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The superflip or 12-flip is a special configuration on a Rubik's Cube, in which all the edge and corner pieces are in the correct permutation, and the eight corners are correctly oriented, but all twelve edges are oriented incorrectly ("flipped").
The term superflip is also used to refer to any algorithm that transforms the Rubik's Cube from its solved state into the superflip configuration.
The superflip is a completely symmetrical combination, which means applying a superflip algorithm to the cube will always yield the same position, irrespective of the orientation in which the cube is held.
The superflip is self-inverse; i.e. performing a superflip algorithm twice will bring the cube back to the starting position.
Furthermore, the superflip is the only nontrivial central configuration of the Rubik's Cube. This means that it is commutative with all other algorithms – i.e. performing any algorithm X followed by a superflip algorithm yields exactly the same position as performing the superflip algorithm first followed by X – and it is the only configuration (except trivially for the solved state) with this property. By extension, this implies that a commutator of a superflip and any other algorithm will always bring the cube back to its solved position.
The table below shows four possible algorithms that transform a solved Rubik's Cube into its superflip configuration, together with the number of moves each algorithm has under each metric:
All the algorithms below are recorded in Singmaster notation:
| Algorithm | Number of turns under: | ||
|---|---|---|---|
| HTM | QTM | STM | |
| 20 | 28 | 19 | |
| 22 | 24 | 22 | |
| 22 | 32 | 16 | |
| 36 | 36 | 24 | |
It has been shown [1] that the shortest path between a solved cube and the superflip requires 20 moves under HTM (the first algorithm is one such example), and that no position requires more moves. Contrary to popular belief, however, the superflip is not unique in this regard: there are many other positions that also require 20 moves.
Under the more restrictive QTM, the superflip requires at least 24 moves (the second algorithm above is one such sequence), [2] [ better source needed ] and is not maximally distant from the solved state. Instead, when superflip is composed with the "four-dot" or "four-spot" position, in which four faces have their centres exchanged with the centres on the opposite face, the resulting position requires 26 moves under QTM. [3]
Under STM, the superflip requires at least 16 moves (as shown by the third algorithm).
The last solution in the table is not optimal under any metric, but is both easiest to learn and fastest to do for humans, as the sequence of moves is very repetitive.
The 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.
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The Rubik's Cube is the original and best known of the three-dimensional sequential move puzzles. There have been many virtual implementations of this puzzle in software. It is a natural extension to create sequential move puzzles in more than three dimensions. Although no such puzzle could ever be physically constructed, the rules of how they operate are quite rigorously defined mathematically and are analogous to the rules found in three-dimensional geometry. Hence, they can be simulated by software. As with the mechanical sequential move puzzles, there are records for solvers, although not yet the same degree of competitive organisation.
The Simple Solution to Rubik's Cube by James G. Nourse is a book that was published in 1981. The book explains how to solve the Rubik's Cube. The book became the best-selling book of 1981, selling 6,680,000 copies that year. It was the fastest-selling title in the 36-year history of Bantam Books.
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The original Rubik's cube was a mechanical 3×3×3 cube puzzle invented in 1974 by the Hungarian sculptor and professor of architecture Ernő Rubik. Extensions of the Rubik's cube have been around for a long time and come in both hardware and software forms. The major extension have been the availability of cubes of larger size and the availability of the more complex cubes with marked centres. The properties of Rubik’s family cubes of any size together with some special attention to software cubes is the main focus of this article. Many properties are mathematical in nature and are functions of the cube size variable.
The Layer by Layer method, also known as the beginners' method, is a method of solving the 3x3x3 Rubik's Cube. Many beginners' methods use this approach, and it also forms the basis of the CFOP speedcubing technique.
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