and blue are arranged in that order in a clockwise arrangement.[11] On early cubes, the position of the colours varied from cube to cube.[12] An internal pivot mechanism enables each face to turn independently, thus mixing up the colours. For the puzzle to be solved, each face must be returned to have only one colour. Similar puzzles have now been produced with various numbers of sides, dimensions, and stickers, not all of them by Rubik.

Although the Rubik’s Cube reached its height of mainstream popularity in the 1980s, it is still widely known and used. Manyspeedcubers continue to practice it and other twisty puzzles and compete for the fastest times in various categories. Since 2003, TheWorld Cube Association, the Rubik’s Cube’s international governing body, has organised competitions worldwide and kept the official world records.


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