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 arrive at the correct or fun solution of the puzzle ...

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 cont ...

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 Dissection (from Latin ' "to cut to pieces"; also called anatomization) is the dismembering of the body of a deceased animal or plant to study its anatomical structure. Autopsy is used in pathology and forensic medicine to determine the cause of ...

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

s. Tiling puzzles may be made from

wood Wood is a porous and fibrous structural tissue found in the stems and roots of trees and other woody plants. It is an organic materiala natural composite of cellulose fibers that are strong in tension and embedded in a matrix of ligni ...

metal A metal (from Greek μέταλλον ''métallon'', "mine, quarry, metal") is a material that, when freshly prepared, polished, or fractured, shows a lustrous appearance, and conducts electricity and heat relatively well. Metals are typi ...

cardboard Cardboard is a generic term for heavy paper-based products. The construction can range from a thick paper known as paperboard to corrugated fiberboard which is made of multiple plies of material. Natural cardboards can range from grey to light b ...

plastic Plastics are a wide range of synthetic or semi-synthetic materials that use polymers as a main ingredient. Their plasticity makes it possible for plastics to be moulded, extruded or pressed into solid objects of various shapes. This adaptab ...

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

computer game Video games, also known as computer games, are electronic games that involves interaction with a user interface or input device such as a joystick, controller, keyboard, or motion sensing device to generate visual feedback. This feedbac ...

s. Tiling puzzles have a long history. Some of the oldest and most famous are

jigsaw puzzle A jigsaw puzzle is a tiling puzzle that requires the assembly of often irregularly shaped interlocking and mosaiced pieces, each of which typically has a portion of a picture. When assembled, the puzzle pieces produce a complete picture. In t ...

s and the

tangram The tangram () is a dissection puzzle consisting of seven flat polygons, called ''tans'', which are put together to form shapes. The objective is to replicate a pattern (given only an outline) generally found in a puzzle book using all seven pie ...

puzzle. Other examples of tiling puzzles include: *

Conway puzzle Conway's puzzle, or blocks-in-a-box, 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 ...

Domino tiling In geometry, a domino tiling of a region in the Euclidean plane is a tessellation of the region by dominoes, shapes formed by the union of two unit squares meeting edge-to-edge. Equivalently, it is a perfect matching in the grid graph formed b ...

, of which the

mutilated chessboard problem The mutilated chessboard problem is a tiling puzzle posed by Max Black in 1946 that asks: Suppose a standard 8×8 chessboard (or checkerboard) has two diagonally opposite corners removed, leaving 62 squares. Is it possible to place 31 domin ...

is one example * Eternity puzzle *

Geometric magic square A geometric magic square, often abbreviated to geomagic square, is a generalization of magic squares invented by Lee Sallows in 2001. A traditional magic square is a square array of numbers (almost always positive integers) whose sum taken in any r ...

* Puzz-3D *

Squaring the square Squaring the square is the problem of tiling an integral square using only other integral squares. (An integral square is a square whose sides have integer length.) The name was coined in a humorous analogy with squaring the circle. Squaring the s ...

* 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