RUBIK S CLOCK
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ClockA clock or chronometer is a device that measures and displays time. The clock is one of the oldest human inventions, meeting the need to measure intervals of time shorter than the natural units such as the day, the lunar month, and the year. Devices operating on several physical processes have been used over the millennia. Some predecessors to the modern clock may be considered "clocks" that are based on movement in nature: A sundial shows the time by displaying the position of a shadow on a flat surface. There is a range of duration timers, a well-known example being the hourglass. Water clocks, along with sundials, are possibly the oldest time-measuring instruments. A major advance occurred with the invention of the verge escapement, which made possible the first mechanical clocks around 1300 in Europe, which kept time with oscillating timekeepers like balance wheels. Traditionally, in horology (the study of timekeeping), the term clock was used for a striking clock, while a clock that did not strike the hours audibly was called a timepiece. This distinction is not generally made any longer. Watches and other timepieces that can be carried on one's person are usually not referred to as clocks. Spring-driven clocks appeared during the 15th century. During the 15th and 16th centuries, clockmaking flourished. The next development in accuracy occurred after 1656 with the invention of the pendulum clock by Christiaan Huygens. A major stimulus to improving the accuracy and reliability of clocks was the importance of precise time-keeping for navigation. The mechanism of a timepiece with a series of gears driven by a spring or weights is referred to as clockwork; the term is used by extension for a similar mechanism not used in a timepiece. The electric clock was patented in 1840, and electronic clocks were introduced in the 20th century, becoming widespread with the development of small battery-powered semiconductor devices. The timekeeping element in every modern clock is a harmonic oscillator, a physical object (resonator) that vibrates or oscillates at a particular frequency. This object can be a pendulum, a balance wheel, a tuning fork, a quartz crystal, or the vibration of electrons in atoms as they emit microwaves, the last of which is so precise that it serves as the formal definition of the second. Clocks have different ways of displaying the time. Analog clocks indicate time with a traditional clock face and moving hands. Digital clocks display a numeric representation of time. Two numbering systems are in use: 12-hour time notation and 24-hour notation. Most digital clocks use electronic mechanisms and LCD, LED, or VFD displays. For the blind and for use over telephones, speaking clocks state the time audibly in words. There are also clocks for the blind that have displays that can be read by touch.
Rubik's CubeThe Rubik's Cube is a 3D combination puzzle invented in 1974 by Hungarian sculptor and professor of architecture Ernő Rubik. Originally called the Magic Cube, the puzzle was licensed by Rubik to be sold by Pentangle Puzzles in the UK in 1978, and then by Ideal Toy Corp in 1980 via businessman Tibor Laczi and Seven Towns founder Tom Kremer. The cube was released internationally in 1980 and became one of the most recognized icons in popular culture. It won the 1980 German Game of the Year special award for Best Puzzle. As of January 2024, around 500 million cubes had been sold worldwide, making it the world's bestselling puzzle game and bestselling toy. The Rubik's Cube was inducted into the US National Toy Hall of Fame in 2014. On the original, classic Rubik's Cube, each of the six faces was covered by nine stickers, with each face in one of six solid colours: white, red, blue, orange, green, and yellow. Some later versions of the cube have been updated to use coloured plastic panels instead. Since 1988, the arrangement of colours has been standardised, with white opposite yellow, blue opposite green, and orange opposite red, and with the red, white, and blue arranged clockwise, in that order. On early cubes, the position of the colours varied from cube to cube. An internal pivot mechanism enables each layer to turn independently, thus mixing up the colours. For the puzzle to be solved, each face must be returned to having only one colour. The Cube has inspired other designers to create a number of similar puzzles with various numbers of sides, dimensions, and mechanisms. Although the Rubik's Cube reached the height of its mainstream popularity in the 1980s, it is still widely known and used. Many speedcubers continue to practice it and similar puzzles and compete for the fastest times in various categories. Since 2003, the World Cube Association (WCA), the international governing body of the Rubik's Cube, has organised competitions worldwide and has recognised world records.
Ernő RubikErnő Rubik (Hungarian: [ˈrubik ˈɛrnøː]; born 13 July 1944) is a Hungarian architect and inventor, widely known for creating the Rubik's Cube (1974), Rubik's Magic, and Rubik's Snake. While Rubik became famous for inventing the Rubik's Cube and his other puzzles, much of his recent work involves the promotion of science in education. Rubik is involved with several organizations such as Beyond Rubik's Cube, the Rubik Learning Initiative and the Judit Polgar Foundation, all of which aim to engage students in science, mathematics, and problem solving at a young age. Rubik studied sculpture at the Academy of Applied Arts and Design in Budapest and architecture at the Technical University, also in Budapest. While a professor of design at the academy, he pursued his hobby of building geometric models. One of these was a prototype of his cube, made of 27 wooden blocks; it took Rubik a month to solve the problem of the cube. It proved a useful tool for teaching algebraic group theory, and in late 1977 Konsumex, Hungary's state trading company, began marketing it. By 1980, Rubik's Cube was marketed throughout the world, and over 100 million authorized units, with an estimated 50 million unauthorized imitations, were sold, mostly during its subsequent three years of popularity. Approximately 50 books were published describing how to solve the puzzle of Rubik's Cube. Following his cube's popularity, Rubik opened a studio to develop designs in 1984; among its products was another popular puzzle toy, Rubik's Magic.
SpeedcubingSpeedcubing or speedsolving is a competitive mind sport centered around the rapid solving of various combination puzzles. The most prominent puzzle in this category is the 3×3×3 puzzle, commonly known as the Rubik's Cube. Participants in this sport are called "speedcubers" (or simply "cubers"), who focus specifically on solving these puzzles at high speeds to get low clock times. The essential aspect of solving these puzzles typically involves executing a series of predefined algorithms in a particular sequence with eidetic prediction and finger tricks. Competitive speedcubing is predominantly overseen by the World Cube Association (WCA), which officially recognizes 17 distinct speedcubing events. These events encompass a range of puzzles, including N×N×N puzzles of sizes varying from 2×2×2 to 7×7×7, and other puzzle forms such as the Pyraminx, Megaminx, Skewb, Square-1, and Rubik's Clock. Additionally, specialized formats such as 3×3, 4×4, and 5×5 blindfolded, 3×3 one-handed (OH), 3×3 Fewest Moves, and 3×3 multi-blind are also regulated and hosted in competitions. As of May 2025, the world record for the fastest single solve of a Rubik's cube in a competitive setting stands at 3.05 seconds. This record was achieved by Xuanyi Geng at the Shenyang Spring 2025 WCA competition event on Apr 13, 2025. Yiheng Wang set the record for the average time of five solves in the 3×3×3 category with 3.91 seconds at Lishui Open 2025 on May 25, 2025. Speedcubing is organized by numerous countries that hold international competitions throughout the year. The widespread popularity of the Rubik's Cube has led to an abundance of online resources, including guides and techniques, aimed at assisting individuals in solving the puzzle.
David SingmasterDavid Breyer Singmaster (14 December 1938 – 13 February 2023) was an American-British mathematician who was emeritus professor of mathematics at London South Bank University, England. He had a huge personal collection of mechanical puzzles and books of brain teasers. He was most famous for being an early adopter and enthusiastic promoter of the Rubik's Cube. His Notes on Rubik's "Magic Cube" which he began compiling in 1979 provided the first mathematical analysis of the Cube as well as providing one of the first published solutions. The book contained his cube notation which allowed the recording of Rubik's Cube moves, and which quickly became the standard. Singmaster was both a puzzle historian and a composer of puzzles, and many of his puzzles were published in newspapers and magazines. In combinatorial number theory, Singmaster's conjecture states that there is an upper bound on the number of times a number other than 1 can appear in Pascal's triangle.
Rubik's ClockThe Rubik's Clock is a mechanical puzzle invented and patented by Christopher C. Wiggs and Christopher J. Taylor. The Hungarian sculptor and professor of architecture Ernő Rubik bought the patent from them to market the product under his name. It was first marketed in 1988. The Rubik's Clock is a two-sided puzzle, each side presenting nine clocks to the puzzler. There are four dials, one at each corner of the puzzle, each allowing the corresponding corner clock to be rotated directly. (The corner clocks, unlike the other clocks, rotate on both sides of the puzzle simultaneously and can never be operated independently. Thus, the puzzle contains only 14 independent clocks.) There are also four pins which span both sides of the puzzle; each pin arranged such that if it is "in" on one side, it is "out" on the other. The state of each pin (in or out) determines whether the adjacent corner clock is mechanically connected to the three other adjacent clocks on the front side or on the back side: thus the configuration of the pins determines which sets of clocks can be turned simultaneously by rotating a suitable dial. The aim of the puzzle is to set all nine clocks to 12 o'clock (straight up) on both sides of the puzzle simultaneously. A method to do so is to start by constructing a cross on both sides (at 12 o’clock) and then solving the corner clocks individually. The Rubik's Clock is listed as one of the 17 WCA events, with records for fastest time to solve one puzzle, and the fastest average time to solve 5 puzzles (discarding the slowest and fastest times). Viable speedsolving methods have been devised that always solve it in 14 moves or less. An example is "7-Simul", which involves performing seven pairs of moves on the front and back of the clock simultaneously and requires mental calculation from the puzzle's initial position to determine some moves. God's number for Clock is 12.
Rubik's Cube groupThe Rubik's Cube group ( G , ⋅ ) {\displaystyle (G,\cdot )} represents the mathematical structure of the Rubik's Cube mechanical puzzle. Each element of the set G {\displaystyle G} corresponds to a cube move, which is the effect of any sequence of rotations of the cube's faces. With this representation, not only can any cube move be represented, but any position of the cube as well, by detailing the cube moves required to rotate the solved cube into that position. Indeed with the solved position as a starting point, there is a one-to-one correspondence between each of the legal positions of the Rubik's Cube and the elements of G {\displaystyle G} . The group operation ⋅ {\displaystyle \cdot } is the composition of cube moves, corresponding to the result of performing one cube move after another. The Rubik's Cube is constructed by labeling each of the 48 non-center facets with the integers 1 to 48. Each configuration of the cube can be represented as a permutation of the labels 1 to 48, depending on the position of each facet. Using this representation, the solved cube is the identity permutation which leaves the cube unchanged, while the twelve cube moves that rotate a layer of the cube 90 degrees are represented by their respective permutations. The Rubik's Cube group is the subgroup of the symmetric group S 48 {\displaystyle S_{48}} generated by the six permutations corresponding to the six clockwise cube moves. With this construction, any configuration of the cube reachable through a sequence of cube moves is within the group. Its operation ⋅ {\displaystyle \cdot } refers to the composition of two permutations; within the cube, this refers to combining two sequences of cube moves together, doing one after the other. The Rubik's Cube group is non-abelian as composition of cube moves is not commutative; doing two sequences of cube moves in a different order can result in a different configuration.
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