In the early morning hours of the first Saturday in January, Tomas Rokicki and several hundred enthusiasts gathered in a large auditorium at the Moscone Center in downtown San Francisco. A major mathematics conference was underway, and Rokicki, a retired programmer living in Palo Alto, California, had helped organize a special two-day session on “serious entertainment mathematics” celebrating the 50th anniversary of the Rubik’s Cube. Erno Rubik, the inventor of the cube, was in charge of the demonstration at 8 a.m. via videoconference from southern Spain.
Hungarian architect, designer, sculptor and retired professor Rubik participated in a Q&A session with Rokicki and his co-organizers, computer scientist Erik Demaine of the Massachusetts Institute of Technology and retired computer scientist Robert Hearn of Portola. Valley, California.
Rokicki asked the first time he solved the Rubik’s Cube: “Did you solve the corners first?”
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These days, new cubers learn by watching tutorials on YouTube at 1.5x the speed. Rokicki recommends the old-fashioned strategy: Go it alone, and discover a solution, even if it takes weeks or months. (It took computer scientist Donald Knuth less than 12 hours to work from his dinner table at night.) Placing the corners first is a common practice, because once the corners are solved, the edges can be placed with relative ease. Rubik said that, yes, he did indeed put the corners first. Rubik, who was known for taking a philosophical approach to cubology and life in general, added: “My method was to understand.”
‘Magic Cubitis’
Rubik dates the Cube to the spring of 1974. He was particularly fascinated by the cube while preparing a course on descriptive geometry and working with the five Platonic solids. But as he wrote in his 2020 memoir, “Cubed, The Puzzle of Us All,” for a long time “it never once occurred to me that I was creating a puzzle.”
By his 30th birthday, in July 1974, he had created the structure, realized its astonishing potential, and—after playing with it intermittently for several months—solved the Cube for the first time. He filed a patent in January 1975, and by the end of 1977, the “Magic Cube” was on display in toy stores in Hungary. He recalled that travelers would take it out “in their suitcases, along with other Hungarian delicacies like sausages and Tokaji wine.”
One of the passionate exporters and ambassadors was David Singmaster, a mathematician who wrote “Notes on Rubik’s ‘Magic Cube.’” In the book, he outlined a notation for the faces—Up (U), Down (D), Right (R), Left (L), Front (F), Back (B)—which provided a way to orient the cube and refer to its pieces, positions, and rotations. He also provided a step-by-step solutions guide. And he mentioned a danger: Dame Kathleen Ollerenshaw, a British politician and amateur mathematician, had developed “‘cubism thumb,’ a form of tendonitis that required minor but delicate surgery to relieve.”
CubeLovers was among the first internet mailing lists—the opening message was posted by an MIT student in July 1980: “I don’t know what we’re going to talk about, but another mailing list wouldn’t hurt (too many).” In March 1981, when the Cube was renamed Rubik and hit American toy stores, cognitive scientist Douglas Hofstadter diagnosed the craze as “cubitis magikia”; “a serious mental disorder accompanied by itching of the fingertips, which can only be relieved by long-term treatment.” contact with a multi-colored cube,” he wrote in a column for Scientific American. He added: “Symptoms often last for months. It’s very contagious.”
By November 1982, the craze had subsided—”Rubik’s Cube: A Craze Ends,” declared The New York Times’ headline. However, it was revived by the World Wide Web in the 1990s. Toy company Spin Master, which now owns the brand, sold 7.4 million units worldwide in 2023, including both the classic Cube and related twisty puzzles. Ben Varadi, co-founder of Spin Master, stated that Rubik has “95% brand awareness”; Almost everyone has heard of this. Rubik’s information also shows that 1 in 7 people on Earth plays with the Cube. “This gives me hope for the world,” Rubik told his audience in San Francisco. “It brings people together.”
Complexity from Simplicity
After the session with Rubik, Rokicki gave a talk about the mathematical aspects of the Cube. He started his speech with the fact that the Cube turns into approximately 43 billion billion colored combinations. “It’s a pretty big number,” he said, probably more than all the grains of sand in the world.
Part of the puzzle’s appeal is its complexity that comes from its simplicity. The cube consists of 20 small “cubes” (eight vertices and 12 edges centered between the vertices) and six face centerpieces attached to the core. The core mechanism is anchored by a 3D cross around which the edge tabs and corner cubes interlock in a geometrically ingenious way, allowing the structure to rotate.
The Cubes display 54 colored faces, nine each in white, red, blue, orange, yellow, and green. In its solved state, the Cube’s six faces are configured so that all nine faces are the same color. Turning the puzzle shuffles the colors – in total, there are exactly 43,252,003,274,489,856,000 possible positions in which the faces can be swapped.
Meanwhile, the puzzle’s basic form (cubic structure) remains unchanged. This feature illustrates group theory, the mathematical study of symmetry: The so-called symmetry group of a geometric object is the sum or group of transformations that can be applied to the object but still preserve the structure. A square has eight symmetries: Each can be rotated or reflected in four directions and still be a square. A flat cube has 48 symmetries. There are about 43 quintillion in a Rubik’s Cube.
Rokicki said these symmetries were a “fantastic feature” and “really give the Cube its elegance.”
Likewise, the fun math meetup featured talks on how to build an origami computer, the art of controlled juggling (rather than chasing balls uncontrollably), and numbered problems in knitting.
Mathematician and mathematics writer Barry Cipra shared the wooden tray puzzle he invented and called the bricklayer’s challenge. Installation: four rows of six brick-like blocks of different lengths. Purpose: To arrange 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 his invitation) and began trying to figure out one of the puzzle’s 2,184 solutions. This enthusiastic subset included Bram Cohen, a computer programmer who designs Rubik’s-like puzzles (and the inventor of BitTorrent, a file-sharing protocol), the Maltese Gear Cube, in collaboration with Oskar van Deventer; and Rivka Lipkovitz, a rising high school senior and speedcubing user (official personal best in competition, 14.71 seconds; personal best at home, 10.75).
Cubic Encounters
There are many ways to solve the cube. During his lecture, Rokicki focused on a specific number: What is the minimum number of moves needed to solve even the most complex positions?
Rokicki began calculating this quantity, known as the God number, in 1999. In 2010, he found the answer: 20. He enlisted the help of many talented people, most notably the German hobbyist cuber and programmer Herbert Kociemba, known for his eponymous algorithm. This feat also benefited from a large amount 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 therefore reducing the computational power required.
Rokicki’s current obsession is to identify all of God’s number locations; he told the audience that they are “extremely rare, really hard to find.” As he spoke, three computers in his home focused on the task; they mine 20 locations — 336 gigabytes total, about 100,000 distances a day. So far, Rokicki has a database of about 100 million. “They are mathematical gems,” he said.
The cube also provides a good challenge for machine learning systems and robots.
And Italian theoretical physicist and composer Maria Mannone invented the “CubeHarmonic,” a musical instrument developed with Japanese collaborators. “It’s a Rubik’s Cube with musical chords on each side, one note on each face,” he explained in an email. “We mix musical chords by mixing the cube.”
Parisian street artist Invader creates “Rubikcubist” works, which consist of figurative canvases structured like a mosaic of hundreds of cubes. Invader’s version of Picasso’s first cubist painting, “Les Demoiselles d’Avignon,” used 1,848 cubes to create 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 for both math majors (those interested in algebra) and non-STEM majors (those learning to solve puzzles, discover patterns, count calculations). design and build configurations and mosaics). “There’s a lot of depth to this puzzle,” Rose said at the conference in San Francisco. One of the reasons Cube has survived is that it’s “so accessible and fun,” she believes.
“It’s a good way to get people to want to learn math,” he added.
So far, all the Platonic solids have been transformed into a variety of complex puzzles. And in continuation of the original, there’s the 4-by-4-by-4 Rubik’s Revenge, the 5-by-5-by-5 Professor’s Cube, and on up to the largest, the 7-by-7-by-7 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). The 256-by-256-by-256 only exists in the virtual world, where it was solved by a team of six in 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 variations of the original. Somehow, the Void was missing the central chambers and internal mechanics that held Rubik’s iconic invention together. Rubik again took a philosophical stance on this subject. “Perfection is an idealistic encounter,” he said. He understood discoveries that come from curiosity, adding things, subtracting things. He preferred the classic combination of partitions and colors. “I also love the sound and movement of the cube,” he said.
Rubik later added that he wasn’t really into puzzles designed just for the sake of them. “I like the puzzling content of life and the universe as it is,” he said.
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