The Rubik’s Cube turns 50

Early on the first Saturday in January, Tomas Rokicki and a few hundred fellow enthusiasts gathered in a vast auditorium at the Moscone Center in downtown San Francisco. A major mathematics conference was underway and Rokicki, a retired programmer based in Palo Alto, California, helped organize a special two-day session on “serious recreational mathematics” celebrating the 50th anniversary of the Rubik’s Cube. Erno Rubik, the inventor of the Cube, was the protagonist of the show at 8am, via videoconference from southern Spain.

Rubik, a retired Hungarian architect, designer, sculptor and professor, participated in a question-and-answer session with Rokicki and his co-organizers, Erik Demaine, a computer scientist at the Massachusetts Institute of Technology, and Robert Hearn, a retired computer scientist, from Portola Vale, California.

Rokicki asked Rubik about the first time he solved the Cube: “Did you solve the corners first?”

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Nowadays, new cubers learn on YouTube, watching tutorials at 1.5x speed. Instead, Rokicki recommends the old-fashioned strategy: take a solitary path and figure out a method of resolution, even if it takes weeks or months. (Computer scientist Donald Knuth took less than 12 hours, starting at his dining table in the evening and working straight until morning.) Corners first is a common path, as once the corners are resolved, the edges can be fitted together. . with relative ease. Rubik said yes, he actually made the turns first. Rubik, who is known for taking a philosophical approach to cubology and life in general, added: “My method was understanding.”

‘Cubitus Magikia’

Rubik dates the Cube to the spring of 1974. Preparing a course on descriptive geometry and tinkering with the five Platonic solids, he became especially interested in the cube. But as he wrote in his 2020 memoir, “Cubed, The Puzzle of Us All,” for a long time “it never occurred to me that I was creating a puzzle.”

Around his 30th birthday, in July 1974, he created the structure, realized its intriguing potential, and – after playing with it on and off for a few months – solved the Cube for the first time. He filed a patent application in January 1975, and in late 1977 the “Magic Cube” debuted in Hungarian toy stores. Travelers enjoyed it “in their luggage, alongside other Hungarian delicacies such as sausage and Tokaji wine,” he recalled.

An avid exporter and ambassador was David Singmaster, a mathematician who wrote the book “Notes on Rubik’s ‘Magic Cube’”. In it he outlined a notation for the faces — Up (U), Down (D), Right (R), Left (L), Front (F), Back (B) — providing a way to orient the Cube and consult its pieces , positions and turns. It has also provided a step-by-step solution guide. And he reported a danger: Dame Kathleen Ollerenshaw, a British politician and recreational mathematician, developed a case of “‘cubist thumb,’ a form of tendonitis that requires minor but delicate surgery for its relief.”

CubeLovers was among the Internet’s first mailing lists—the inaugural message was sent by an MIT student in July 1980: “I don’t know what we’ll talk about, but another mailing list can’t hurt (much).” In March 1981, with the Rubik’s Cube having been renamed and populating American toy stores, cognitive scientist Douglas Hofstadter diagnosed the mania as “cubitis magikia” – “a severe mental disorder accompanied by itching of the fingertips, which only can be relieved by prolonged treatment. contact with a multicolored cube,” he wrote in his column for Scientific American. He added: “Symptoms often last for months. Highly contagious.”

By November 1982, the craze had subsided—“Rubik’s Cube: The Craze Is Over,” declared a headline in The New York Times. But it was resurrected in the 1990s by the World Wide Web. As of 2023, Spin Master, the toy company that now owns the brand, has sold 7.4 million units globally, including the classic Cube and related twisty puzzles. Ben Varadi, co-founder of Spin Master, noted that Rubik’s has “95% brand recognition” – practically everyone has heard of it. Rubik’s lore also states that 1 in 7 people on Earth has played with the Cube. “This gives me hope for the world,” Rubik told his San Francisco audience. “It brings people together.”

Complexity of Simplicity

After the session with Rubik, Rokicki gave a talk on mathematical aspects of the Cube. He started with the fact that it mixes into about 43 billion billion colored combinations. “A fairly large number,” he said, possibly more than all the grains of sand in the world.

Part of the puzzle’s appeal is the complexity that emerges from its simplicity. The Cube is made up of 20 smaller “cubes” (eight corners and 12 edges centered between the corners) and six center face pieces attached to the core. The central mechanism is anchored by a 3D cross, around which tabs on the edge and corner hubs interlock in a geometrically ingenious way that allows the structure to rotate.

The cubes display 54 colored facets, nine each of white, red, blue, orange, yellow and green. In its resolved state, the Cube’s six faces are configured so that all nine facets are the same color. Flipping the puzzle shuffles the colors – in total there are precisely 43,252,003,274,489,856,000 possible positions in which the facets can be swapped.

At the same time, the essential shape of the puzzle – its cubicness – remains unchanged. This characteristic demonstrates group theory, the mathematical study of symmetry: the so-called symmetry group of a geometric object is the collection, or group, of transformations that can be applied to the object, but which, even so, leave the structure preserved. A square has eight symmetries: it can be rotated or reflected four ways each and is still a square. A simple cube has 48 symmetries. The Rubik’s Cube is about 43 quintillion.

These symmetries are a “fantastic property,” said Rokicki, which “really gives the Cube its elegance.”

In the same spirit, the recreational math meeting included talks on how to build an origami computer; the controlled art of juggling (versus “joggling”, chasing balls uncontrollably); and enumerative problems in knitting.

Barry Cipra, a mathematician and math writer, shared a wooden tray puzzle he invented called the bricklayer’s challenge. The setup: four rows of six brick-like blocks of varying lengths. The goal: arrange the bricks so that none of their vertical joints line up between adjacent horizontal rows.

As Cipra spoke, several audience members rushed onto the stage (at her invitation) and got to work trying to find one of the 2,184 solutions to the puzzle. Among this subset of enthusiasts were Bram Cohen, a computer programmer (and inventor of BitTorrent, a file-sharing protocol) who creates Rubik’s-like puzzles such as the Maltese Gear Cube (in collaboration with Oskar van Deventer); and Rivka Lipkovitz, high school senior and speedcuber (official personal record in competition, 14.71 seconds; personal record at home, 10.75).

Cubic Encounters

There are many ways to solve the Cube. During his talk, Rokicki focused on one specific number: What is the minimum number of moves needed to solve even the most confusing positions?

Rokicki decided to calculate this quantity, known as God’s number, in 1999. In 2010 he found the answer: 20. He enlisted the help of many talented people, especially Herbert Kociemba, a German amateur cuber and programmer known for his eponymous algorithm. The feat also benefited from a lot of computer time donated by Google and another algorithm that took advantage of the Cube’s symmetries, reducing the number of calculations required by a factor of 48 and, in turn, reducing the computing power required.

Rokicki’s current obsession is identifying all of God’s number positions — they are “extremely rare, very hard to find,” he told the audience. As he spoke, three computers in his home were working on this task – their combined 336 gigabytes excavate about 100,000 distances – 20 positions per day. So far, Rokicki has a database of around 100 million. “These are mathematical gems,” he said.

The Cube is also a good challenge for machine learning systems and robots.

And Maria Mannone, an Italian theoretical physicist and composer, invented the “CubeHarmonic”, a musical instrument developed with Japanese collaborators. “It’s a Rubik’s cube where, on each face, there are musical chords, a note on each facet,” she explained via email. “By shuffling the cube, we shuffle musical chords.”

Parisian street artist Invader creates “Rubikcubista” works, figurative canvases configured as a mosaic with hundreds of cubes. Invader’s version of “Les Demoiselles d’Avignon,” Picasso’s first Cubist painting, used 1,848 cubes to make a reproduction the same size as the original.

Lauren Rose, a mathematician at Bard College in New York, uses the Cube as a teaching tool in courses for both math students (who delve deeper into algebra) and non-STEM students (they learn to solve the puzzle, explore patterns , count your configurations, and design and build mosaics). “There is a lot of depth to this puzzle,” Rose said at the conference in San Francisco. She believes part of the reason the Cube has endured is that it is “so accessible and fun.”

“It’s a good way to get people to want to learn math,” she added.

So far, all Platonic solids have been transformed into twisty variants of puzzles. And going back to the original, there’s the 4 by 4 by 4 Rubik’s Revenge, the 5 by 5 by 5 Professor’s Cube and going up to the 7 by 7 by 7, the largest cube used in World Cube Association competitions. The 21 by 21 by 21 is the largest cube generally available on the mass market ($1,499.99). 256 by 256 by 256 exists only in the virtual world, where it was solved by a team of six people with 633,494 moves in a cumulative time of about 96 hours.

During the Q&A session, Rokicki asked Rubik about the hollow Void Cube by Japanese inventor Katsuhiko Okamoto, who created dozens of variants of the original. Somehow, Void is missing the central cubicles and internal mechanics that hold Rubik’s iconic invention together. On this subject, Rubik philosophized again. “Perfection is an idealistic encounter,” he said. He understood explorations driven by curiosity, adding something, taking something away. He preferred the classic combination of cubes and colors. “I also love the sound of the Cube, the movement,” he said.

Rubik later added that he was not very fond of puzzles designed just to be puzzles. He said, “I love the intriguing content of life and the universe as it is.”

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