Tiling puzzles are
puzzleA puzzle is a problem or enigma that tests the ingenuity of the solver. In a basic puzzle, one is intended to piece together objects in a logical way in order to come up with the desired shape, picture or solution...
s involving two-dimensional
packing problemPacking problems are one area where mathematics meets puzzles . Many of these problems stem from real-life problems with packing items.In a packing problem, you are given:...
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 puzzleA dissection puzzle, also called a transformation 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 dissection puzzle...
s.
Tiling puzzles may be made from
woodWood is an organic material; in the strict sense wood is produced as secondary xylem in the stems of trees . In a living tree it transfers water and nutrients to the leaves and other growing tissues, and has a support function, enabling woody plants to reach large sizes or to stand up for themselves...
,
metalA metal is a chemical element that is a good conductor of both electricity and heat, forms cations and ionic bonds with non-metals. In chemistry, a metal is an element, compound, or alloy characterized by high electrical conductivity. In a metal, atoms readily lose electrons to form positive ions...
,
cardboardCorrugated fiberboard is a paper-based material consisting of a fluted corrugated sheet and one or two flat linerboards. It is widely used in the manufacture of corrugated boxes and shipping containers....
,
plasticPlastic is the general common term for a wide range of synthetic or semisynthetic organic amorphous solid materials suitable for the manufacture of industrial products...
or any other sheet-material.
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Tiling puzzles are
puzzleA puzzle is a problem or enigma that tests the ingenuity of the solver. In a basic puzzle, one is intended to piece together objects in a logical way in order to come up with the desired shape, picture or solution...
s involving two-dimensional
packing problemPacking problems are one area where mathematics meets puzzles . Many of these problems stem from real-life problems with packing items.In a packing problem, you are given:...
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 puzzleA dissection puzzle, also called a transformation 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 dissection puzzle...
s.
Tiling puzzles may be made from
woodWood is an organic material; in the strict sense wood is produced as secondary xylem in the stems of trees . In a living tree it transfers water and nutrients to the leaves and other growing tissues, and has a support function, enabling woody plants to reach large sizes or to stand up for themselves...
,
metalA metal is a chemical element that is a good conductor of both electricity and heat, forms cations and ionic bonds with non-metals. In chemistry, a metal is an element, compound, or alloy characterized by high electrical conductivity. In a metal, atoms readily lose electrons to form positive ions...
,
cardboardCorrugated fiberboard is a paper-based material consisting of a fluted corrugated sheet and one or two flat linerboards. It is widely used in the manufacture of corrugated boxes and shipping containers....
,
plasticPlastic is the general common term for a wide range of synthetic or semisynthetic organic amorphous solid materials suitable for the manufacture of industrial products...
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 puzzleA 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
TangramThe 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.-History:The Tangram may have roots in the yanjitu furniture set of the...
puzzle.
Other examples of tiling puzzles include:
- 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
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 problemThe 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
The eternity puzzle was a geometric puzzle with a million-pound prize, created by Christopher Monckton, who put up half the money himself, the other half being put up by underwriters in the London insurance market. The puzzle was distributed by the Ertl Company.The puzzle consisted of filling a...
- 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
A square with sides equal to a unit length multiplied by an integer is called an integral square.Squaring the square is the problem of tiling one integral square using only other integral squares....
- Tantrix
Tantrix is a hexagonal tile-based abstract strategy game invented by Mike McManaway from New Zealand. Each of the 56 different Bakelite 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...
- 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
A pentomino is a polyomino composed of five congruent squares, connected along their edges ....
es
Many three-dimensional
mechanical puzzleA 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.
See also
- Dissection puzzle
A dissection puzzle, also called a transformation 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 dissection puzzle...
- 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
A sliding puzzle, sliding block puzzle, or sliding tile puzzle challenges a player to slide usually flat pieces along certain routes to establish a certain end-configuration....
- Tessellation
A tessellation or tiling of the plane is a collection of plane figures that fills the plane with no overlaps and no gaps. One may also speak of tessellations of the parts of the plane or of other surfaces. Generalizations to higher dimensions are also possible. Tessellations frequently appeared in...
- Wang tile
Wang tiles , first proposed by mathematician, logician, and philosopher Hao Wang in 1961, are a class of formal systems. They are modelled visually by equal-sized squares with a color on each edge which can be arranged side by side so that abutting edges of adjacent tiles have the same color; the...