Mathematical puzzles make up an integral part of

recreational mathematics Recreational mathematics is mathematics carried out for recreation (entertainment) rather than as a strictly research-and-application-based professional activity or as a part of a student's formal education. Although it is not necessarily limited ...

. They have specific rules, but they do not usually involve competition between two or more players. Instead, to solve such a

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 ...

, the solver must find a solution that satisfies the given conditions. Mathematical puzzles require mathematics to solve them.

Logic puzzle A logic puzzle is a puzzle deriving from the mathematics, mathematical field of deductive reasoning, deduction. History The logic puzzle was first produced by Charles Lutwidge Dodgson, who is better known under his pen name Lewis Carroll, the a ...

s are a common type of mathematical puzzle.

Conway's Game of Life The Game of Life, also known as Conway's Game of Life or simply Life, is a cellular automaton devised by the British mathematician John Horton Conway in 1970. It is a zero-player game, meaning that its evolution is determined by its initial ...

and

fractals In mathematics, a fractal is a Shape, geometric shape containing detailed structure at arbitrarily small scales, usually having a fractal dimension strictly exceeding the topological dimension. Many fractals appear similar at various scale ...

, as two examples, may also be considered mathematical puzzles even though the solver interacts with them only at the beginning by providing a set of initial conditions. After these conditions are set, the rules of the puzzle determine all subsequent changes and moves. Many of the puzzles are well known because they were discussed by

Martin Gardner Martin Gardner (October 21, 1914May 22, 2010) was an American popular mathematics and popular science writer with interests also encompassing magic, scientific skepticism, micromagic, philosophy, religion, and literatureespecially the writin ...

in his "Mathematical Games" column in Scientific American. Mathematical puzzles are sometimes used to motivate students in teaching elementary school math problem solving techniques.Kulkarni, D
Enjoying Math: Learning Problem Solving With KenKen Puzzles
, A textbook for teaching with KenKen Puzzles.

Creative thinking Creativity is the ability to form novel and valuable ideas or works using one's imagination. Products of creativity may be intangible (e.g. an idea, scientific theory, literary work, musical composition, or joke), or a physical object (e.g. a ...

or "

thinking outside the box Thinking outside the box (also thinking out of the box or thinking beyond the box and, especially in Australian English, Australia, thinking outside the square) is an idiom that means to think differently, unconventionally, or from a new perspecti ...

"often helps to find the solution.

List of mathematical puzzles

Numbers, arithmetic, and algebra

* Cross-figures or cross number puzzles * Dyson numbers * Four fours * KenKen * Water pouring puzzle * The monkey and the coconuts * Pirate loot problem *

Verbal arithmetic Verbal arithmetic, also known as alphametics, cryptarithmetic, cryptarithm or word addition, is a type of mathematical game consisting of a mathematical equation among unknown numbers, whose numerical digit, digits are represented by Letter (alpha ...

s * 24 Game

Combinatorial

Cryptograms A cryptogram is a type of puzzle that consists of a short piece of encryption, encrypted text. Generally the cipher used to encrypt the text is simple enough that the cryptogram can be solved by hand. Substitution ciphers where each letter is ...

Fifteen Puzzle The 15 puzzle (also called Gem Puzzle, Boss Puzzle, Game of Fifteen, Mystic Square and more) is a sliding puzzle. It has 15 square tiles numbered 1 to 15 in a frame that is 4 tile positions high and 4 tile positions wide, with one unoccupied pos ...

* Kakuro * Rubik's Cube and other sequential movement puzzles * Str8ts a number puzzle based on sequences *

Sudoku Sudoku (; ; originally called Number Place) is a logic puzzle, logic-based, combinatorics, combinatorial number-placement puzzle. In classic Sudoku, the objective is to fill a 9 × 9 grid with digits so that each column, each row, and ...

* Sujiko * Think-a-Dot * Tower of Hanoi * Bridges Game

Analytical or differential

* Ant on a rubber rope * See also:

Zeno's paradoxes Zeno's paradoxes are a series of philosophical arguments presented by the ancient Greek philosopher Zeno of Elea (c. 490–430 BC), primarily known through the works of Plato, Aristotle, and later commentators like Simplicius of Cilicia. Zeno de ...

Probability

Monty Hall problem The Monty Hall problem is a brain teaser, in the form of a probability puzzle, based nominally on the American television game show ''Let's Make a Deal'' and named after its original host, Monty Hall. The problem was originally posed (and solved ...

Tiling, packing, and dissection

Bedlam cube The Bedlam cube is a solid dissection puzzle invented by British puzzle expert Bruce Bedlam. Design The puzzle consists of thirteen polycubic pieces: twelve pentacubes and one tetracube. The objective is to assemble these pieces into a 4 ...

* Conway puzzle *

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 ...

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 ...

Pentomino A pentomino (or 5-omino) is a polyomino of order 5; that is, a polygon in the Plane (geometry), plane made of 5 equal-sized squares connected edge to edge. The term is derived from the Greek word for '5' and "domino". When rotation symmetry, rota ...

es tiling *

Slothouber–Graatsma puzzle The Slothouber–Graatsma puzzle is a packing problem that calls for packing six 1 × 2 × 2 blocks and three 1 × 1 × 1 blocks into a 3 × 3 × 3 box. The solution to this puzzle is unique (up to mirror reflections and rotations). It was named a ...

Soma cube The Soma cube is a mechanical puzzle#Assembly, solid dissection puzzle invented by Danish polymath Piet Hein (scientist), Piet Hein in 1933 during a lecture on quantum mechanics conducted by Werner Heisenberg. Seven different Polycube, pieces ...

* T puzzle * Tangram

Involves a board

Peg solitaire Peg Solitaire, Solo Noble, Solo Goli, Marble Solitaire or simply Solitaire is a board game for one player involving movement of pegs on a board with holes. Some sets use marbles in a board with indentations. The game is known as solitaire in Bri ...

* Nine dots problem

Chessboard tasks

Eight queens puzzle The eight queens puzzle is the problem of placing eight chess queens on an 8×8 chessboard so that no two queens threaten each other; thus, a solution requires that no two queens share the same row, column, or diagonal. There are 92 solutions. ...

Knight's Tour A knight's tour is a sequence of moves of a knight on a chessboard such that the knight visits every square exactly once. If the knight ends on a square that is one knight's move from the beginning square (so that it could tour the board again im ...

No-three-in-line problem The no-three-in-line problem in discrete geometry asks how many points can be placed in the n\times n grid so that no three points lie on the same line. The problem concerns lines of all slopes, not only those aligned with the grid. It was intro ...

Topology, knots, graph theory

The fields of

knot theory In topology, knot theory is the study of knot (mathematics), mathematical knots. While inspired by knots which appear in daily life, such as those in shoelaces and rope, a mathematical knot differs in that the ends are joined so it cannot be und ...

and

topology Topology (from the Greek language, Greek words , and ) is the branch of mathematics concerned with the properties of a Mathematical object, geometric object that are preserved under Continuous function, continuous Deformation theory, deformat ...

, especially their non-intuitive conclusions, are often seen as a part of recreational mathematics. *

Disentanglement puzzle Disentanglement puzzles (also called entanglement puzzles, tanglement puzzles, tavern puzzles or topological puzzles) are a type or group of mechanical puzzle that involves disentangling one piece or set of pieces from another piece or set of pie ...

s *

Seven Bridges of Königsberg The Seven Bridges of Königsberg is a historically notable problem in mathematics. Its negative resolution by Leonhard Euler, in 1736, laid the foundations of graph theory and prefigured the idea of topology. The city of Königsberg in Prussia ...

* Water, gas, and electricity * Slitherlink

Mechanical

* Rubik's Cube * Think-a-Dot * Matchstick puzzle

0-player puzzles

* Flexagon * Polyominoes

References

External links

Historical Math Problems/Puzzles
at

Mathematical Association of America The Mathematical Association of America (MAA) is a professional society that focuses on mathematics accessible at the undergraduate level. Members include university A university () is an educational institution, institution of tertiary edu ...

''Convergence'' {{Polyforms *