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A simple trick to design your own solutions for Rubik's cubes

Mathologer

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  • Recommended by 3 people: 3 on Hacker News.
  • A classic. People kept recommending it from 2019 to 2022.

Beginner. No background in the topic needed.

1.6M views10 years ago3 recommendations

Computer scienceAlgorithmsMath for programmers

Mathologer explains how to use commutators and group theory concepts to design your own solutions for the Rubik's cube and other symmetric puzzles.

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 qedcat.com/rubiks_cube/ 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: youtu.be/k3IEpugNfJY The Rubik's cube animations in this video were produced using the program CubeTwister by Werner Randelshofer: randelshofer.ch/cubetwister/ Thank you also to Danil Dmitriev the official Mathologer translator for Russian for his subtitles. Enjoy :)

Why it's here

3 people recommend this

What people say. Recommended as a highly accessible explanation of group theory and algorithmic thinking applied to solving Rubik's cubes.

EdwardCoffinon Hacker News • Recommends

On “The Mathematics of the Rubik’s Cube (2009) [pdf]”

This 15 minute video is a pretty accessible explanation of a technique for solving Rubik's-type puzzles: A simple trick to design your own solutions for Rubik's cubes 1 1 link to this video
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foxeson Hacker News • Recommends

On “The Mathematics of the Rubik’s Cube (2009) [pdf]”

Mathologer has a nice video explaining how to solve a cube, and they are really using group theory :), link to this video . The key take away is that all you need to do is find a few basic operations (swapping an edge/corner/center) that leaves the rest of the cube unchanged, and then your job is basically done, you apply these until you have a solved cube. This might approach might not give you the optimal algorithm, which has been shown to be able to solve any Rubik's Cube in 20 turns or less 0. 0 link
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lupireon Hacker News • Recommends

On “2D Rubik’s Cube solution visualization”

It's a huge leap to get past the first layer. Your curt rate of progress suggests that your strategy will not solve the cube in your lifetime. And it's almost impossible to do it without taking notes on paper or computer. (If that were doable, their wouldn't be so many walkthroughs). Solving the cube is a hard applied group theory "homework" problem. This video explains the principles of solving a Rubik's cube on your own. link to this video
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celiason Hacker News • Mentions

On “Speedsolving Rubik's Cube: 8355 Method”

Are you thinking of the Mathologer video "A simple trick to design your own solutions for Rubik's cubes" link to this video
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