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

, 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 mathematical field of deduction. History The logic puzzle was first produced by Charles Lutwidge Dodgson, who is better known under his pen name Lewis Carroll, the author of ''Alice's Adventures in W ...

s are a common type of mathematical puzzle.

Conway's Game of Life The Game of Life, also known simply as 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 state, requiring no furt ...

and

fractals In mathematics, a fractal is a 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 scales, as ill ...

, 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 scientific skepticism, micromagic, philosophy, religion, and literatureespecially the writings of L ...

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 a phenomenon whereby something new and valuable is formed. The created item may be intangible (such as an idea, a scientific theory, a musical composition, or a joke) or a physical object (such as an invention, a printed literary ...

or "

thinking outside the box Thinking outside the box (also thinking out of the box or thinking beyond the box and, especially in Australia, thinking outside the square) is a metaphor that means to think differently, unconventionally, or from a new perspective. The phrase al ...

"often helps to find the solution.

List of mathematical puzzles

''This list is not complete.''

Numbers, arithmetic, and algebra

* Cross-figures or cross number puzzles
Maths Problems
*

Dyson number Dyson may refer to: * Dyson (surname), people with the surname Dyson * Dyson (company), a Singaporean multinational home appliances company founded by James Dyson * Dyson (crater), a crater on the Moon * Dyson (operating system), a Unix general- ...

s * Four fours *

KenKen KenKen and KenDoku are trademarked names for a style of arithmetic and logic puzzle invented in 2004 by Japanese math teacher Tetsuya Miyamoto,

Water pouring puzzle Water pouring puzzles (also called water jug problems, decanting problems, measuring puzzles, or Die Hard with a Vengeance puzzles) are a class of puzzle involving a finite collection of water jugs of known integer capacities (in terms of a liq ...

The monkey and the coconuts The monkey and the coconuts is a mathematical puzzle in the field of Diophantine analysis that originated in a magazine fictional short story involving five sailors and a monkey on a desert island who divide up a pile of coconuts; the problem is ...

Pirate loot problem The pirate game is a simple mathematical game. It is a multi-player version of the ultimatum game. The game There are five rational pirates Piracy is an act of robbery or criminal violence by ship or boat-borne attackers upon another ...

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 digits are represented by letters of the alphabet. T ...

s * 24 Game

Combinatorial

Cryptograms A cryptogram is a type of puzzle that consists of a short piece of 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 replaced by ...

Fifteen Puzzle The 15 puzzle (also called Gem Puzzle, Boss Puzzle, Game of Fifteen, Mystic Square and many others) is a sliding puzzle having 15 square tiles numbered 1–15 in a frame that is 4 tiles high and 4 tiles wide, leaving one unoccupied tile positio ...

Kakuro Kakuro or Kakkuro or Kakoro ( ja, カックロ) is a kind of logic puzzle that is often referred to as a mathematical transliteration of the crossword. Kakuro puzzles are regular features in many math-and-logic puzzle publications across the worl ...

Rubik's Cube The Rubik's Cube is a 3-D combination puzzle originally invented in 1974 by Hungarian sculptor and professor of architecture Ernő Rubik. Originally called the Magic Cube, the puzzle was licensed by Rubik to be sold by Pentangle Puzzles in t ...

and other sequential movement puzzles * Str8ts a number puzzle based on sequences *

Sudoku Sudoku (; ja, 数独, sūdoku, digit-single; originally called Number Place) is a logic-based, combinatorics, combinatorial number-placement puzzle. In classic Sudoku, the objective is to fill a 9 × 9 grid with digits so that each co ...

* Sujiko *

Think-a-Dot The Think-a-Dot was a mathematical toy invented by Joseph Weisbecker and manufactured by E.S.R., Inc. during the 1960s that demonstrated automata theory. It had eight coloured disks on its front, and three holes on its top – left, right, ...

Tower of Hanoi The Tower of Hanoi (also called The problem of Benares Temple or Tower of Brahma or Lucas' Tower and sometimes pluralized as Towers, or simply pyramid puzzle) is a mathematical game or puzzle consisting of three rods and a number of disks of v ...

* Bridges Game

Analytical or differential

* Ant on a rubber rope * See also:

Zeno's paradoxes Zeno's paradoxes are a set of philosophical problems generally thought to have been devised by Greek philosopher Zeno of Elea (c. 490–430 BC) to support Parmenides' doctrine that contrary to the evidence of one's senses, the belief in plurality ...

Probability

Monty Hall problem The Monty Hall problem is a brain teaser, in the form of a probability puzzle, loosely based 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 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 ...

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 cont ...

Pentomino Derived from the Greek word for ' 5', and "domino", a pentomino (or 5-omino) is a polyomino of order 5, that is, a polygon in the plane made of 5 equal-sized squares connected edge-to-edge. When rotations and reflections are not considered t ...

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 solid dissection puzzle invented by Danish polymath Piet Hein in 1933 during a lecture on quantum mechanics conducted by Werner Heisenberg. Seven pieces made out of unit cubes must be assembled into a 3×3×3 cube. The pie ...

T puzzle The T puzzle is a tiling puzzle consisting of four polygonal shapes which can be put together to form a capital T. The four pieces are usually one isosceles right triangle, two right trapezoids and an irregular shaped pentagon. Despite its apparen ...

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 ...

Involves a board

Peg solitaire Peg solitaire, Solo Noble 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 Britain and as peg solitaire in ...

* 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 introd ...

Topology, knots, graph theory

The fields of

knot theory In the mathematical field of topology, knot theory is the study of 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 ...

and

topology In mathematics, topology (from the Greek words , and ) is concerned with the properties of a geometric object that are preserved under continuous deformations, such as stretching, twisting, crumpling, and bending; that is, without closing ho ...

, 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 piec ...

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 (n ...

* Water, gas, and electricity *

Slitherlink Slitherlink (also known as Fences, Takegaki, Loop the Loop, Loopy, Ouroboros, Suriza and Dotty Dilemma) is a logic puzzle developed by publisher Nikoli. Rules Slitherlink is played on a rectangular lattice of dots. Some of the squares formed by ...

Mechanical

0-player puzzles

Flexagon In geometry, flexagons are flat models, usually constructed by folding strips of paper, that can be ''flexed'' or folded in certain ways to reveal faces besides the two that were originally on the back and front. Flexagons are usually square or ...

Polyominoes A polyomino is a plane geometric figure formed by joining one or more equal squares edge to edge. It is a polyform whose cells are squares. It may be regarded as a finite subset of the regular square tiling. Polyominoes have been used in p ...

References

External links

Historical Math Problems/Puzzles
at Mathematical Association of America ''Convergence'' {{Polyforms *