2MX - 2006/07

3MX - 2007/08

Du er besøkende nr.

(Teller nullstilt 23. august 2007)

Er det noen som husker denne?

Ideen med å presentere kuben på disse matematikksidene henger sammen med tankegangen bak løsning av kuben: Både metodikk i tankegangen, løsning av puslerier samt antall kombinasjoner er viktige momenter i matematisk tankegang. Derfor lenkes denne sida fra generelle matematikksider samt fra sannsynlighetsregninga - dvs. kombinatorikken.

Antall plasseringer av de 27 - egentlig 26 - småkubene er interessant matematikk:

Hvor mange mulige kombinasjoner blir dette?

Historikk        Løsning        Hvor fort kan det gjøres?

Men det går jo an å bygge seg en kubeløser i lego:

Den offisielle Rubik-sida, http://www.rubiks.com/, inneholder denne historikken:

BRIEF HISTORY OF THE CUBE
Every invention has an official birth date. For the Cube this date is 1974 when the first working prototype came into being and a patent application was drafted. The place was Budapest, the capital of Hungary. The inventor's name is now a household word. At the time, Erno Rubik was a lecturer in the Department of Interior Design at the Academy of Applied Arts and Crafts in Budapest.

Although 1974 marks the inauguration of the Cube, the processes that led to the invention began a few years earlier, nor was the identity of the inventor a fortuitous accident. Erno Rubik had a passionate interest in geometry, in the study of 3D forms, in construction and in exploring the hidden possibilities of combinations of forms and material in theory and in practice.

In the course of his teaching, Erno Rubik preferred to communicate his ideas by the use of actual models, made from paper, cardboard, wood or plastic, challenging his students to experiment by manipulating clearly constructed and easily interpreted forms. It was the realization that even the simplest elements, cleverly duplicated and manipulated, yield an abundance of multiple forms that was the first step on the long road that led finally to the Cube.

Although possibly the most original of all invented puzzles, the Cube was not created in a vacuum. Its classical antecedents are great puzzles in their own right. The Tangram, originating from ancient China, merely consists of 5 triangles, a square and a parallelogram, simple elements that yield a multitude of interesting figures. The Pentomino, invented by Solomon W Golomb, has 12 different elements, each one made up of five squares joined together, displaying all the possible configurations of the five combined squares. Pentomino poses the fascinating geometric problem of constructing various rectangles. Piet Hein's Soma Cube is, in a sense, a three dimensional version of Pentominos. It resembles Rubik's Cube both in shape and in the large number of ways its seven elements can be assembled into a 3x3x3 cube. Finally, there is Sam Loyd's well known 15 puzzle, with it's numbered tiles locked together yet moving separately, so that by pushing them about they can be set in sequential order and scrambled at will. Viewing these puzzles places Rubik's Cube in a context and highlights just what a breakthrough creation the Cube really is.

What Erno Rubik's set out to do was create a three dimensional object, of high aesthetic value, which was not only richer in configuration variations and more of a mental challenge than any puzzle in existence, but would also continue to be ONE, SELF-CONTAINED WHOLE, throughout its manifold transformations.

This objective seemed at first as impossible to achieve as the 3-axial rotation of the Cube appears on first encounter. After conceiving the idea of the 3x3x3 Cube, Erno Rubik first tried to hold together the elements of a simpler, 2x2x2 cube, by means of an elastic rubber construction that threaded its way through all 8 elements. Even at this simple level it soon became clear that such a device could not work. The alternatives then available, such as magnets and the obvious tongue and grooves system, could not cope with the complexity of the different junctions and movements that each element required. Erno Rubik realized that only a totally original concept could provide a satisfactory solution.

The inspiration came on a lazy, summer day as he was watching the Danube flow by. Rubik's eye was attracted by some pebbles, whose sharp edges have been rubbed and smoothed away in the course of time bringing into being rounded shapes of great but simple beauty. The interior of the Cube elements had to have the same rounded architecture. The brilliant interior mechanism, which is basically cylindrical, took some time to reach its final form. For ease of manipulation, the balance between tightness and looseness had to be just right, tolerances had to be exact. Finally, the 54 outer surfaces of the individual elements were given their colors. Lots of different decorative patterns, with numbers and symbols as well as diverse color combinations were tried, but none of them worked nearly as well as the six simple but distinct colors, each one unifying and differentiating one single face of the Cube.

When the Cube was complete, Erno Rubik demonstrated it to his students and let some of his friends play with it. The effect was instantaneous. Once somebody laid his hands on the Cube it was difficult to get it back!

The compulsive interest of friends and students in the Cube caught its creator completely by surprise and it was months before any thought was given to the possibility of producing it on an industrial scale.

Eventually a manufacturer took on the job of tooling up for mass production and making the puzzle available to the public at large. Given the inner complexity of the Cube, and the then prevailing economic conditions in communist Hungary, this was by no means an easy undertaking. It is to the credit of the two men at the helm of the toy production firm of Politechnika, President Lehel Takacz and Chief Engineer Ferencz Manczur that they at once perceived enough merit in the Cube to accept this task. The process of turning the hand made object into thousands of low cost, mass manufactured units was slow. It took the best part of three years, but at last, towards the end of 1977 the first Cubes appeared on the shelves of the Budapest toyshops.

During 1978, without any promotion or publicity, the Cube began very slowly to make its way through the hands of fascinated youths into homes, playgrounds and schools. Word of mouth spread the news and by the beginning of 1979 there were enthusiastic circles of Cube devotees in various parts of Hungary.

With the country being both physically and culturally behind the iron curtain at the time, the growing popularity of the Cube did not cross over to the West for quite some time. Not surprisingly, two men of Hungarian origin who had established their lives in the West built the bridge, which eventually enabled the Cube to cross the divide.

Dr Tibor Laczi, born in Budapest, educated in Vienna and employed by a major German computer manufacturer "discovered" the Cube on one of his frequent business trips to Hungary. He fell in love with it, and sensing its potential consumer appeal, brought it to the Nuremberg Toy Fair in February 1979 in the hope of finding a potential German toy distributor. He did not meet with a great deal of success but he did stumble across an individual who at that point of the Cube's history was destined to make a crucial difference.

Tom Kremer, a successful toy and game inventor himself, whose mother language was also Hungarian, ran at the time his own marketing and licensing company. Seven Towns Ltd., based in London, was widely respected throughout the international toy industry as a product developer working not only with its own ideas but also representing professional inventors from all over the world.

The two men made a pact, there and then, to translate the Hungarian success of the Cube onto the world stage. Dr Ladzi headed back to Hungary to pave the way with the prevailing Hungarian bureaucracy whilst Tom Kremer set off on a world tour of toy manufacturers. He was convinced that to realize the Cube's full commercial potential it had to have the marketing muscle, the promotional power and distribution network of a major international company. Unfortunately he found none of the leading players in the field shared his enthusiasm. Although impressed by the Cube, the general view within the industry estimated its prospects to be poor. Its "faults" were numerous: Too difficult and expensive to manufacture, impossible to demonstrate its fascination on TV, too abstract, too cerebral, too quiet, a challenge for the esoteric academic mind rather than a puzzle meant for the young and the general public.

Undeterred by this universal rejection, and spurred on by his firm belief in the exceptional quality of the toy, Tom Kremer, now armed with a convincing marketing plan, continued his search for a viable partner. After many disappointments, he succeeded in persuading Stewart Sims, Vice President of Marketing of the Ideal Toy Corporation, to come to Hungary, to see with his own eyes the Cube in play. It was now September 1979, by which time the Cube had gained a sufficient degree of popularity to be seen occasionally in the street, on trams, in cafes, each time in the hands of someone turning and twisting it, completely absorbed. After five days of convoluted negotiations between a skeptical American capitalist and an obstinate communist organization largely ignorant of the operation of a free market, with Laczi and Kremer desperately holding the two sides together, an order for one million cubes was signed amidst much handshaking and great relief all round.

In the meanwhile, quite independently of these developments, David Singmaster, an English mathematician, became deeply interested in the theoretical problems and ramifications raised by the Cube in his own field. He wrote a newspaper article in June 1979, the first one to appear outside Hungary, which brought the Cube to the attention of academic circles world wide and led indirectly to another milestone in its history: an article in Scientific American, with a cover picture, by Douglas Hotstadter an acknowledged authority in the field of Recreational Mathematics.

Apart from a small seepage across the Hungarian borders, the Cube made its international debut at the Toy Fairs of London, Paris, Nuremberg and New York in January/February, 1980. With Erno Rubik demonstrating his own creation, the Cube made an immediate impact. The trade buyers were impressed, orders rolled in. There was just one problem: there were no Cubes! Western quality standards and packaging norms meant drastic changes in the Hungarian manufacturing process. This, as with any change under a communist in regime, was slow in coming. Communication between New York and Budapest, given the linguistic and cultural differences, despite the frequent interventions of Tom Kremer, were not easy.

The flow of products from Hungary began in May 1980. As soon as the Cube found its way into the hands of consumers it became evident that the initial order of one million pieces for the first year would not be anywhere near sufficient to meet the growing demand. From the very beginning it was a characteristic of the Cube that no matter how fast production increased, demand grew faster. Contrary to what the leaders of the Toy Industry had expected, for the next two and a half years the problem was not one of selling Cubes but of supplying them. From 1 million the figures started to grow quickly to 2, to 3, to 5 million and then, in 1981 exploded exponentially. Production centers had to expand from Hungary to Hong Kong, Taiwan, Costa Rica and Brazil, taking up the capacities of many separate factories in each center.

The challenge of trying to master the Cube, to be able to restore all of its six sides to the original colors seemed to have a mesmeric effect on an amazing variety of individuals right across age, occupation, wealth and social standing. Grandmothers, bank managers, baseball players, pilots, librarians, park attendants could be seen working away at their Cubes at any hour of the day. In restaurants the Cube would feature on tables side by side with salt and pepper pots, handled with greater frequency than either. But it was the young, schoolboys and students, who were in the vanguard of what was fast becoming a massive movement that swept across the world. They were the ones who proved most adept at solving the puzzle; they were the ones to form special cubists clubs, to organize competitions, to suffer from Rubik's wrist playing continuously for hours and days with an object that simply could not be put down.

The difficulty of solving the Cube and the absolute compulsion to solve it generated over 60 books offering desperately needed help. They in turn generated more addicts, displaying with evident pride their newly acquired prowess.

After winning the highest prize for outstanding inventions in Hungary, in 1980 the Cube won top toy awards in Germany, France, Britain and the U.S. by 1981 it entered the New York Museum of Modern Art as an exhibit. The Cube achieved such a universal presence and penetrated so deeply the fabric of our society that "Rubik's Cube", by 1982 a household term, became part of the Oxford English Dictionary.

It is difficult to estimate the total number of Cubes sold throughout the world. In the period of 1980-1982, partly because demand far outstripped supply, a huge variety of pirate, unauthorized products of inferior quality came onto the market from opportunistic Taiwanese, Korean and Hong Kong vendors. Although the Ideal Toy Corporation won a number of court cases in Holland, Britain, the U.S. and other countries, it was impossible to stem the tide. It is safe to assume that the figure exceeds 100 million, it is certain that it was significantly greater than that.

Interestingly, the legal defense of the Cube was never based on the original patent, this only applied in Hungary. It was the "Rubik" trademark, Erno Rubik's copyright on the object itself and the "passing off" laws, which secured, and continues to secure adequate protection of the Cube against unauthorized copies in all countries throughout the world.

In effect, as the Cube was initially created as a one-off object, with an inherent artistic merit, the Rubik copyright applies not only to the 3D object itself but also to any graphic representation of it in print or on screen, until 70 years after the creator's death.

Given the extraordinary volumes of sales, both legitimate and illegitimate, it was inevitable that eventually a saturation point would be reached. The market in Cubes collapsed, shops and factories remaindered their stocks and for some time from 1983 onwards the Cube became unavailable. The Ideal Toy Corp. was bought by CBS and CBS itself got out of toys in 1985.

The toy business being largely fashion oriented, the industry gave up on the Cube, considering it a fad, albeit an unprecedented one. Not so Tom Kremer. He had always considered the Cube to be one of the all time great classic toys, worthy to be placed alongside such permanent fixtures as Monopoly, Scrabble and Mr. Potato Head. So in 1985 his company, Seven Towns, acquired all the rights to the "Rubik's Cube". Biding their time, they re-introduced the Cube, without any hype, very gradually in selected key markets, beginning in 1991. Compared to the giant waves of the early eighties, sales were just a trickle in the first few years. However, in 1995, Oddzon a dynamic Californian based company took over the distribution of the Cube with dramatic results. In 1996 in the US alone over 300,000 Cubes were sold with the numbers growing in 1997 and 1998. In Japan, where Tsukuda is still the faithful original Rubik's Cube distributor, sales have exceeded 100,000 in 1997 and in Britain sales are also pushing the 100,000 mark. The pattern is the same world over. The Cube is staging a come back.

But now, in its second incarnation, the Cube is part of a family of puzzles and games which bear the stamp of the genius who created the greatest three dimensional puzzle the world has ever known.

Erno Rubik has not changed much over the years. Working closely with Seven Towns, he is still deeply engaged in creating new games and puzzles, and remains one of the principal beneficiaries of what proved to be a spectacularly successful invention.