Tiling puzzle
Encyclopedia
Tiling puzzles are puzzle
Puzzle
A puzzle is a problem or enigma that tests the ingenuity of the solver. In a basic puzzle, one is intended to put together pieces in a logical way in order to come up with the desired solution...

s involving two-dimensional packing problem
Packing problem
Packing problems are a class of optimization problems in mathematics which involve attempting to pack objects together , as densely as possible. Many of these problems can be related to real life packaging, storage and transportation issues...

s in which a number of flat shapes have to be assembled into a larger given shape without overlaps (and often without gaps). Some tiling puzzles ask you to dissect a given shape first and then rearrange the pieces into another shape. Other tiling puzzles ask you to dissect a given shape while fulfilling certain conditions. The two latter types of tiling puzzles are also called dissection puzzle
Dissection puzzle
A dissection puzzle, also called a transformation puzzle or Richter Puzzle, is a tiling puzzle where a solver is given a set of pieces that can be assembled in different ways to produce two or more distinct geometric shapes. The creation of new dissection puzzles is also considered to be a type of...

s.

Tiling puzzles may be made from wood
Wood
Wood is a hard, fibrous tissue found in many trees. It has been used for hundreds of thousands of years for both fuel and as a construction material. It is an organic material, a natural composite of cellulose fibers embedded in a matrix of lignin which resists compression...

, metal
Metal
A metal , is an element, compound, or alloy that is a good conductor of both electricity and heat. Metals are usually malleable and shiny, that is they reflect most of incident light...

, cardboard, plastic
Plastic
A plastic material is any of a wide range of synthetic or semi-synthetic organic solids used in the manufacture of industrial products. Plastics are typically polymers of high molecular mass, and may contain other substances to improve performance and/or reduce production costs...

or any other sheet-material. Many tiling puzzles are now available as computer games.

Tiling puzzles have a long history. Some of the oldest and most famous are jigsaw puzzle
Jigsaw puzzle
A jigsaw puzzle is a tiling puzzle that requires the assembly of numerous small, often oddly shaped, interlocking and tessellating pieces.Each piece usually has a small part of a picture on it; when complete, a jigsaw puzzle produces a complete picture...

s and the Tangram
Tangram
The tangram is a dissection puzzle consisting of seven flat shapes, called tans, which are put together to form shapes. The objective of the puzzle is to form a specific shape using all seven pieces, which may not overlap...

puzzle.

Other examples of tiling puzzles include:
• Conway puzzle
Conway puzzle
Conway's puzzle is a packing problem using rectangular blocks, named after its inventor, mathematician John Conway. It calls for packing thirteen 1 × 2 × 4 blocks, one 2 × 2 × 2 block, one 1 × 2 × 2 block, and three 1 × 1 × 3 blocks into a 5 × 5 × 5 box....

• Domino tiling
Domino tiling
A domino tiling of a region in the Euclidean plane is a tessellation of the region by dominos, shapes formed by the union of two unit squares meeting edge-to-edge...

, of which the mutilated chessboard problem
Mutilated chessboard problem
The mutilated chessboard problem is a tiling puzzle introduced by and discussed by Martin Gardner in his Scientific American column "Mathematical Games." The problem is as follows:...

is one example
• Eternity puzzle
Eternity puzzle
Eternity is a tiling puzzle created by Christopher Monckton and launched by the Ertl Company in June 1999. Consisting of 209 pieces, it was marketed as being practically unsolveable, with a £1 million prize on offer for whoever could solve it within four years. The prize was paid out in October...

• Puzz-3D
Puzz-3D
Puzz-3D is the brand name of three-dimensional jigsaw puzzles, manufactured by Hasbro . Unlike traditional puzzles which are composed of series of flat pieces with parts of an image on them, when put together, create a single unified image, the Puzz-3D series of puzzles are composed on plastic...

• Squaring the square
Squaring the square
Squaring the square is the problem of tiling an integral square using only other integral squares. The name was coined in a humorous analogy with squaring the circle. Squaring the square is an easy task unless additional conditions are set...

• Tantrix
Tantrix
Tantrix is a hexagonal tile-based abstract game invented by Mike McManaway from New Zealand. Each of the 56 different tiles in the set contains three lines, going from one edge of the tile to another. No two lines on a tile have the same colour. There are four colours in the set: red, yellow,...

• T puzzle
T puzzle
The T puzzle is a puzzle the object of which is to assemble four shapes into the form of a letter T.-External links:* at MathWorld*...

• Pentomino
Pentomino
A pentomino is a polyomino composed of five congruent squares, connected along their edges ....

es

Many three-dimensional mechanical puzzle
Mechanical puzzle
A mechanical puzzle is a puzzle presented as a set of mechanically interlinked pieces.- History :The oldest known mechanical puzzle comes from Greece and appeared in the 3rd century BC....

s can be regarded as three-dimensional tiling puzzles.

• Dissection puzzle
Dissection puzzle
A dissection puzzle, also called a transformation puzzle or Richter Puzzle, is a tiling puzzle where a solver is given a set of pieces that can be assembled in different ways to produce two or more distinct geometric shapes. The creation of new dissection puzzles is also considered to be a type of...

• Polyform
Polyform
In recreational mathematics, a polyform is a plane figure constructed by joining together identical basic polygons. The basic polygon is often a convex plane-filling polygon, such as a square or a triangle. More specific names have been given to polyforms resulting from specific basic polygons, as...

s
• Sliding puzzle
Sliding puzzle
A sliding puzzle, sliding block puzzle, or sliding tile puzzle is a puzzle that challenges a player to slide usually flat pieces along certain routes to establish a certain end-configuration....

• Tessellation
Tessellation
A tessellation or tiling of the plane is a pattern of plane figures that fills the plane with no overlaps and no gaps. One may also speak of tessellations of parts of the plane or of other surfaces. Generalizations to higher dimensions are also possible. Tessellations frequently appeared in the art...

• Wang tile
Wang tile
Wang tiles , first proposed by mathematician, logician, and philosopher Hao Wang in 1961, are a class of formal systems...