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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. Edge pairs are often referred to as "dedges," from double edges.
20:
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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. There are several ways to make the centre pieces distinguishable, which would make an odd centre permutation visible.
108:
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. Nearly all manufacturers of 4×4×4 use similar mechanisms.
104:
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.
606:
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
327:
A method similar to the Yau method is called Hoya. It was invented by Jong-Ho Jeong. It involves the same steps as Yau, but in a different order. It starts with all centers being solved except for 2 adjacent centers. Then form a cross on the bottom, then solve the last two centers. After this, it is
323:
Another method is the Yau method, named after Robert Yau. The Yau method is similar to the reduction method, and it is the most common method used by speedcubers. The Yau methods starts by solving two centers on opposite sides. Three cross dedges are then solved. Next, the four remaining centers are
142:
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!/(24) arrangements. The reducing factor comes about because there are 24 (4!) ways to arrange the four pieces of a given
99:
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
336:
When reducing the 4×4×4 to a 3×3×3, 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 3×3×3. The first is two edge pieces reversed on one edge, resulting in the colours of that edge not matching the rest of the cubies
111:
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
103:
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
319:
There are several methods that can be used to solve the puzzle. One such method is the reduction method, so called because it effectively reduces the 4×4×4 to a 3×3×3. Cubers first group the centre pieces of common colours together, then pair edges that show the same two colours. Once this is
310:
Some versions of the cube have one of the centre pieces marked with a logo, distinguishing it from the other three of the same colour. Since there are four distinguishable positions for this piece, the number of permutations is quadrupled, yielding 2.96×10 possibilities. Any of the four possible
115:
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
107:
The
Eastsheen version of the cube, which is slightly smaller at 6cm 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
150:
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
146:
The 24 edges cannot be flipped, due to the internal shape of the pieces. 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.
1296:
in their "Top 100 Games of 1982", finding that it helped to solve the original Rubik's Cube that the center pieces did not move, but noted "That's not true of this
Supercube, which has added an extra row of subcubes in all three dimensions."
151:
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.
50:
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 center faces can no longer be used for identification.
245:
43:
until a somewhat last-minute decision changed the puzzle's name to attract fans of the original Rubik's Cube. Unlike the original puzzle (and other puzzles with an odd number of layers like the
659:
The record for mean of three blindfolded solves is 1 minute, 6.46 seconds (including inspection), also set by
Stanley Chapel at PBQ Oxford 2024, with the times of 1:01.14, 1:04.03 and 1:14.20.
468:
Notice that these two edge pieces are swapped. The second is two edge pairs being swapped with each other (PLL parity), may be two corners swapped instead depending on situation and/or method:
135:
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
610:
Direct solving of a 4×4×4 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.
160:
2107:
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The world record for fastest average of five solves (excluding fastest and slowest solves) is 19.38 seconds, also set by
2412:
1698:
648:
The world record for fastest blindfolded solve is 51.96 seconds (including inspection), set by
Stanley Chapel of the
2143:
2216:
2474:
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1722:
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errors. These positions are still solvable; however, special algorithms must be applied to fix the errors.
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2196:
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47:), it has no fixed faces: the center faces (four per face) are free to move to different positions.
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exchange a pair of face centres by cycling 3 face centres, two of which are visually identical.
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done, turning only the outer layers of the cube allows it to be solved like a 3×3×3 cube.
8:
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240:{\displaystyle {\frac {8!\times 3^{7}\times 24!^{2}}{24^{7}}}\approx 7.40\times 10^{45}.}
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44:
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solved. Afterwards, any remaining edges are solved. This reduces down to a 3x3x3 cube.
39:. It was released in 1981. Invented by Péter Sebestény, the cube was nearly called the
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1987:
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turning one side through a 30° angle and prying an edge upward until it dislodges.
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Early Rubik's
Revenge cube, with white opposite blue, and yellow opposite green
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Schmittberger, R. Wayne, ed. (November 1982). "The Top 100 Games 1982".
19:
1956:
1946:
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A disassembled Rubik's
Revenge, showing all the pieces and central ball
1506:
645:, with the times of (17.60), 18.49, 19.37, (23.80) and 20.28 seconds.
328:
identical to Yau, finishing the edges, and solving the cube as a 3x3.
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Eastsheen cube on the left, official Rubik's
Revenge on the right
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1240:
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906:
863:
735:
723:
2015:
1889:
1677:
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on 28th January 2023 at 4BLD in a Madison Hall 2023, in
618:
The world record fastest solve is 15.71 seconds, set by
1413:
1398:
641:
on 19 March 2023 at Arizona Speedcubing Spring 2023 in
311:
positions for this piece could be regarded as correct.
1672:
Beginner/Intermediate solution to the Rubik's Revenge
1597:
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163:
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1686:
A collection of pretty patterns for Rubik's Revenge
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339:
1651:by Dan Harris, 'Rubik's Revenge' pages 100-120.
1544:
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1520:
307:or 7.4 quattuordecillion on the short scale).
154:This gives a total number of permutations of
132:There are 8 corners, 24 edges and 24 centres.
1723:
1622:
1122:Top 5 solvers by blindfolded average of 3
1730:
1716:
1436:"Reduction Method - Speedsolving.com Wiki"
626:on June 8th 2024 at CMT Evergreen 2024 in
1737:
1661:, with Herbert Taylor and M. Razid Black.
123:
90:
82:
74:
66:
58:
18:
1655:The Winning Solution to Rubik's Revenge
2447:
1696:Program Rubik's Cube 3D Unlimited size
1643:Rubik's Revenge: The Simplest Solution
972:(21.99), 21.53, 21.59, (20.40), 21.89
944:22.36, (26.61), 21.30, (17.98), 21.05
914:20.73, 18.86, (17.63), (27.46), 20.12
884:17.62, 22.52, (23.47), (17.29), 19.34
856:(17.60), 18.49, 19.37, (23.80), 20.28
812:Top 5 solvers by average of 5 solves
1711:
1616:
2434:1982 World Rubik's Cube Championship
1603:"4x4x4 Blindfolded Average Rankings"
1460:"Yau method - Speedsolving.com Wiki"
979:Top 5 solvers by blindfolded solve
2428:The Simple Solution to Rubik's Cube
1579:"4x4x4 Blindfolded Single Rankings"
303:septillion, 7.4 septilliard on the
13:
1636:
1504:
1482:
116:(opposite red) instead of orange.
14:
2491:
1799:Rubik's family cubes of all sizes
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1498:
1065:Please Be Quiet Bukit Jalil 2023
780:Altona Algorithms Attempt 2 2021
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911:FLIP Open 11: Road to Euros 2024
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63:A scrambled Rubik's Revenge cube
2413:Rubik's Cube in popular culture
1680:Advanced direct solving method.
1420:Cubic Circular Issues 3 & 4
853:Arizona Speedcubing Spring 2023
805:Hawai'i Big Island Winter 2024
663:Top 5 solvers by single solve
119:
1476:
1452:
1428:
1405:Cubic Circular Issue 7 & 8
1354:
599:These situations are known as
337:on either face (OLL parity):
128:Scrambled and partially turned
1:
1348:
299:possible permutations (about
95:A disassembled Eastsheen cube
23:A solved Rubik's Revenge cube
1394:United States Patent 5992850
1383:United States Patent 4421311
1282:
1115:WCA World Championship 2023
1040:Singapore Championship 2023
1015:4BLD in a Madison Hall 2023
314:
54:
35:) is a 4×4×4 version of the
16:4×4×4 Rubik's cube variation
7:
1300:
969:Singapore Championship 2023
10:
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2376:Thistlethwaite's algorithm
1629:. No. 33. p. 42.
1362:"Rubik's Cube How to Play"
1276:1:37.92, 1:39.72, 1:29.38
1248:1:23.27, 1:25.83, 1:43.26
1220:1:20.63, 1:25.93, 1:33.68
1217:Nacionales Argentinas 2023
1192:1:19.22, 1:19.07, 1:21.94
1164:1:01.14, 1:04.03, 1:14.20
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1273:Glasgow Summer - SBO 2024
1090:Jaqueca Di Tella V2 2023
728:French Championship 2023
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1819:5×5×5 (Professor's Cube)
1692:at the Speedsolving Wiki
1605:. World Cube Association
1581:. World Cube Association
1557:. World Cube Association
1555:"4x4x4 Average Rankings"
1533:. World Cube Association
1245:Fyris Side 'n Blind 2022
654:Wisconsin, United States
2419:Rubik, the Amazing Cube
1814:4×4×4 (Rubik's Revenge)
1690:4x4x4 Parity Algorithms
1531:"4x4x4 Single Rankings"
2397:World Cube Association
2272:Anthony Michael Brooks
2232:Krishnam Raju Gadiraju
241:
129:
96:
88:
80:
72:
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24:
2475:1980s fads and trends
2390:Official organization
2044:Truncated icosahedron
1649:Speedsolving the Cube
1485:"solving the revenge"
956:Seung Hyuk Nahm (남승혁)
242:
127:
94:
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70:
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22:
1809:3×3×3 (Rubik's Cube)
1464:www.speedsolving.com
1440:www.speedsolving.com
643:San Jose, California
161:
2465:Single-player games
2084:Virtual combination
1916:combination puzzles
1878:combination puzzles
1804:2×2×2 (Pocket Cube)
1645:by William L. Mason
1189:Guangdong Open 2021
1123:
1027:Hill Pong Yong Feng
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701:CMT Evergreen 2024
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628:Evergreen, Colorado
250:The full number is
31:(also known as the
2381:Rubik's Cube group
2227:Prithveesh K. Bhat
2151:Rubik's Revolution
2026:Great dodecahedron
1778:Oskar van Deventer
1701:2009-03-09 at the
1343:Combination puzzle
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33:4×4×4 Rubik's Cube
25:
2480:Ideal Toy Company
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1843:Variations of the
1773:Panagiotis Verdes
1674:by Chris Hardwick
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139:×3 combinations.
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2406:Related articles
2310:
2309:
2257:David Singmaster
2217:Shotaro Makisumi
2192:Jessica Fridrich
2170:Renowned solvers
2086:puzzles (>3D)
2034:Alexander's Star
1988:Pyraminx Crystal
1920:
1919:
1862:Nine-Colour Cube
1834:8×8×8 (V-Cube 8)
1829:7×7×7 (V-Cube 7)
1824:6×6×6 (V-Cube 6)
1746:Puzzle inventors
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2182:Édouard Chambon
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1703:Wayback Machine
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1161:PBQ Oxford 2024
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897:Sebastian Weyer
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820:Fastest average
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714:Sebastian Weyer
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2336:Layer by Layer
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2282:Feliks Zemdegs
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987:Fastest Solve
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671:Fastest solve
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650:United States
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2455:Rubik's Cube
2426:
2417:
2313:Speedsolving
2287:Collin Burns
2242:Frank Morris
2207:Rowe Hessler
2124:Missing Link
1975:Dodecahedron
1937:Pyraminx Duo
1845:Rubik's Cube
1813:
1739:Rubik's Cube
1654:
1648:
1642:
1624:
1618:
1607:. Retrieved
1583:. Retrieved
1559:. Retrieved
1535:. Retrieved
1510:. Retrieved
1500:
1488:. Retrieved
1478:
1467:. Retrieved
1463:
1454:
1443:. Retrieved
1439:
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1400:
1389:
1378:
1366:. Retrieved
1364:. DMFB&C
1356:
1313:Rubik's Cube
1293:
1287:
1286:
1130:Fastest mean
1102:Tommy Cherry
990:Competition
674:Competition
658:
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467:
335:
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249:
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120:Permutations
114:
110:
106:
102:
98:
49:
40:
37:Rubik's Cube
32:
28:
26:
2359:Mathematics
2341:CFOP method
2320:Speedcubing
2297:Mátyás Kuti
2252:Gilles Roux
2247:Lars Petrus
2177:Yu Nakajima
2129:Rubik's 360
2117:Derivatives
2103:MagicCube7D
2098:MagicCube5D
2093:MagicCube4D
2011:Impossiball
2003:Icosahedron
1942:Pyramorphix
1924:Tetrahedron
1876:Other cubic
1867:Sudoku Cube
1768:Tony Fisher
1763:Uwe Mèffert
1678:'K4' Method
1507:"K4 Method"
1307:Pocket Cube
1133:Competition
823:Competition
2470:1980s toys
2449:Categories
2202:Kevin Hays
1957:Octahedron
1947:BrainTwist
1753:Ernő Rubik
1609:2024-08-10
1585:2024-08-10
1561:2024-08-10
1537:2024-08-10
1469:2020-05-21
1445:2020-05-21
1349:References
305:long scale
45:5×5×5 cube
2371:Superflip
2306:Solutions
2277:Mats Valk
2237:Tyson Mao
1914:Non-cubic
1905:Gear Cube
1895:Dino Cube
1857:Bump Cube
1852:Void Cube
1659:Minh Thai
1292:included
1283:Reception
753:NAC 2024
315:Solutions
222:×
216:≈
187:×
174:×
55:Mechanics
2292:Max Park
2222:Toby Mao
2212:Leyan Lo
2052:Tuttminx
1983:Megaminx
1932:Pyraminx
1900:Square 1
1794:Overview
1699:Archived
1684:Patterns
1337:V-Cube 8
1331:V-Cube 7
1325:V-Cube 6
1301:See also
1055:1:09.98
881:NAC 2024
839:Max Park
687:Max Park
635:Max Park
620:Max Park
2346:Optimal
2329:Methods
2072:(2x3x3)
1512:15 June
1490:15 June
1368:3 March
1339:(8×8×8)
1333:(7×7×7)
1327:(6×6×6)
1321:(5×5×5)
1315:(3×3×3)
1309:(2×2×2)
1263:1:35.67
1235:1:30.79
1207:1:26.75
1179:1:20.08
1151:1:06.46
1105:1:20.34
1080:1:18.86
1030:1:01.01
637:of the
622:of the
2062:Cuboid
1425:, 1982
1410:, 1985
1136:Times
1005:51.96s
959:21.67s
931:21.57s
901:19.90s
871:19.83s
843:19.38s
826:Times
795:18.65s
770:17.98s
743:17.29s
718:17.13s
691:15.71s
601:parity
2016:Dogic
1890:Skewb
1626:Games
1289:Games
1514:2012
1492:2012
1370:2016
1127:Name
984:Name
817:Name
668:Name
301:7401
219:7.40
27:The
1657:by
296:000
293:000
290:000
287:336
284:574
281:498
278:974
275:093
272:874
269:869
266:901
263:564
260:841
257:196
254:401
2451::
1594:^
1570:^
1546:^
1522:^
1462:.
1438:.
656:.
630:.
230:45
226:10
205:24
190:24
137:8!
1731:e
1724:t
1717:v
1612:.
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1494:.
1472:.
1448:.
1372:.
252:7
235:.
209:7
198:2
194:!
182:7
178:3
171:!
168:8
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