|
|
| Line 1: |
Line 1: |
| [[File:Rubiks revenge solved.jpg|thumb|right|Rubik's Revenge in solved state]]
| | Today I am sharing a dark experience with you as I am from this darkness today. Whoa! Google Chrome has crashed was the disaster that struck on me early this morning. My blood flow seemed to stop for a few minutes. Next I regained my senses plus decided to fix Chrome crash.<br><br>Another answer would be to offer the computer program with a fresh msvcr71 file. Frequently, once the file has been corrupted or damaged, it might no longer be able to function like it did before so it's just natural to substitute the file. Simply download another msvcr71.dll file within the internet. Often, the file will come inside a zip structure. Extract the files within the zip folder and region them accordingly in this location: C:\Windows\System32. Afterward, re-register the file. Click Start plus then choose Run. Once the Run window appears, sort "cmd". Press Enter and then sort "regsvr32 -u msvcr71.dll" followed by "regsvr32 msvcr71.dll". Press Enter again plus the file must be registered accordingly.<br><br>Perfect Optimizer also has to remove junk files plus is fully Windows Vista compatible. Many registry product simply don't have the time and income to research Windows Vista errors. Because best optimizer has a big customer base, they do have the time, income plus reasons to support completely help Windows Vista.<br><br>Windows errors could be caused by any amount of factors, nevertheless there's almost usually 1 cause. There's a hidden piece of your program that is responsible for creating 90% of all Windows errors, and it's called the 'registry'. This is the central database for your system and is where your computer stores all its program files and settings. It's a quite important part of Windows, that is should be capable to function. However, it's equally among the biggest causes of problems on a PC.<br><br>So to fix this, you just should be capable to create all registry files non-corrupted again. This usually dramatically speed up the loading time of the computer plus allows you to do a large amount of items on it again. And fixing these files couldn't be simpler - you only need to use a tool called a [http://bestregistrycleanerfix.com/tune-up-utilities tuneup utilities 2014].<br><br>If you think that there are issues with the d3d9.dll file, then we have to replace it with a modern functioning file. This will be done by performing a series of procedures and you are able to start by obtaining "d3d9.zip" from the server. Then we have to unzip the "d3d9.dll" file found on the difficult drive of the computer. Proceed by finding "C:\Windows\System32" and then finding the existing "d3d9.dll" on a PC. Once found, rename the file "d3d9.dll to d3d9BACKUP.dll" and then copy-paste this new file to "C:\Windows\System32". After which, press "Start" followed by "Run" or look "Run" on Windows Vista & 7. As soon as a box shows up, kind "cmd". A black screen might then appear plus you need to sort "regsvr32d3d9.dll" plus then click "Enter". This task usually help we to replace the aged file with the fresh copy.<br><br>Whenever the registry is corrupt or full of mistakes, the signs may be felt by the computer owner. The slow performance, the frequent system crashes plus the nightmare of all computer owners, the blue screen of death.<br><br>So inside summary, when comparing registry cleaning, make certain that that the 1 you choose provides we the following.A backup and restore facility, quickly operation, automatic deletion facility, start-up administration, an easy technique of contact plus a cash back guarantee. |
| | |
| The '''Rubik's Revenge''' (also known as the '''Master Cube''') is the 4×4×4 version of [[Rubik's Cube]]. It was released in 1981. Invented by Péter Sebestény, the Rubik's Revenge was nearly called the '''Sebestény Cube''' until a somewhat last-minute decision changed the puzzle's name to attract fans of the original Rubik's Cube.{{Citation needed|date=December 2008}} Unlike the original puzzle (and the [[Professor's Cube|5×5×5 cube]]), it has no fixed facets: the centre facets (four per face) are free to move to different positions.
| |
| | |
| Methods for solving the 3×3×3 cube work for the edges and corners of the 4×4×4 cube, as long as one has correctly identified the relative positions of the colours — since the centre facets can no longer be used for identification.
| |
| | |
| ==Mechanics==
| |
| [[File:Rubiks revenge scrambled.jpg|thumb|right|Rubik's Revenge in scrambled state]]
| |
| [[File:Rubiks Revenge 1982.JPG|thumb|right|Early Rubik's Revenge cube, with white opposite blue and green opposite yellow]]
| |
| [[File:Eastsheen vs. Rubik 4x4.jpg|thumb|An Eastsheen cube is on the left, and an official Rubik's Revenge is on the right.]]
| |
| [[File:Unassembled Rubik's Revenge.JPG|thumb|A disassembled Rubik's Revenge, showing all the pieces and central ball]]
| |
| [[File:Disassembled Eastsheen 4×4×4.jpg|thumb|A disassembled Eastsheen 4×4×4]]
| |
| The puzzle consists of 56 unique miniature cubes ("cubies") on the surface. These consist of 24 centres which show one colour each, 24 edges which show two colours each, and 8 corners which show three colours each. The original Rubik's Revenge can be taken apart without much difficulty, typically by turning one side through a 30° angle and prying an edge upward until it dislodges.
| |
| | |
| The original mechanism designed by Sebestény uses a grooved ball to hold the centre pieces in place. The edge pieces are held in place by the centres and the corners are held in place by the edges, much like the original cube. There are three mutually perpendicular grooves for the centre pieces to slide through. Each groove is only wide enough to allow one row of centre pieces to slide through it. The ball is shaped to prevent the centre pieces of the other row from sliding, ensuring that the ball remains aligned with the outside of the cube. Turning one of the centre layers moves either just that layer or the ball as well.<ref name="Sebestény patent">[http://www.freepatentsonline.com/4421311.html United States Patent 4421311]</ref>
| |
| | |
| The [[Eastsheen]] version of the cube, which is slightly smaller at 6 cm to an edge, has a completely different mechanism. Its mechanism is very similar to Eastsheen's version of the Professor's cube, instead of the ball-core mechanism. There are 42 pieces (36 movable and six fixed) completely hidden within the cube, corresponding to the centre rows on the Professor's Cube. This design is more durable than the original and also allows for screws to be used to tighten or loosen the cube. The central spindle is specially shaped to prevent it from becoming misaligned with the exterior of the cube.<ref name="Eastsheen patent">[http://www.freepatentsonline.com/5992850.html United States Patent 5992850]</ref>
| |
| | |
| There are 24 edge pieces which show two coloured sides each, and eight corner pieces which show three colours. Each corner piece or pair of edge pieces shows a unique colour combination, but not all combinations are present (for example, there is no piece with both red and orange sides, if red and orange are on opposite sides of the solved Cube). The location of these cubes relative to one another can be altered by twisting the layers of the cube, but the location of the coloured sides relative to one another in the completed state of the puzzle cannot be altered: it is fixed by the relative positions of the centre squares and the distribution of colour combinations on edge and corner pieces.
| |
| | |
| For most recent Cubes, the colours of the stickers are red opposite orange, yellow opposite white, and green opposite blue. However, there also exist Cubes with alternative colour arrangements (yellow opposite green, blue opposite white and red opposite orange). The Eastsheen version has purple (opposite red) instead of orange.
| |
| | |
| ===Permutations===
| |
| [[File:Rubiks revenge tilt.jpg|thumb|none|Rubik's Revenge with a tilted side]]
| |
| There are 8 corners, 24 edges and 24 centres.
| |
| | |
| Any permutation of the corners is possible, including odd permutations. Seven of the corners can be independently rotated, and the orientation of the eighth depends on the other seven, giving [[factorial|8!]]×3<sup>7</sup> combinations.
| |
| | |
| There are 24 centres, which can be arranged in 24! different ways. Assuming that the four centres of each colour are indistinguishable, the number of permutations is reduced to 24!/(4!<sup>6</sup>) arrangements. The reducing factor comes about because there are 4! ways to arrange the four pieces of a given colour. This is raised to the sixth power because there are six colours. An odd permutation of the corners implies an odd permutation of the centres and vice versa; however, even and odd permutations of the centres are indistinguishable due to the identical appearance of the pieces.<ref name="Cubic Circular 7 & 8">[http://www.jaapsch.net/puzzles/cubic7.htm#p11 Cubic Circular Issue 7 & 8] [[David Singmaster]], 1985</ref> There are several ways to make the centre pieces distinguishable, which would make an odd centre permutation visible.
| |
| | |
| The 24 edges cannot be flipped, because the internal shape of the pieces is asymmetrical. Corresponding edges are distinguishable, since they are mirror images of each other. Any permutation of the edges is possible, including odd permutations, giving 24! arrangements, independently of the corners or centres.
| |
| | |
| Assuming the cube does not have a fixed orientation in space, and that the permutations resulting from rotating the cube without twisting it are considered identical, the number of permutations is reduced by a factor of 24. This is because all 24 possible positions and orientations of the first corner are equivalent because of the lack of fixed centres. This factor does not appear when calculating the permutations of N×N×N cubes where N is odd, since those puzzles have fixed centres which identify the cube's spatial orientation.
| |
| | |
| This gives a total number of permutations of
| |
| :<math>\frac{8! \times 3^7 \times 24!^2}{4!^6 \times 24} \approx 7.40 \times 10^{45}.</math> | |
| | |
| The full number is 7 401 196 841 564 901 869 874 093 974 498 574 336 000 000 000 possible permutations<ref name="Cubic Circular 3 & 4">[http://www.jaapsch.net/puzzles/cubic3.htm#p14 Cubic Circular Issues 3 & 4] [[David Singmaster]], 1982</ref> (about 7,401 septillion or 7.4 septilliard on the [[names of large numbers|long scale]] or 7.4 quattuordecillion on the short scale).
| |
| | |
| Some versions of Rubik's Revenge have one of the centre pieces marked with a logo, distinguishing it from the other three of the same colour. This increases the number of distinguishable permutations by a factor of four to 2.96×10<sup>46</sup>, although any of the four possible positions for this piece could be regarded as correct.
| |
| | |
| ==Solutions==
| |
| There are several methods that can be used to solve a Rubik's Revenge. The most common method is '''reduction''', so called because it effectively reduces the 4x4x4 to a 3x3x3. Cubers first group the centre pieces of common colours together, then pair edges that show the same two colours. Once this is done, turning only the outer layers of the cube allows it to be solved like a 3×3×3 cube. However, certain positions that cannot be solved on a standard 3×3×3 cube may be reached. There are two possible problems not found on the 3x3x3. The first is two edge pieces reversed on one edge, resulting in the colours for that edge not matching the rest of the cubies on either face:
| |
| {{Rubik's Revenge face|=
| |
| |=|r| | |r|=
| |
| |y| |r|r| |g|=
| |
| |y| | | | |g|=
| |
| |y| | | | |g|=
| |
| |y| | | | |g|=
| |
| |=|b|b|b|b|=
| |
| |10px}} Notice that these two edge pieces are swapped. The second is two edge pairs being swapped with each other:
| |
| {{Rubik's Revenge face|=
| |
| |=|r|y|y|r|=
| |
| |y| | | | |g|=
| |
| |r| | | | |g|=
| |
| |r| | | | |g|=
| |
| |y| | | | |g|=
| |
| |=|b|b|b|b|=
| |
| |10px}} These situations are known as [[Parity of a permutation|parity]] errors. These positions are still solvable; however, special algorithms must be applied to fix the errors.<ref>{{cite web|last=Morris|first=Frank|title=solving the revenge|url=http://bigcubes.com/4x4x4/4x4x4.html|accessdate=15 June 2012}}</ref>
| |
| | |
| Some methods are designed to avoid the parity errors described above. For instance, solving the corners and edges first and the centres last would avoid such parity errors. Once the rest of the cube is solved, any permutation of the centre pieces can be solved. Note that it is possible to apparently exchange a pair of face centres by cycling 3 face centres, two of which are visually identical.
| |
| | |
| Direct solving of a 4x4x4 is uncommon, but possible, with methods such as K4. Doing so mixes a variety of techniques and is heavily reliant on commutators for the final steps.<ref name=k4>{{cite web|last=Barlow|first=Thom|title=K4 Method|url=http://snk.digibase.ca/k4/index.htm|accessdate=15 June 2012}}</ref>
| |
| | |
| ==World records==
| |
| The world record single fastest time is 24.66 seconds set by [[Feliks Zemdegs]] of Australia at Lifestyle Seasons Summer 2014.<ref>[[World Cube Association]] [http://www.worldcubeassociation.org/results/e.php?i=444 Official Results - 4×4×4 Cube]</ref> The world record for an average of five solves is held by Sebastian Weyer with a time of 29.17 seconds set at the Frankfurt Cube Days 2012.<ref>[[World Cube Association]] [http://worldcubeassociation.org/results/c.php?i=FrankfurtOpen2012&allResults=1#444 Official Results - Frankfurt Open 2012].</ref> Marcell Endrey of Hungary holds the world record for solving the 4x4x4 cube blindfolded in 2 minutes, 30.62 seconds.<ref>[[World Cube Association]] [http://www.worldcubeassociation.org/results/regions.php?regionId=&eventId=444bf&years=&mixed=Mixed Official Results - 4×4×4 Cube Blindfolded].</ref>
| |
| | |
| ==See also==
| |
| * [[Pocket Cube]] (2×2×2)
| |
| * [[Rubik's Cube]] (3×3×3)
| |
| * [[Professor's Cube]] (5×5×5)
| |
| * [[V-Cube 6]] (6×6×6)
| |
| * [[V-Cube 7]] (7×7×7)
| |
| * [[Combination puzzles]]
| |
| | |
| == References ==
| |
| <references/>
| |
| | |
| ==Further reading==
| |
| * Rubik's Revenge: The Simplest Solution by William L. Mason
| |
| *Speedsolving the Cube by Dan Harris, 'Rubik's Revenge' pages 100-120.
| |
| *The Winning Solution to Rubik's Revenge by [[Minh Thai]], with Herbert Taylor and M. Razid Black.
| |
| | |
| ==External links==
| |
| {{commonscat|Rubik's Revenge}}
| |
| * [http://www.speedcubing.com/chris/4-solution.html Beginner/Intermediate solution to the Rubik's Revenge] by Chris Hardwick
| |
| * [http://snk.digibase.ca/k4/ 'K4' Method] Advanced direct solving method.
| |
| * [http://www.randelshofer.ch/rubik/patterns_revenge.html Patterns] A collection of pretty patterns for Rubik's Revenge
| |
| * [http://kubrub.googlepages.com/rubikscube Program Rubik's Cube 3D Unlimited size]
| |
| | |
| {{Rubik's Cube}}
| |
| | |
| [[Category:Rubik's Cube]]
| |
| [[Category:Combination puzzles]]
| |
| [[Category:Mechanical puzzles]]
| |
| [[Category:Puzzles]]
| |
Today I am sharing a dark experience with you as I am from this darkness today. Whoa! Google Chrome has crashed was the disaster that struck on me early this morning. My blood flow seemed to stop for a few minutes. Next I regained my senses plus decided to fix Chrome crash.
Another answer would be to offer the computer program with a fresh msvcr71 file. Frequently, once the file has been corrupted or damaged, it might no longer be able to function like it did before so it's just natural to substitute the file. Simply download another msvcr71.dll file within the internet. Often, the file will come inside a zip structure. Extract the files within the zip folder and region them accordingly in this location: C:\Windows\System32. Afterward, re-register the file. Click Start plus then choose Run. Once the Run window appears, sort "cmd". Press Enter and then sort "regsvr32 -u msvcr71.dll" followed by "regsvr32 msvcr71.dll". Press Enter again plus the file must be registered accordingly.
Perfect Optimizer also has to remove junk files plus is fully Windows Vista compatible. Many registry product simply don't have the time and income to research Windows Vista errors. Because best optimizer has a big customer base, they do have the time, income plus reasons to support completely help Windows Vista.
Windows errors could be caused by any amount of factors, nevertheless there's almost usually 1 cause. There's a hidden piece of your program that is responsible for creating 90% of all Windows errors, and it's called the 'registry'. This is the central database for your system and is where your computer stores all its program files and settings. It's a quite important part of Windows, that is should be capable to function. However, it's equally among the biggest causes of problems on a PC.
So to fix this, you just should be capable to create all registry files non-corrupted again. This usually dramatically speed up the loading time of the computer plus allows you to do a large amount of items on it again. And fixing these files couldn't be simpler - you only need to use a tool called a tuneup utilities 2014.
If you think that there are issues with the d3d9.dll file, then we have to replace it with a modern functioning file. This will be done by performing a series of procedures and you are able to start by obtaining "d3d9.zip" from the server. Then we have to unzip the "d3d9.dll" file found on the difficult drive of the computer. Proceed by finding "C:\Windows\System32" and then finding the existing "d3d9.dll" on a PC. Once found, rename the file "d3d9.dll to d3d9BACKUP.dll" and then copy-paste this new file to "C:\Windows\System32". After which, press "Start" followed by "Run" or look "Run" on Windows Vista & 7. As soon as a box shows up, kind "cmd". A black screen might then appear plus you need to sort "regsvr32d3d9.dll" plus then click "Enter". This task usually help we to replace the aged file with the fresh copy.
Whenever the registry is corrupt or full of mistakes, the signs may be felt by the computer owner. The slow performance, the frequent system crashes plus the nightmare of all computer owners, the blue screen of death.
So inside summary, when comparing registry cleaning, make certain that that the 1 you choose provides we the following.A backup and restore facility, quickly operation, automatic deletion facility, start-up administration, an easy technique of contact plus a cash back guarantee.