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Today, the patents have expired and many Chinese companies produce copies of, and in nearly all cases, improvements upon, the Rubik and V-Cube designs. Nichols assigned his patent to his employer Moleculon Research Corp.

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In , Ideal lost the patent infringement suit and appealed. Even while Rubik's patent application was being processed, Terutoshi Ishigi, a self-taught engineer and ironworks owner near Tokyo, filed for a Japanese patent for a nearly identical mechanism, which was granted in Japanese patent publication JP Until , when an amended Japanese patent law was enforced, Japan's patent office granted Japanese patents for non-disclosed technology within Japan without requiring worldwide novelty. In the United States, Rubik was granted U.

Patent 4,, on 29 March , for the Cube. This patent expired in Rubik's Brand Ltd. The trademarks have been upheld by a ruling of the General Court of the European Union on 25 November in a successful defence against a German toy manufacturer seeking to invalidate them. However, European toy manufacturers are allowed to create differently shaped puzzles that have a similar rotating or twisting functionality of component parts such as for example Skewb , Pyraminx or Impossiball.

On 10 November , Rubik's Cube lost a ten-year battle over a key trademark issue. The European Union 's highest court, the Court of Justice ruled that the puzzle's shape was not sufficient to grant it trademark protection. A standard Rubik's Cube measures 5. The puzzle consists of twenty-six unique miniature cubes, also called "cubies" or "cubelets". Each of these includes a concealed inward extension that interlocks with the other cubes while permitting them to move to different locations.

These provide structure for the other pieces to fit into and rotate around. So there are twenty-one pieces: a single core piece consisting of three intersecting axes holding the six centre squares in place but letting them rotate, and twenty smaller plastic pieces which fit into it to form the assembled puzzle. Each of the six centre pieces pivots on a screw fastener held by the centre piece, a "3D cross". A spring between each screw head and its corresponding piece tensions the piece inward, so that collectively, the whole assembly remains compact, but can still be easily manipulated.

The screw can be tightened or loosened to change the "feel" of the Cube. Newer official Rubik's brand cubes have rivets instead of screws and cannot be adjusted. Consequently, it is a simple process to "solve" a Cube by taking it apart and reassembling it in a solved state. There are six central pieces which show one coloured face, twelve edge pieces which show two coloured faces, and eight corner pieces which show three coloured faces.

Each piece shows a unique colour combination, but not all combinations are present for example, if red and orange are on opposite sides of the solved Cube, there is no edge piece with both red and orange sides. However, Cubes with alternative colour arrangements also exist; for example, with the yellow face opposite the green, the blue face opposite the white, and red and orange remaining opposite each other.

Douglas Hofstadter , in the July issue of Scientific American , pointed out that Cubes could be coloured in such a way as to emphasise the corners or edges, rather than the faces as the standard colouring does; but neither of these alternative colourings has ever become popular. The puzzle was originally advertised as having "over 3,,, three billion combinations but only one solution".

There are 8! Each corner has three possible orientations, although only seven of eight can be oriented independently; the orientation of the eighth final corner depends on the preceding seven, giving 3 7 2, possibilities. There are 12! When arrangements of centres are also permitted, as described below, the rule is that the combined arrangement of corners, edges, and centres must be an even permutation. Eleven edges can be flipped independently, with the flip of the twelfth depending on the preceding ones, giving 2 11 2, possibilities.


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The preceding figure is limited to permutations that can be reached solely by turning the sides of the cube. If one considers permutations reached through disassembly of the cube, the number becomes twelve times larger:. This is because there is no sequence of moves that will swap a single pair of pieces or rotate a single corner or edge cube.

Thus there are twelve possible sets of reachable configurations, sometimes called "universes" or " orbits ", into which the Cube can be placed by dismantling and reassembling it. The preceding numbers assume the center faces are in a fixed position. If one considers turning the whole cube to be a different permutation, then each of the preceding numbers should be multiplied by A chosen color can be on one of six sides, and then one of the adjacent colors can be in one of four positions; this determines the positions of all remaining colors.

The original Rubik's Cube had no orientation markings on the centre faces although some carried the words "Rubik's Cube" on the centre square of the white face , and therefore solving it does not require any attention to orienting those faces correctly. However, with marker pens, one could, for example, mark the central squares of an unscrambled Cube with four coloured marks on each edge, each corresponding to the colour of the adjacent face; a cube marked in this way is referred to as a "supercube".

Some Cubes have also been produced commercially with markings on all of the squares, such as the Lo Shu magic square or playing card suits. Cubes have also been produced where the nine stickers on a face are used to make a single larger picture, and centre orientation matters on these as well. Thus one can nominally solve a Cube yet have the markings on the centres rotated; it then becomes an additional test to solve the centres as well.

Marking the Rubik's Cube's centres increases its difficulty because this expands the set of distinguishable possible configurations. In particular, when the Cube is unscrambled apart from the orientations of the central squares, there will always be an even number of centre squares requiring a quarter turn. Thus orientations of centres increases the total number of possible Cube permutations from 43,,,,,, 4.

When turning a cube over is considered to be a change in permutation then we must also count arrangements of the centre faces. Nominally there are 6! When the orientations of centres are also counted, as above, this increases the total number of possible Cube permutations from 88,,,,,,, 8. In Rubik's cubers' parlance, a memorised sequence of moves that has a desired effect on the cube is called an algorithm. This terminology is derived from the mathematical use of algorithm , meaning a list of well-defined instructions for performing a task from a given initial state, through well-defined successive states, to a desired end-state.

Each method of solving the Rubik's Cube employs its own set of algorithms, together with descriptions of what effect the algorithm has, and when it can be used to bring the cube closer to being solved. Many algorithms are designed to transform only a small part of the cube without interfering with other parts that have already been solved so that they can be applied repeatedly to different parts of the cube until the whole is solved.

For example, there are well-known algorithms for cycling three corners without changing the rest of the puzzle or flipping the orientation of a pair of edges while leaving the others intact. Some algorithms do have a certain desired effect on the cube for example, swapping two corners but may also have the side-effect of changing other parts of the cube such as permuting some edges.

Such algorithms are often simpler than the ones without side-effects and are employed early on in the solution when most of the puzzle has not yet been solved and the side-effects are not important. Most are long and difficult to memorise. Towards the end of the solution, the more specific and usually more complicated algorithms are used instead. For example, one such "level" could involve solving cubes which have been scrambled using only degree turns. These subgroups are the principle underlying the computer cubing methods by Thistlethwaite and Kociemba , which solve the cube by further reducing it to another subgroup.

These directions are as one is looking at the specified face. The letters x , y , and z are used to indicate that the entire Cube should be turned about one of its axes, corresponding to R, U, and F turns respectively. When x , y or z are primed, it is an indication that the cube must be rotated in the opposite direction. When they are squared, the cube must be rotated degrees. The most common deviation from Singmaster notation, and in fact the current official standard, is to use "w", for "wide", instead of lowercase letters to represent moves of two layers; thus, a move of Rw is equivalent to one of r.

For methods using middle-layer turns particularly corners-first methods there is a generally accepted "MES" extension to the notation where letters M , E , and S denote middle layer turns. It was used e. Lowercase letters f b u d l r refer to the inner portions of the cube called slices.

An alternative notation, Wolstenholme notation, [55] is designed to make memorising sequences of moves easier for novices. This notation uses the same letters for faces except it replaces U with T top , so that all are consonants. Addition of a C implies rotation of the entire cube, so ROC is the clockwise rotation of the cube around its right face.

Middle layer moves are denoted by adding an M to corresponding face move, so RIM means a degree turn of the middle layer adjacent to the R face. Singmaster notation was not widely known at the time of publication.

Rubik's Cube

Horizontal planes were noted as tables, with table 1 or T1 starting at the top. Vertical front to back planes were noted as book, with book 1 or B1 starting from the left. Vertical left to right planes were noted as windows, with window 1 or W1 starting at the front. Using the front face as a reference view, table moves were left or right, book moves were up or down, and window moves were clockwise or anticlockwise. Although there are a significant number of possible permutations for the Rubik's Cube, a number of solutions have been developed which allow solving the cube in well under moves.

Many general solutions for the Rubik's Cube have been discovered independently. After sufficient practice, solving the Cube layer by layer can be done in under one minute. Other general solutions include "corners first" methods or combinations of several other methods. In , David Singmaster and Alexander Frey hypothesised that the number of moves needed to solve the Rubik's Cube, given an ideal algorithm, might be in "the low twenties".

A solution commonly used by speedcubers was developed by Jessica Fridrich. It is similar to the layer-by-layer method but employs the use of a large number of algorithms, especially for orienting and permuting the last layer. The cross is done first, followed by first layer corners and second layer edges simultaneously, with each corner paired up with a second-layer edge piece, thus completing the first two layers F2L. Fridrich's solution requires learning roughly algorithms but allows the Cube to be solved in only 55 moves on average. A now well-known method was developed by Lars Petrus.

One of the advantages of this method is that it tends to give solutions in fewer moves. For this reason, the method is also popular for fewest move competitions. The Roux Method, developed by Gilles Roux , is similar to the Petrus method in that it relies on block building rather than layers, but derives from corners-first methods. Next, the corners of the top layer are solved. The cube can then be solved using only moves of the U layer and M slice.

Most beginner solution methods involve solving the cube one layer at a time, using algorithms that preserve what has already been solved. The easiest layer by layer methods require only 3—8 algorithms. In , thirteen-year-old Patrick Bossert developed a solution for solving the cube, along with a graphical notation, designed to be easily understood by novices. In , Denny Dedmore published a solution described using diagrammatic icons representing the moves to be made, instead of the usual notation.

Philip Marshall's The Ultimate Solution to Rubik's Cube takes a different approach, averaging only 65 twists yet requiring the memorisation of only two algorithms. The cross is solved first, followed by the remaining edges, then five corners, and finally the last three corners. The most move optimal online Rubik's Cube solver programs use Herbert Kociemba's Two-Phase Algorithm which can typically determine a solution of 20 moves or less. The user has to set the colour configuration of the scrambled cube and the program returns the steps required to solve it.

Speedcubing or speedsolving is the practice of trying to solve a Rubik's Cube in the shortest time possible. There are a number of speedcubing competitions that take place around the world. Since , the winner of a competition is determined by taking the average time of the middle three of five attempts. However, the single best time of all tries is also recorded.

The World Cube Association maintains a history of world records. In addition to the main 3x3x3 event, the WCA also holds events where the cube is solved in different ways: [78]. In Blindfolded Solving, the contestant first studies the scrambled cube i. Their recorded time for this event includes both the time spent memorizing the cube and the time spent manipulating it. The event is scored not by time but by the number of points achieved after the one hour time limit has elapsed. The number of points achieved is equal to the number of cubes solved correctly, minus the number of cubes unsolved after the end of the attempt, where a greater number of points is better.

If multiple competitors achieve the same number of points, rankings are assessed based on the total time of the attempt, with a shorter time being better. In Fewest Moves solving, the contestant is given one hour to find a solution and must write it down. There are many variations [] of the original cube, some of which are made by Rubik. The mechanical products include the Rubik's Magic, , and Twist.

Also, electronics like the Rubik's Revolution and Slide were also inspired by the original.

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Sliding a finger across its faces causes its patterns of coloured lights to rotate the same way they would on a mechanical cube. The TouchCube also has buttons for hints and self-solving, and it includes a charging stand. The Cube has inspired an entire category of similar puzzles, commonly referred to as twisty puzzles , which includes the cubes of different sizes mentioned above as well as various other geometric shapes.

Some such shapes include the tetrahedron Pyraminx , the octahedron Skewb Diamond , the dodecahedron Megaminx , the icosahedron Dogic. There are also puzzles that change shape such as Rubik's Snake and the Square One. Some puzzles have also been created in the shape of the Kepler-Poinsot polyhedra , such as Alexander's Star a great dodecahedron. Puzzles have been built resembling the Rubik's Cube or based on its inner workings.

Some custom puzzles are not derived from any existing mechanism, such as the Gigaminx v1. These puzzles usually have a set of masters 3D printed, which then are copied using moulding and casting techniques to create the final puzzle. Other Rubik's Cube modifications include cubes that have been extended or truncated to form a new shape. Most shape mods can be adapted to higher-order cubes. Puzzles like the Rubik's Cube can be simulated by computer software , which provide functions such as recording of player metrics, storing scrambled Cube positions, conducting online competitions, analysing of move sequences, and converting between different move notations.


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The site has various interactive objects based on Rubik's Cube. Customised versions of Rubik's Cube can be created and uploaded. From Wikipedia, the free encyclopedia. See also: Rubik's Cube in popular culture. This section needs additional citations for verification. Please help improve this article by adding citations to reliable sources.

Unsourced material may be challenged and removed. Main article: Optimal solutions for Rubik's Cube. Main article: Speedcubing. Main article: Rubik's Cube in popular culture. Fotheringham's Sporting Pastimes. Anova Books. BBC News Magazine. Retrieved 28 April A Biographical Encyclopedia of Scientists. IMHO, the value of word scrambles and word find puzzles as homework is suspect. They may help with spelling, I suppose, and definitions in some formats, but appear to have little to offer in terms of helping students better understand and apply concepts. So, if using your resource helps students complete "busy work" assignments more efficiently, hurrah for time management!

It's been shared with others who "get stuck". My daughter calls it my word cheater, I call it assistance when necessary! Very easy to understand the results and we love it! Thanks so much! I seem like a pro playing scrabble online. This site is my little secret weapon. Helped me get extra credit in school with brainteasers! Bookmarked, shared and enjoyed! Thanks for letting us smile and conquer a difficult homework. Googled "word finder" and came here because of description, "find words for poetry.

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Brain freeze, helps to thaw it. It wasn't shown in results I just tried it and it works. Otherwise, it tries to unscramble it as a single word. It also unscrambles as "coed caretaking" and "certain dockage". My computer beat your computer. I will use the site in the future when I am up against it!! The first word list contains all of the officially allowable Scrabble words. The second word list is for spell checking documents. There are many obscure words that are not in either list. I am working on additional word lists. If you entered a valid email, I'll let you know when it works.

Otherwise, it tries to find those three letters next to each other.

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Didn't you have the "any order" box checked to find "Octahedral"? Its Freakonomics. That explains why it wouldn't be in either word list. The math for doing searches and unscrambles on word lists with , words or more is pretty intense. Add to that the popularity of this page and the server might sometimes lag a bit.

That being said, I might move the comments to another page if the list gets much longer. Thank you!! Thx to all those guys and girls that helped to create it! It was just me, lol. Did you find this page randomly? LOL ". I've gotten my Text Twist score up to over 11,, now. Before your site, I always crashed the game by ,! I also like the rest of your site and its very useful contents.

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You are a genius!

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It should do what you need. Any one know? I love scrambled word games, was really a great help. It worked great. Made my grandson happy ". Can anyone comment on this?