A combination puzzle, also known as a sequential move puzzle, is a
puzzle which consists of a set of pieces which can be manipulated into
different combinations by a group of operations. The puzzle is solved
by achieving a particular combination starting from a random
(scrambled) combination. Often, the solution is required to be some
recognisable pattern such as 'all like colours together' or 'all
numbers in order'. The most famous of these puzzles is the original
Rubik's Cube, a cubic puzzle in which each of the six faces can be
independently rotated. Each of the six faces is a different colour,
but each of the nine pieces on a face is identical in colour, in the
solved condition. In the unsolved condition colours are distributed
amongst the pieces of the cube. Puzzles like the
Rubik's Cube
Contents 1 Properties 1.1 Regular cuboids 1.1.1 Pattern variations 1.2 Irregular cuboids 1.3 Other polyhedra 1.4 Other geometric shapes 1.5 NonRubik style threedimensional 1.6 Twodimensional 1.7 Onedimensional 1.8 Geared puzzles 2 See also 3 References 4 External links Properties[edit] There have been many different shapes of Rubik type puzzles constructed. As well as cubes, all of the regular polyhedra and many of the semiregular and stellated polyhedra have been made. Regular cuboids[edit] A cuboid is a rectilinear polyhedron. That is, all its edges form right angles. Or in other words (in the majority of cases), a box shape. A regular cuboid, in the context of this article, is a cuboid puzzle where all the pieces are the same size in edge length. Pieces are often referred to as "cubies". Picture Data Comments Commercial name: Pocket Cube Geometric shape: Cube Piece configuration: 2×2×2 Main article: Pocket Cube Simpler to solve than the standard cube in that only the algorithms for the corner pieces are required. It is nevertheless surprisingly nontrivial to solve. Commercial name: Rubik's Cube Geometric shape: Cube Piece configuration: 3×3×3 Main article: Rubik's Cube The original Rubik's Cube Commercial name: Rubik's Revenge Geometric shape: Cube Piece configuration: 4×4×4 Main article: Rubik's Revenge Solution is much the same as 3×3×3 cube except additional (and relatively simple) algorithm(s) are required to unscramble the centre pieces and edges and additional parity not seen on the 3x3x3 Rubik's Cube. Commercial name: Professor's Cube Geometric shape: Cube Piece configuration: 5×5×5 Main article: Professor's Cube Solution is much the same as 3×3×3 cube except additional (and relatively simple) algorithm(s) are required to unscramble the centre pieces and edges. Commercial name: VCUBE
Geometric shape: Cube
Piece configuration: 2×2×2 to 11×11×11
Main articles: V
Cube
Panagiotis Verdes
4Dimensional puzzle Geometric shape: Tesseract Piece configuration: 3×3×3×3 Main article: Ndimensional sequential move puzzles This is the 4dimensional analog of a cube and thus cannot actually be constructed. However, it can be drawn or represented by a computer. Significantly more difficult to solve than the standard cube, although the techniques follow much the same principles. There are many other sizes of virtual cuboid puzzles ranging from the trivial 3×3 to the 5dimensional 7×7×7×7×7 which has only been solved twice so far.[1] Slim Tower or Tower Cube[2][3] Rubik's Tower[4][5] 3×4×4[6] 2×2×6[7] Nonuniform cuboids Geometric shape: Cuboid Piece configuration (1st): 2×2×3 Piece configuration (2nd): 2×3×3 Piece configuration (3rd): 3×4×4 Piece configuration (4th): 2×2×6 Most of the puzzles in this class of puzzle are generally custom made
in small numbers. Most of them start with the internal mechanism of a
standard puzzle. Additional cubie pieces are then added, either
modified from standard puzzles or made from scratch. The four shown
here are only a sample from a very large number of examples. Those
with two or three different numbers of even or odd rows also have the
ability to change their shape. The Tower
Cube
[1] Siamese cubes Geometric shape: Fused cubes Piece configuration: two 3×3×3 fused 1×1×3 Siamese cubes are two or more puzzles that are fused so that some
pieces are common to both cubes. The picture here shows two 3×3×3
cubes that have been fused. The largest example known to exist is in
The
Puzzle
[2] Extended cubes Geometric shape: Box Piece configuration: 3×3×5 These puzzles are made by bonding additional cubies to an existing puzzle. They therefore do not add to the complexity of the puzzle configuration, they just make it look more complex. Solution strategies remain the same, though a scrambled puzzle can have a strange appearance. [3] Commercial name: Boob cube Geometric shape: Box Piece configuration: 1×1×2 Very possibly the simplest regular cuboid puzzle to solve. Completely trivial solution as the puzzle consists of only two cubies. Commercial name: Void cube
Geometric shape:
Menger Sponge
Solutions to this cube is similar to a regular 3x3x3 except that oddparity combinations are possible with this puzzle. This cube uses a special mechanism due to absence of a central core. Pattern variations[edit] There are many puzzles which are mechanically identical to the regular cuboids listed above but have variations in the pattern and colour of design. Some of these are custom made in very small numbers, sometimes for promotional events. The ones listed in the table below are included because the pattern in some way affects the difficulty of the solution or is notable in some other way. Picture Data Comments Commercial name: Junior Cube
Geometric shape: Cube
Piece configuration: 2×2×2
Main article: Pocket
Cube
Mechanically identical to the Pocket Cube. However, much easier to solve as it only uses two colours. [4] Commercial name: Fooler Cube Geometric shape: Cube Piece configuration: 3×3×3 Mechanically identical to the standard 3×3×3 cube but not a real puzzle since all the faces are the same colour. There are also cubes which have only three colours, either one colour per pair of opposite faces or one colour per layer. Also known as the Dodo cube. Commercial name: Calendar Cube Geometric shape: Cube Piece configuration: 3×3×3 Mechanically identical to the standard 3×3×3 cube, but with specially printed stickers for displaying the date. Much easier to solve since five of the six faces are ignored. Ideal produced a commercial version during the initial cube craze. Sticker sets are also available for converting a normal cube into a calendar. [5]
Rubik's Cube
Mechanically identical to the standard 3×3×3 cube. However the pieces are in some way tactile to allow operation by blind persons, or to solve blindfolded. The cube pictured is the original "Blind Man's Cube" made by Politechnika. This is coloured the same as the standard cube, but there is an embossed symbol on each square which corresponds to a colour. Commercial Name: Magic Cube Geometric shape: Cube Piece configuration: 3×3×3 Mechanically identical to the standard 3×3×3 cube. However, the numbers on the centre pieces force the solver to become aware that each one can be in one of four orientations, thus hugely increasing the total number of combinations. The number of combinations of centre face orientations is 46. However, odd combinations (overall odd number of rotations) of the centre faces cannot be achieved with legal operations. The increase is therefore x211 over the original making the total approximately 1024 combinations. This adds to the difficulty of the puzzle but not astronomically; only one or two additional algorithms are required to effect a solution. Note that the puzzle can be treated as a number magic square puzzle on each of the six faces with the magic constant being 15 in this case. [6] Patterned cubes Geometric shape: Cube Piece configuration: 3×3×3 Mechanically identical to the standard 3×3×3 cube. The pattern, which is often a promotional logo or pictures of performers, will usually have the effect of making the orientation of the centre pieces 'count' in the solution. The solution is therefore the same as the 'Magic Square' cube above. Commercial name:
Sudoku
Identical to the
Rubik's Cube
Over The Top Commercial name: Over The Top Geometric shape: Cube Piece configuration: 17x17x17 Inventor: Oskar van Deventer A remarkable extension to the basic Rubik's Cube. Experimental; made by 3D printing of plastic. Corners are much larger in proportion, and edge pieces match that larger dimension; they are narrow, and do not resemble cubes. The rest of the cubelets are 15x15 arrays on each side of the whole cube; as planned, they would be only 4 mm on a side. The original mechanism is a 3x3x3 core, with thin "vanes" for the center edges; the rest of the cubelets fill in the gaps. The core has a sphere at its center. Surrounding the core were six concentric spherical shells (or more, depending on your definition). The scheme is quite different from that of Panagiotis Verdes, the inventor of the V Cubes. Once built, however, the mechanism had excessive friction, and Mr. van Deventer redesigned it for a much simpler structure. Mr. van Deventer is a noted inventor of puzzles.[citation needed] As of 2017, it is being mass produced by the Chinese company YuXin. Irregular cuboids[edit] An irregular cuboid, in the context of this article, is a cuboid puzzle where not all the pieces are the same size in edge length. This category of puzzle is often made by taking a larger regular cuboid puzzle and fusing together some of the pieces to make larger pieces. In the formulae for piece configuration, the configuration of the fused pieces is given in brackets. Thus, (as a simple regular cuboid example) a 2(2,2)x2(2,2)x2(2,2) is a 2×2×2 puzzle, but it was made by fusing a 4×4×4 puzzle. Puzzles which are constructed in this way are often called "bandaged" cubes. However, there are many irregular cuboids that have not (and often could not) be made by bandaging. Picture Data Comments Commercial name: Skewb Geometric shape: Cube Piece configuration: 3x3x3 Main article: Skewb Similar to the original Rubik's Cube, the
Skewb
[7] Bandaged Cubes Geometric shape: Cube Piece configuration: various The example shown in the link is a simple example of a large number of bandaged cubes that have been made. A bandaged cube is a cube where some of the pieces are stuck together. Commercial name: Square One Geometric shape: Cube Main article: Square One (puzzle) A variation on the original
Rubik's Cube
Golden Cube Commercial name: Tony Fisher's Golden Cube Geometric shape: Cube First rotational puzzle created that has just one colour,[11] requiring the solver to restore the puzzle to its original cube form without colour aids. Commercial name: Lan Lan Rex
Cube
Other polyhedra[edit] Picture Data Comments Commercial Name: Pyraminx Geometric shape: Tetrahedron Piece configuration: 3×3×3 Main article: Pyraminx Tetrahedralshaped puzzle with axes on the corners and trivial tips. It was invented in 1970 by Uwe Mèffert. Commercial Name: Pyramorphix Geometric shape: Tetrahedron Piece configuration: 2×2×2 Main article: Pyramorphix Edge turning tetrahedron shaped puzzle with a 2×2×2 cube mechanism. Commercial Name: Megaminx Geometric shape: Dodecahedron Piece configuration: 3×3×3 Main article: Megaminx 12sided polyhedron puzzle similar to
Rubik's Cube
Commercial Name: Gigaminx, Teraminx, Petaminx Geometric shape: Dodecahedron Piece configuration: gigaminx is 5x5x5, teraminx is 7x7x7, petaminx is 9x9x9
Megaminx
Commercial Name: Impossiball Geometric shape: Rounded icosahedron Piece configuration: 2x2x2 Main article: Impossiball Rounded icosahedron puzzle similar to Pocket
Cube
Commercial Name: Alexander's Star Geometric shape: Great dodecahedron Piece configuration: 3x3x3 Main article: Alexander's Star 12sided
Nonconvex uniform polyhedron
Commercial Name: BrainTwist Geometric shape: Tetrahedron Piece configuration: 2x2x2 Main article: BrainTwist The
BrainTwist
Commercial Name: Dogic Geometric shape: Icosahedron Piece configuration: 4x4x4 Main article: Dogic The Dogic is an icosahedron cut into 60 triangular pieces around its 12 tips and 20 face centers. Commercial Name:
Skewb
An octahedral variation on the Skewb, it is a deepcut puzzle very
similar to the
Skewb
Commercial Name:
Skewb
While appearing more difficult than the
Skewb
Commercial Name: Barrel Cube Geometric shape: Octagonal Prism Piece configuration: 3×3×3 Mechanically identical to the 3×3×3 cube. It does, however, have an interesting difference in its solution. The vertical corner columns are different colours to the faces and do not match the colours of the vertical face columns. The corner columns can therefore be placed in any corner. On the face of it, this makes the solution easier, however odd combinations of corner columns cannot be achieved by legal moves. The solver may unwittingly attempt an odd combination solution, but will not be aware of this until the last few pieces. Commercial Name: Diamond Cube Geometric shape: Rhombicuboctahedron Piece configuration: 3×3×3 Mechanically identical to the 3×3×3 cube although the example
pictured is easier to solve due to the restricted colour scheme. This
puzzle is a rhombicuboctahedron but not a uniform one as the edge
pieces are oblong rather than square. There is in existence a similar
puzzle actually called
Rhombicuboctahedron
Commercial Name:
Pyraminx
A dodecahedron cut into 20 corner pieces and 40 edge pieces. It is similar to the Megaminx, but is deeper cut, giving edges that behave differently from the Megaminx's edges when twisted. Commercial Name: Magic 120cell
Geometric shape: 120cell
Piece configuration: 3×3×3×3
Main article:
Ndimensional sequential move puzzles
Virtual 4dimensional puzzle, the 4D analogue of the Megaminx. Other geometric shapes[edit] Picture Data Comments Commercial Name: Magic Ball Geometric shape: Sphere Piece configuration: 3×3×3 Also known as Rubik's Sphere. Mechanically identical to the 3×3×3 cube in operation and solution. The only practical difference is that it is rather hard to grip. This accounts for the poor condition of this specimen, as the coloured stickers tend to get forced off in use. NonRubik style threedimensional[edit] Picture Data Comments Commercial Name: Rubik's Clock Piece configuration: 3×3×2 12position dials Main article: Rubik's Clock
Rubik's Clock
Commercial Name: Rubik's Snake Piece configuration: 1x1x24 Main article: Rubik's Snake Some would not count this as a combinational puzzle despite it bearing the Rubik name. Also known as Rubik's Twist. There is no one solution to this puzzle but multiple different shapes can be made.[12] Twodimensional[edit] Picture Data Comments Sliding piece puzzle Piece configuration: 7×7 Main article: Sliding puzzle These ubiquitous puzzles come in many sizes and designs. The traditional design is with numbers and the solution forms a magic square. There have been many different designs, the example shown here uses graphic symbols instead of numbers. The solution requires that there are no repeated symbols in any row column or diagonal. The picture shows the puzzle unsolved. Sliding piece puzzle with picture Piece configuration: 7×7 Main article: Sliding puzzle Mechanically, no different from the puzzle above. However, the picture on the pieces gives it something of the nature of a jigsaw puzzle, in addition to being a combination puzzle. Note that the picture consists of a multitude of polyhedra which have been made into Rubik puzzles. Fifteen puzzle Piece configuration: 4×41 Main article: Fifteen puzzle The original sliding piece puzzle. Rubik's Magic Main article: Rubik's Magic Not entirely 2D. Involves flipping parts back onto itself. Rubik's Master Magic Main article: Rubik's Magic: Master Edition The five ringed version of the Rubik's Magic Commercial name:2D Magic Cube
Geometric shape:Square
Piece configuration: 3×3
Main article:
Ndimensional sequential move puzzles
Another virtual puzzle in the Rubik series, but this time a very simple one. Klotski Piece configuration: 4×52 with some fused pieces Main article: Klotski A traditional sliding piece puzzle. There are now endless variations of this original puzzle implemented as computer games. Geranium Piece configuration: 5 intersecting circular rotational groups of oddly shaped pieces A rotating piece puzzle. Some rank its difficulty very high compared to complex 3D puzzles.[13] There are other versions of this puzzle type including "Mini", "Pocket" and "Super", which have 2, 3 and 10 intersecting circles. There is an "Upgrade" mod which splits some of the large pieces into smaller ones. This puzzle's current production status is unknown. Onedimensional[edit] Tricky Animals. The puzzle consists of a permutation of animals. The user has three buttons to solve the puzzle: A: permutes the first two animals. X: permutes the animals in the middle. B: permutes the last two animals. There are over 1500 puzzles in increasing difficulty. Geared puzzles[edit] This section may be in need of reorganization to comply with Wikipedia's layout guidelines. Please help by editing the article to make improvements to the overall structure. (June 2017) (Learn how and when to remove this template message) Picture Data Comments 3x3 Gear cube, solved Gear cube This twisty puzzle was invented by Oskar van Deventer. Gear cube extreme Gear mixup Gear 5x5 gear cube ultimate David's Gear Cube Gear shift See also[edit] Ndimensional sequential move puzzles Puck puzzle References[edit] ^ "MagicCube5D Hall of Insanity".
^ "2×2×3 (aka: Slim Tower)". TwistyPuzzles.com.
^ "Tower Cube" (in Japanese). Gentosha Education.
^ "2×3×3". TwistyPuzzles.com.
^ "Rubik's Tower 2×2×4".
^ "Specter Cube". TwistyPuzzles.com.
^ "2×2×6". TwistyPuzzles.com.
^ "Collection of cube puzzles". The
Puzzle
External links[edit] A large database of twisty puzzles
The
Puzzle
v t e Rubik's Cube
Puzzle
Ernő Rubik Uwe Mèffert Tony Fisher Panagiotis Verdes Oskar van Deventer Rubik's Cubes Overview
2×2×2 (Pocket Cube)
3×3×3 (Rubik's Cube)
4×4×4 (Rubik's Revenge)
5×5×5 (Professor's Cube)
6×6×6 (V
Cube
Cubic variations Helicopter Cube
Skewb
Square 1
Sudoku
Noncubic variations Tetrahedron Pyraminx
Pyraminx
Octahedron
Skewb
Dodecahedron
Megaminx
Icosahedron Impossiball Dogic Great dodecahedron Alexander's Star Truncated icosahedron Tuttminx Cuboid Floppy
Cube
Virtual variations (>3D) MagicCube4D MagicCube5D MagicCube7D Magic 120cell Derivatives Missing Link Rubik's 360 Rubik's Clock Rubik's Magic Master Edition Rubik's Revolution Rubik's Snake Rubik's Triamid Rubik's Cheese Renowned solvers Erik Akkersdijk Yu Nakajima Bob Burton, Jr. Jessica Fridrich Chris Hardwick Rowe Hessler Leyan Lo Shotaro Makisumi Toby Mao Tyson Mao Frank Morris Lars Petrus Gilles Roux David Singmaster Ron van Bruchem Eric Limeback Anthony Michael Brooks Mats Valk Feliks Zemdegs Collin Burns Lucas Etter Solutions Speedsolving Speedcubing Methods Layer by Layer CFOP Method Roux Method Corners First Optimal Mathematics God's algorithm
Superflip
Thistlethwaite's algorithm
Rubik's Cube
Official organization World
Cube
Related articles
Rubik's Cube
