Combination puzzles

Combination puzzles, also called sequential move puzzles, consist of a set of pieces which can be manipulated into different combinations by a group of operations. The puzzle consists of 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 randomly distributed amongst the pieces of the cube.

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 Rubiks 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.

Typically, these puzzles are simple in concept but can be fiendishly difficult to solve. Their popularity lies in this very thing; everyone can understand what is required and the operations needed to achieve it, but few can actually do it. Also, a brightly coloured 'toy' is inherently more interesting than dry mathematical equations, even though they are equivalent.

Although a mechanical realisation 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 realised entirely in virtual space or as a set of mathematical statements. In fact, there are some puzzles that can "only" be realised in virtual space. An example is the 4-dimensional 3x3x3x3 tesseract puzzle.

Puzzle 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. It seems, in fact, that solid geometry is hard pressed to come up with a shape that "cannot" be made into a combination puzzle.

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.

Other Polyhedra

2D Puzzles

ee also

*
*N-dimensional sequential move puzzles

Notes

External links

* [http://www.twistypuzzles.com A large database of Rubik type puzzles.]
* [http://www.superliminal.com/cube/cube.htm 4-D/5-D Rubik's Cube Simulator]
* [http://www.puzzlemuseum.com/ The Puzzle Museum]
* [http://www.rubiks.com/ Rubik's official site]
* [http://www.hungarianbookstore.com/rubik.htm Short Cube history and Erno Rubik biography]