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
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 virtual 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. 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 Non-Rubik style three-dimensional * 1.6 Two-dimensional * 1.7 One-dimensional * 1.8 Geared puzzles * 2 See also * 3 References * 4 External links PROPERTIES There have been many different shapes of Rubik type puzzles constructed. As well as cubes, all of the regular polyhedra and many of the semi-regular and stellated polyhedra have been made. REGULAR CUBOIDS 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:
Commercial name: Rubik's Cube
Geometric shape:
Commercial name: Rubik's Revenge
Geometric shape:
Commercial name: Professor's Cube
Geometric shape:
Commercial name: V-CUBE
Geometric shape:
4-Dimensional puzzle
Geometric shape:
* Slim Tower or Tower
Non-uniform cuboids
Geometric shape:
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
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. 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:
Pattern Variations 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:
Commercial name: Fooler Cube
Geometric shape:
Commercial name: Calendar Cube
Geometric shape:
Commercial Name: Magic Cube
Geometric shape:
Patterned cubes
Geometric shape:
Commercial name:
Over The Top Commercial name: Over The Top
Geometric shape:
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. As of 2017, it is being mass produced by the Chinese company YuXin. IRREGULAR CUBOIDS 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:
Bandaged Cubes
Geometric shape:
A bandaged cube is a cube where some of the pieces are stuck together. Commercial name: Square One
Geometric shape:
Golden Cube Commercial name: Tony Fisher\'s Golden Cube
Geometric shape:
Commercial name: Lan Lan Rex
OTHER POLYHEDRA PICTURE DATA COMMENTS Commercial Name: Pyraminx
Geometric shape:
Commercial Name: Pyramorphix
Geometric shape:
Commercial Name: Megaminx
Geometric shape:
Commercial Name: Gigaminx, Teraminx, Petaminx
Geometric shape:
Commercial Name: Impossiball
Geometric shape: Rounded icosahedron
Piece configuration: 2x2x2
Main article:
Commercial Name: Alexander's Star
Geometric shape:
Commercial Name: BrainTwist
Geometric shape:
Commercial Name: Dogic
Geometric shape:
Commercial Name:
Commercial Name:
Commercial Name: Barrel Cube
Geometric shape:
Commercial Name: Diamond Cube
Geometric shape:
Commercial Name:
Commercial Name: Magic 120-cell
Geometric shape:
OTHER GEOMETRIC SHAPES PICTURE DATA COMMENTS Commercial Name: Magic Ball
Geometric shape:
NON-RUBIK STYLE THREE-DIMENSIONAL PICTURE DATA COMMENTS Commercial Name: Rubik's Clock
Piece configuration: 3×3×2 12-position dials
Main article: 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. TWO-DIMENSIONAL PICTURE DATA COMMENTS Sliding piece puzzle
Piece configuration: 7×7
Main article:
Sliding piece puzzle with picture
Piece configuration: 7×7
Main article:
Fifteen puzzle
Piece configuration: 4×4-1
Main article:
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:
Klotski
Piece configuration: 4×5-2 with some fused pieces
Main article:
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 |