A simple trick to design your own solutions for Rubik's cubes
Why Hacker News recommends it
Recommended as an accessible explanation of how Rubik's cube solving relates to group theory.
What it is
Mathologer shows a simple idea, the commutator, that lets anyone who can solve the first layer design their own full Rubik's cube solution. The same idea carries over to other symmetric twisty puzzles such as the Megaminx.
Recommended by 3 HN commenters across 2 different months, 2019 to 2022.
What Hacker News said
Recommends EdwardCoffin · 2019-02 · 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] [this video]
Recommends foxes · 2019-02 · 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 :), [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]
Recommends lupire · 2022-11 · 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. [this video]
Cites celias · 2022-05 · 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" [this video]