Today's Edition
NEW YORK TIMES
Bright and early on the first Saturday in January, Tomas Rokicki and a few hundred fellow enthusiasts gathered in a vast lecture hall at the Moscone Centre in downtown San Francisco. A big math conference was underway and Rokicki, a retired programmer based in Palo Alto, California, had helped organise a two-day special session about “serious recreational mathematics” celebrating the 50th anniversary of the Rubik’s Cube. Erno Rubik, the Cube’s inventor, was top of the show at 8am, via videoconference from the south of Spain.
Rubik, a Hungarian architect, designer, sculptor and retired professor, took part in a Q&A session with Rokicki and his co-organisers, Erik Demaine, a computer scientist at Massachusetts Institute of Technology, and Robert Hearn, a retired computer scientist, of Portola Valley, California.
Rokicki asked Rubik about the first time he solved the Cube: “Did you solve corners-first?” These days, new cubers learn on YouTube, watching tutorials at 1.5x speed. Rokicki instead recommends the old-fashioned strategy: Set out on a lone path and discover a solving method, even if it takes weeks or months. (It took computer scientist Donald Knuth less than 12 hours, starting at his dining table in the evening and working straight through to the morning.) Corners-first is a common route, since once the corners are solved, the edges can be slotted in with relative ease. Rubik said that, yes, he indeed did corners-first. Rubik, who is known to take a philosophical approach to cubology and to life in general, added: “My method was understanding.”
Rubik dates the Cube to the spring of 1974. Preparing a course on descriptive geometry and tinkering with the five Platonic solids, he had become especially taken by the cube. But, as he wrote in his 2020 memoir, “Cubed, The Puzzle of Us All”, for quite a while it “never once occurred to me that I was creating a puzzle”.
By about the time of his 30th birthday, in July 1974, he had created the structure, realised its puzzling potential and – after playing with it intermittently for a few months – solved the Cube for the first time. He submitted a patent application in January 1975, and by the end of 1977 the “Magic Cube”” had debuted in toy stores in Hungary. Travelers spirited it out “in their luggage, next to other Hungarian delicacies like sausage and Tokaji wine”, he recalled.
Rubik’s lore also holds that one in seven people on Earth have played with the Cube. “It gives me hope about the world,” Rubik told his audience in San Francisco. “It brings people together.”
After the session with Rubik, Rokicki gave a talk on mathematical aspects of the Cube. He started with the fact that it scrambles into some 43 billion billion colourful combinations. “A reasonably big number,” he said, possibly more than all the grains of sand in the world.
The cubies display 54 colourful facets, nine each of white, red, blue, orange, yellow and green. In its solved state, the Cube’s six faces are configured such that all nine facets are the same colour. Turning the puzzle scrambles the colours – in total, there are precisely 43,252,003,274,489,856,000 possible positions into which the facets can be permuted.
All the while, the puzzle’s essential form – its cubic-ness – remains unchanged. This feature demonstrates group theory, the mathematical study of symmetry: A so-called symmetry group of a geometric object is the collection, or group, of transformations that can be applied to the object but that nonetheless leave the structure preserved. A square has eight symmetries: It can be rotated or reflected four ways each and it’s still a square. A plain cube has 48 symmetries. The Rubik’s Cube has some 43 quintillion.
These symmetries are a “fantastic property”, Rokicki said, that “really gives the Cube its elegance”.
Rubik added later that he wasn’t so keen on puzzles that are designed merely to be puzzles. He said: “I love the puzzling content of life and the universe as it is.”
