Product Code Database
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. Many such puzzles are mechanical puzzles of Polyhedron, consisting of multiple layers of pieces along each axis which can rotate independently of each other. Collectively known as twisty puzzles, the archetype of this kind of puzzle is the Rubik's Cube. Each rotating side is usually marked with different colours, intended to be scrambled, then solved by a sequence of moves that sort the facets by colour. Generally, combination puzzles also include mathematically defined examples that have not been, or are impossible to, physically construct.
The mechanical construction of the puzzle will usually define the rules by which the combination of pieces can be altered. This leads to some limitations on what combinations are possible. For instance, in the case of the Rubik's Cube, there are a large number of combinations that can be achieved by randomly placing the coloured stickers on the cube, but not all of these can be achieved by manipulating the cube rotations. Similarly, not all the combinations that are mechanically possible from a disassembled cube are possible by manipulation of the puzzle. Since neither unpeeling the stickers nor disassembling the cube is an allowed operation, the possible operations of rotating various faces limit what can be achieved.
Although a mechanical realization of the puzzle is usual, it is not actually necessary. It is only necessary that the rules for the operations are defined. The puzzle can be realized entirely in Virtuality space or as a set of mathematical statements. In fact, there are some puzzles that can only be realized in virtual space. An example is the 4-dimensional 3×3×3×3 tesseract puzzle, simulated by the MagicCube4D software.
| Commercial name: Pocket Cube | 2×2×2 | Simpler to solve than the standard cube in that only the for the corner pieces are required. It is nevertheless surprisingly non-trivial to solve. | |||
| Commercial name: Rubik's Cube | 3×3×3 | (5 events) | The original Rubik's Cube | ||
| Commercial name: Rubik's Revenge | 4×4×4 | (2 events) | 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 | 5×5×5 | (2 events) | 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: V-CUBE | 2×2×2 to 11×11×11 | 6×6×6 and 7×7×7 8×8×8 and higher | Panagiotis Verdes holds a patent to a method which is said to be able to make cubes up to 11×11×11. He has fully working products for 2×2×2 - 9×9×9 cubes. | ||
| 4-Dimensional puzzle | 3×3×3×3 | This is the 4-dimensional 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 5-dimensional 7×7×7×7×7 which has only been solved twice so far. However, the 6×6×6×6×6 has only been solved once, since its parity does not remain constant (due to not having proper center pieces) | |||
| Non-uniform cuboidsCuboid | (1st): 2×2×3 (2nd): 2×3×3 (3rd): 3×4×4 (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 was manufactured by Chronos and distributed by company Gentosha Education; it is the third "Okamoto Cube" (invented by Katsuhiko Okamoto). It does not change form, and the top and bottom colours do not mix with the colours on the sides. | |||
| Siamese cubesFused cubes | 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 Museum and consists of three 5×5×5 cubes that are siamese fused 2×2×5 in two places. there is also a "2 3x3x3 fused 2x2x2" version called the fused cube. The first Siamese cube was made by Tony Fisher in 1981.Slocum, Jerry (2009), The Cube. The Ultimate Guide to the World’s Best Selling Puzzles Published by Black Dog & Leventhal Publishers, Inc () This has been credited as the first example of a "handmade modified rotational puzzle". | |||
| Commercial name: Void cubeMenger Sponge with 1 iteration | 3x3x3-7. | Solutions to this cube is similar to a regular 3x3x3 except that odd-parity combinations are possible with this puzzle. This cube uses a special mechanism due to absence of a central core. | |||
| Commercial name: Crazy cube type I Crazy cube type IICube | 4x4x4. | The inner circles of a Crazy cube 4x4x4 move with the second layer of each face. On a crazy cube type I, they are internally connected in such a way that they essentially move as 8 distinct pieces, not 24. To solve such a cube, think of it as a 2x2x2 (pocket cube) trapped inside a 4x4x4 (Rubik's Revenge). Solve the 2x2x2 first, then solve the 4x4x4 by making exchanges only. Solving the type II is much more difficult. | |||
| Commercial name: Over The Top | Cube | 17x17x17 | Experimental cube made by 3-D printing of plastic invented by Oskar van Deventer. 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. As of 2023, it is being mass produced by the Chinese companies YuXin and ShengShou. |
| 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. | |
| 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 are required to affect 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. |
| Commercial name: Skewb Geometric shape: Cube Piece configuration: 3x3x3 | Similar to the original Rubik's Cube, the Skewb differs in that its four axes of rotation pass through the corners of the cube rather than the centres of the faces. As a result, it is a deep-cut puzzle in which each twist scrambles all six faces. | ||
| Bandaged Cubes Geometric shape: Cube Piece configuration: various | This is a simple example of one a large number of bandaged cube types 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 | A variation on the original Rubik's Cube where it can be turned in such a manner as to distort the cubical shape of the puzzle. The Square One consists of three layers. The upper and lower layers contain kite and triangular pieces. The middle layer contains two trapezoid pieces, which together may form an irregular hexagon or a square. Square One is an example of another very large class of puzzle — cuboid puzzles which have cubies that are not themselves all cuboid. | ||
| Golden Cube | Commercial name: Tony Fisher's Golden Cube Geometric shape: Cube | First rotational puzzle created that has just one colour, requiring the solver to restore the puzzle to its original cube form without colour aids. | |
| Commercial name: Lan Lan Rex Cube (Flower Box) Geometric shape: Cube | |||
| Commercial name: Mixup Cube Geometric shape: Cube | Invented by Oskar van Deventer, it looks like a disproportional Rubik's Cube, but it allows the middle layer to turn 45 degrees and swap center pieces with edge pieces. | ||
| Commercial name: Ivy Cube Geometric shape: Cube | A puzzle which has 3 sides on each face,it has 4 axis of rotation and 4 'floating' corners. It has a center piece resembling a leaf on each side |
| Commercial Name: Pyraminx | 3×3×3 | Tetrahedral-shaped puzzle with axes on the corners and trivial tips. It was invented in 1970 by Uwe Mèffert. | ||
| Commercial Name: Pyramorphix | 2×2×2 | Edge turning tetrahedron shaped puzzle with a 2×2×2 cube mechanism. | ||
| Commercial Name: BrainTwist | 2x2x2 | The BrainTwist is a unique tetrahedral puzzle with an ability to "flip", showing only half of the puzzle at a time. | ||
| Commercial Name: Skewb Diamond | 3x3x3 | An octahedral variation on the Skewb, it is a deep-cut puzzle very similar to the Skewb and is a dual-polyhedron transformation. | ||
| Commercial Name: Megaminx | 3×3×3 | 12-sided polyhedron puzzle similar to Rubik's Cube in operation and solution. | ||
| Commercial Name: Gigaminx, Teraminx, PetaminxDodecahedron |
| Megaminx variants with multiple layers per face. The Gigaminx has 2 layers per face, for a total of 5 layers per edge; the Teraminx has 3 layers per face, 7 layers per edge; and the Petaminx has 4 layers per face, 9 layers per edge. | ||
| Commercial Name: Skewb Ultimate | 3x3x3 | While appearing more difficult than the Skewb Diamond, it is functionally very similar to the Skewb and Skewb Diamond. The puzzle is cut in a different manner but the same solutions can be used to solve it by identifying what pieces are equivalent. Because faces of the Skewb Diamond correspond to corners of the Skewb Ultimate, an additional constraint on the orientation of these pieces appears. Any Skewb Diamond solution thus requires a few additions in order to solve the Skewb Ultimate. | ||
| Commercial Name: Pyraminx Crystal Geometric shape: Piece configuration: | 3x3x3 | A dodecahedron cut into 20 corner pieces and 30 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: Alexander's Star
Great dodecahedron | 3x3x3 | 12-sided Nonconvex uniform polyhedron puzzle similar to Rubik's Cube in operation and solution. | ||
| Commercial Name: Impossiball | 2x2x2 | Rounded icosahedron puzzle similar to Pocket Cube in operation and solution. | ||
| Commercial Name: Dogic | 4x4x4 | The Dogic is an icosahedron cut into 60 triangular pieces around its 12 tips and 20 face centers. | ||
| Commercial Name: Magic 120-cell
120-cell | 3×3×3×3 | Virtual 4-dimensional puzzle, the 4-D analogue of the Megaminx. |
| Name: holey burr puzzles with level > 1 Piece configuration: 6 interlocking sticks | A holey burr puzzle is characterised by internal holes, which usually allow for sliding movements of individual pieces or groups of pieces. The level of a holey burr puzzle specifies how many sliding movements are necessary to assemble or disassemble the puzzle. | |
| Commercial Name: Minus Cube Piece configuration: 2×2×2-1 sliding cubes | The Minus Cube is a 3D mechanical variant of the n-puzzle. It consists of a bonded transparent plastic box containing seven small cubes. There is an empty space the size of one small cube inside the box and the small cubes are moveable inside the box by tilting the box causing a cube to fall into the space. | |
| Commercial Name: Rubik's Clock Piece configuration: 3×3×2 12-position dials | Rubik's Clock is a two-sided puzzle, each side presenting nine clocks to the puzzler. There are four wheels, one at each corner of the puzzle, each allowing the corresponding corner clock to be rotated directly. There are also four pins next to the center clock, which control the rotation of the four adjacent clock faces. | |
| Commercial Name: Rubik's Snake Piece configuration: 1x1x24 | Some would not count this as a combinational puzzle though it bears the Rubik name. Also known as Rubik's Twist. There is no one solution to this puzzle but multiple different shapes can be made.Tony Durham, New Scientist, page 209, 9 September 1982 | |
| Commercial Name: Snake Cube Piece configuration: 1x1x27 or 1x1x64 | The cubelets are connected by an elastic band running through them. They can rotate freely. The aim of the puzzle is to arrange the chain in such a way that they will form 3 x 3 x 3 or 4 x 4 x 4 cube. |
| Sliding piece puzzle Piece configuration: 7×7 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 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: 4×4-1 The original sliding piece puzzle. | ||
| Rubik's Magic | Not entirely 2D. Involves flipping parts back onto itself. | |
| Rubik's Master Magic | The five ringed version of the Rubik's Magic | |
| Commercial name:2D Magic Cube Geometric shape:Square Piece configuration: 3×3 Another virtual puzzle in the Rubik series, but this time a very simple one. | ||
| Klotski Piece configuration: 4×5-2 with some fused pieces 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. 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. |
| Gear Cube | This twisty puzzle was invented by Oskar van Deventer. Edge pieces are gears that turn when faces turn and force opposite faces to turn together. Despite its appearance it is considered easier than the Rubik's Cube. |
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