Wolfram Computation Meets Knowledge

The Rubik’s Cube: 40 Years of Geometrical Abandon

In 1974, a Hungarian professor of architecture by the name of Ernő Rubik came up with a seemingly simple idea: to create a small, 2x2x2 rotating cube made up of sub-cubes to use as a teaching tool for his students. Little did he know that this device, which was originally intended simply to help visualize moving parts in three dimensions (and didn’t even work that well), would develop into a puzzle that continues, to this day, to plague and fascinate minds of all ages.

Minds, for example, like mine. Most younger siblings get hand-me-down clothes, books, or toys—but when I was thirteen years old, my big brother placed a dented and worn colorful plastic cube into my hands. The stickers were peeling and falling off, it was rickety and hard to turn, but I didn’t care, it was perfect.

My very own Rubik’s cube.

Over the following hours and days, my brother coached me on the algorithms while I desperately stretched my brain to conceptualize what exactly I was trying to do. How do I get the color I want to go to the proper place without ruining everything else? It was challenging, and I loved that. Before long, we were racing each other to see who could solve it the fastest.

For those (rare few!) who are not familiar with the timeless Rubik’s cube, the most popular variation of this puzzle is the 3x3x3. The cube is made up of smaller sub-cubes, with one of six colors on each outward-facing side. Each face of the cube can rotate, and the goal is to successfully align the sub-cubes such that each face is a single color.

Sounds easy in theory, right? (Oh, and no peeling off and rearranging the stickers!)

Give it a virtual-try and see for yourself:


This puzzle has intrigued people of all ages for 40 years. To this day, there are mind-boggling gurus who can solve these puzzles in mere seconds (or blindfolded… or both). There are eager, mathematically inclined students solving them underneath their desks during class. And there are thousands of people who fiddle with these puzzles aimlessly in their spare time wondering if, maybe this time, they might just happen accidentally upon the solution.

There’s something universally fascinating in this simple concept. It’s a device that managed to permeate the minds of the mainstream population and turn some of the most conceptually challenging aspects of mathematics into a fun and interesting puzzle worth exploring.

And we can explore it even further in Mathematica, too! Some smart people have made a few Demonstrations about Rubik’s cubes, from number theory and cube variations to the mechanisms behind its motion.

Or how about having Mathematica solve a physical Rubik’s cube—from a couple photographs?

In the video below, Wolfram’s own Luc Barthelet walks through the image processing used in his code, which analyzes a physical Rubik’s cube from just two pictures and animates a video of a fully rendered virtual version of the cube being solved.

So, whether you’re a dedicated speed-solver or a passive puzzle-lover, this little cube just might teach you something new. (Or at the very least, entertain you on long car rides.) Now get cubing!


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  1. I can solve Rubik’s cube only on wan way :) Nice article

  2. Hi Allison. Many thanks for embedding the Rubik’s cube from the Wolfram Demonstration Project,
    But I would like to know if the code of the program that presents Luc Barthelet in the video can be obtained from somewhere or not. In the personal attracted my attention to the way in which resolves and i’d love to see the code to learn more about Mathematica. Thank you for sharing this excellent article for all the lovers of the rubik´s cube.