Tiling puzzles are
puzzle
A puzzle is a game, problem, or toy that tests a person's ingenuity or knowledge. In a puzzle, the solver is expected to put pieces together ( or take them apart) in a logical way, in order to find the solution of the puzzle. There are differe ...
s involving two-dimensional
packing problem
Packing problems are a class of optimization problems in mathematics that involve attempting to pack objects together into containers. The goal is to either pack a single container as densely as possible or pack all objects using as few conta ...
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 players to
dissect a given shape first and then rearrange the pieces into another shape. Other tiling puzzles ask players to dissect a given shape while fulfilling certain conditions. The two latter types of tiling puzzles are also called
dissection puzzles.
Tiling puzzles may be made from
wood
Wood is a structural tissue/material found as xylem in the stems and roots of trees and other woody plants. It is an organic materiala natural composite of cellulosic fibers that are strong in tension and embedded in a matrix of lignin t ...
,
metal
A metal () is a material that, when polished or fractured, shows a lustrous appearance, and conducts electrical resistivity and conductivity, electricity and thermal conductivity, heat relatively well. These properties are all associated wit ...
,
cardboard,
plastic
Plastics are a wide range of synthetic polymers, synthetic or Semisynthesis, semisynthetic materials composed primarily of Polymer, polymers. Their defining characteristic, Plasticity (physics), plasticity, allows them to be Injection moulding ...
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 puzzles and the
tangram puzzle.
Other examples of tiling puzzles include:
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Conway puzzle
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Domino tiling, of which the
mutilated chessboard problem is one example
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Eternity puzzle
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Geometric magic square
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Puzz-3D
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Squaring the square
Squaring the square is the problem of tessellation, tiling an integral square using only other integral squares. (An integral square is a square (geometry), square whose sides have integer length.) The name was coined in a humorous analogy with sq ...
*
Tantrix
*
T puzzle
Many three-dimensional
mechanical puzzle
A mechanical puzzle is a puzzle presented as a set of mechanically interlinked pieces in which the solution is to manipulate the whole object or parts of it. While puzzles of this type have been in use by humanity as early as the 3rd century BC ...
s can be regarded as three-dimensional tiling puzzles.
See also
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Dissection puzzle
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Edge-matching puzzle
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Polyform
In recreational mathematics, a polyform is a plane figure or solid compound constructed by joining together identical basic polygons. The basic polygon is often (but not necessarily) a convex plane-filling polygon, such as a square or a trian ...
s
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Sliding puzzle
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Tessellation
A tessellation or tiling is the covering of a surface, often a plane, using one or more geometric shapes, called ''tiles'', with no overlaps and no gaps. In mathematics, tessellation can be generalized to higher dimensions and a variety ...
References
{{DEFAULTSORT:Tiling Puzzle
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Tessellation