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By Siobhan Roberts
Erno Rubik, the inventor of the Rubik’s Cube, credits it with being created in the spring of 1974. He was preparing for a course in descriptive geometry and fiddling with the five Platonic solids when he became fascinated with the Rubik’s Cube. But as he wrote in his 2020 memoir, “The Cube, the Puzzle for Us All,” for a long time “I never thought of myself as creating a puzzle.”
In July 1974, on his 30th birthday, he designed the structure, realized its puzzle-solving potential, and, after playing with it on and off for several months, cracked the cube for the first time. In January 1975, he filed a patent application, and by the end of 1977, the Rubik’s Cube debuted in toy stores in Hungary. Travelers, he recalled, were sneaking it away “in their suitcases, next to other Hungarian delicacies like sausages and Tokaji wine.”
One enthusiastic exporter and ambassador was mathematician David Singmaster, who wrote the book Notes on the Rubik’s Cube. In it, he outlined the symbols for the Rubik’s Cube—up (U), down (D), right (R), left (L), front (F), back (B)—provided a method for orienting the cube and indicated the pieces, their locations, and their turns. He also provided a step-by-step guide to solving it. He also reported on a hazard: British politician and amateur mathematician Dame Catherine O’Learynshaw developed “stereoscopic thumb,” a tendinitis that required minor but delicate surgery to relieve.
CubeLovers was one of the earliest Internet mailing lists, with its first message sent in July 1980 by an MIT student: “I don’t know what we’ll discuss, but another mailing list can’t go far.” In March 1981, the Cube was renamed Rubik and became a hit in American toy stores, prompting cognitive scientist Douglas Hofstadter to diagnose the craze as “cube mania” — “a severe mental disorder accompanied by itching of the fingertips that can only be relieved by prolonged contact with colored cubes,” he wrote in a column for Scientific American. He added: “Symptoms often last for months. Highly contagious.”
In November 1982, the craze died down—“The Rubik’s Cube: The Mania Is Over,” read a headline in The New York Times. But in the 1990s, the World Wide Web made the Rubik’s Cube popular again. In 2023, Spin Master, the toy company that owns the brand, has sold 7.4 million units worldwide, including the classic Rubik’s Cube and related twisted puzzles. Spin Master co-founder Ben Varadi notes that the Rubik’s Cube has “95% brand awareness”—almost everyone has heard of it. Cube lore also claims that one in seven people on the planet has played with it. “It gives me hope for the world,” Rubik told the audience in San Francisco. “It brings people together.”
According to Tomas Rokick, a Rubik’s Cube enthusiast, there are about 43 billion billion colorful combinations of puzzles. “That’s a pretty big number,” he said, probably more than all the grains of sand in the world.
Part of the magic of the Rubik’s Cube lies in its complexity in its simplicity. The Rubik’s Cube is made up of 20 smaller “cubes” (eight corners and 12 sides between the corners) and six faceted center pieces connected to a core. The core mechanism is held in place by a 3D cross around which the protrusions on the edge and corner cubes interlock in a clever geometric way, allowing the structure to rotate.
The cube has 54 colored faces, 9 each of white, red, blue, orange, yellow, and green. In the cube’s unlocked state, the cube’s 6 faces are configured so that all 9 faces are the same color. Rotating the cube scrambles the colors – there are a total of 43,252,003,274,489,856,000 possible positions in which the faces can be arranged into different shapes.
At the same time, the basic shape of the Rubik’s Cube – a cubic shape – remains the same. This feature embodies group theory, the mathematical study of symmetries: the so-called symmetry group of a geometric object is a collection or group of transformations that can be applied to the object and still preserve its structure. A square has eight symmetries: it can be rotated or reflected in four ways and still remain a square. A regular cube has 48 symmetries. The Rubik’s Cube has about 43 quadrillion symmetries.
Erno Rubik
These symmetries are a “marvelous property,” Rokitsky said, “that really gives the cube its elegance.” In the same spirit, the entertaining math gathering also included discussions on how to build an origami computer; the controlled art of juggling (as opposed to “wobbling,” the uncontrolled pursuit of a ball); and enumeration problems in knitting.
There are many ways to solve the Rubik’s Cube. In his lecture, Rokitch zeroed in on a specific number: What is the fewest number of moves required to solve the most confusing situation?
In 1999, Rokic began calculating this value, known as God’s Number. In 2010, he found the answer: 20. He had help from many talented people, not least Herbert Kociemba, a German amateur Rubik’s Cube enthusiast and programmer known for his eponymous algorithm. The feat was also made possible by a large donation of computer time from Google and another algorithm that exploited the symmetries of the Rubik’s Cube to reduce the number of required calculations by a factor of 48, thereby reducing the required computing power.
Rokitch is currently obsessed with identifying the locations of all the God numbers — they are “extremely rare and very hard to find,” he told the audience. As he spoke, three computers in his home began the task — they have a total of 336 GB, mining about 100,000 distance-20 locations a day. So far, Rokitch has a database of about 100 million. “They are mathematical gems,” he said. –The New York Times
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