Category: Recreational mathematics

Go and mathematics
The game of Go is one of the most popular games in the world. As a result of its elegant and simple rules, the game has long been an inspiration for mathematical research. Shen Kuo, an 11th century Ch
Equation xy = yx
In general, exponentiation fails to be commutative. However, the equation holds in special cases, such as
Simple magic cube
A simple magic cube is the lowest of six basic classes of magic cubes. These classes are based on extra features required. The simple magic cube requires only the basic features a cube requires to be
Mathematical fallacy
In mathematics, certain kinds of mistaken proof are often exhibited, and sometimes collected, as illustrations of a concept called mathematical fallacy. There is a distinction between a simple mistake
100 prisoners problem
The 100 prisoners problem is a mathematical problem in probability theory and combinatorics. In this problem, 100 numbered prisoners must find their own numbers in one of 100 drawers in order to survi
Arithmetic billiards
In recreational mathematics, arithmetic billiards provide a geometrical method to determine the least common multiple and the greatest common divisor of two natural numbers by making use of reflection
Hundred-dollar, Hundred-digit Challenge problems
The Hundred-dollar, Hundred-digit Challenge problems are 10 problems in numerical mathematics published in 2002 by Nick Trefethen. A $100 prize was offered to whoever produced the most accurate soluti
Mathemalchemy is a traveling art installation dedicated to a celebration of the intersection of art and mathematics. It is a collaborative work led by Duke mathematician Ingrid Daubechies and fiber ar
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 edu
Age of the captain
The age of the captain is a mathematical word problem which cannot be answered even though there seems to be plenty of information supplied. It was given for the first time by Gustave Flaubert in a le
The Game of Logic
The Game of Logic is a book, published in 1886, written by the English mathematician Charles Lutwidge Dodgson (1832–1898), better known under his literary pseudonym Lewis Carroll.In addition to his we
Grundy's game
Grundy's game is a two-player mathematical game of strategy. The starting configuration is a single heap of objects, and the two players take turn splitting a single heap into two heaps of different s
Nasik magic hypercube
No description available.
Numberphile is an educational YouTube channel featuring videos that explore topics from a variety of fields of mathematics. In the early days of the channel, each video focused on a specific number, b
Mathematics and fiber arts
Ideas from mathematics have been used as inspiration for fiber arts including quilt making, knitting, cross-stitch, crochet, embroidery and weaving. A wide range of mathematical concepts have been use
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 b
Rithmomachia (also known as Rithmomachy, Arithmomachia, Rythmomachy, Rhythmomachy, The Philosophers' Game, and other variants) is an early European mathematical board game. Its earliest known descript
Magic hypercube
In mathematics, a magic hypercube is the k-dimensional generalization of magic squares and magic cubes, that is, an n × n × n × ... × n array of integers such that the sums of the numbers on each pill
Fibonacci nim
Fibonacci nim is a mathematical subtraction game, a variant of the game of nim. Players alternate removing coins from a pile, on each move taking at most twice as many coins as the previous move, and
Maris–McGwire–Sosa pair
In recreational mathematics, Maris–McGwire–Sosa pairs (MMS pairs, also MMS numbers) (sequence in the OEIS) are two consecutive natural numbers such that adding each number's digits (in base 10) to the
Postage stamp problem
The postage stamp problem is a mathematical riddle that asks what is the smallest postage value which cannot be placed on an envelope, if the latter can hold only a limited number of stamps, and these
Kobon triangle problem
The Kobon triangle problem is an unsolved problem in combinatorial geometry first stated by Kobon Fujimura (1903-1983). The problem asks for the largest number N(k) of nonoverlapping triangles whose s
Chessboard paradox
The chessboard paradox or paradox of Loyd and Schlömilch is a falsidical paradox based on an optical illusion. A chessboard or a square with a side length of 8 units is cut into four pieces. Those fou
Mathematical puzzle
Mathematical puzzles make up an integral part of recreational mathematics. They have specific rules, but they do not usually involve competition between two or more players. Instead, to solve such a p
Ant on a rubber rope
The ant on a rubber rope is a mathematical puzzle with a solution that appears counterintuitive or paradoxical. It is sometimes given as a worm, or inchworm, on a rubber or elastic band, but the princ
Map folding
In the mathematics of paper folding, map folding and stamp folding are two problems of counting the number of ways that a piece of paper can be folded. In the stamp folding problem, the paper is a str
Projective Set (game)
Projective Set (sometimes shortened to ProSet) is a real-time card game derived from the older game Set.The deck contains cards consisting of colored dots; some cards are laid out on the table and pla
Nim is a mathematical game of strategy in which two players take turns removing (or "nimming") objects from distinct heaps or piles. On each turn, a player must remove at least one object, and may rem
A polyknight is a plane geometric figure formed by selecting cells in a square lattice that could represent the path of a chess knight in which doubling back is allowed. It is a polyform with square c
Sudoku (/suːˈdoʊkuː, -ˈdɒk-, sə-/; Japanese: 数独, romanized: sūdoku, lit. 'digit-single'; originally called Number Place) is a logic-based, combinatorial number-placement puzzle. In classic Sudoku, the
FRACTRAN is a Turing-complete esoteric programming language invented by the mathematician John Conway. A FRACTRAN program is an ordered list of positive fractions together with an initial positive int
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
Patterns in nature
Patterns in nature are visible regularities of form found in the natural world. These patterns recur in different contexts and can sometimes be modelled mathematically. Natural patterns include symmet
Bulgarian solitaire
In mathematics and game theory, Bulgarian solitaire is a card game that was introduced by Martin Gardner. In the game, a pack of cards is divided into several piles. Then for each pile, remove one car
Almost integer
In recreational mathematics, an almost integer (or near-integer) is any number that is not an integer but is very close to one. Almost integers are considered interesting when they arise in some conte
Prime reciprocal magic square
A prime reciprocal magic square is a magic square using the decimal digits of the reciprocal of a prime number. Consider a unit fraction, like 1/3 or 1/7. In base ten, the remainder, and so the digits
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 a
Rope-burning puzzle
In recreational mathematics, rope-burning puzzles are a class of mathematical puzzle in which one is given lengths of rope, fuse cord, or shoelace that each burn for a given amount of time, and matche
Von Neumann's elephant
Von Neumann's elephant is a problem in recreational mathematics, consisting of constructing a planar curve in the shape of an elephant from only four fixed parameters. It originated from a discussion
Maekawa's theorem
Maekawa's theorem is a theorem in the mathematics of paper folding named after Jun Maekawa. It relates to flat-foldable origami crease patterns and states that at every vertex, the numbers of valley a
Goat problem
The goat problem is either of two related problems in recreational mathematics involving at least figuratively a tethered goat (horse, bull) grazing a circular area: the interior grazing problem and t
Moving sofa problem
In mathematics, the moving sofa problem or sofa problem is a two-dimensional idealisation of real-life furniture-moving problems and asks for the rigid two-dimensional shape of largest area A that can
Jeep problem
The jeep problem, desert crossing problem or exploration problem is a mathematics problem in which a jeep must maximize the distance it can travel into a desert with a given quantity of fuel. The jeep
Topswops (and the variants Topdrops, Bottomswops and Bottomdrops) are mathematical problems devised and analysed by the British mathematician John Conway in 1973. Contrary to other games and problems
Mathematics of Sudoku
The mathematics of Sudoku refers to the use of mathematics to study Sudoku puzzles to answer questions such as "How many filled Sudoku grids are there?", "What is the minimal number of clues in a vali
Mountain climbing problem
In mathematics, the mountain climbing problem is a problem of finding the conditions that two functions forming profiles of a two-dimensional mountain must satisfy, so that two climbers can start on t
Hexagonal tortoise problem
The hexagonal tortoise problem (Korean: 지수귀문도; Hanja: 地數龜文圖; RR: jisugwimundo) was invented by Korean aristocrat and mathematician Choi Seok-jeong, who lived from 1646 to 1715. It is a mathematical pr
Egyptian fraction
An Egyptian fraction is a finite sum of distinct unit fractions, such as That is, each fraction in the expression has a numerator equal to 1 and a denominator that is a positive integer, and all the d
Subtract a square
Subtract-a-square (also referred to as take-a-square) is a two-player mathematical subtraction game. It is played by two people with a pile of coins (or other tokens) between them. The players take tu
Proizvolov's identity
In mathematics, Proizvolov's identity is an identity concerning sums of differences of positive integers. The identity was posed by Vyacheslav Proizvolov as a problem in the 1985 All-Union Soviet Stud
Toy problem
In scientific disciplines, a toy problem or a puzzlelike problem is a problem that is not of immediate scientific interest, yet is used as an expository device to illustrate a trait that may be shared
Two-cube calendar
A two-cube calendar is a consisting of two cubes with faces marked by digits 0 through 9. Each face of each cube is marked with a single digit, and it is possible to arrange the cubes so that any chos
A pseudo-polyomino, also called a polyking, polyplet or hinged polyomino, is a plane geometric figure formed by joining one or more equal squares edge-to-edge or corner-to-corner at 90°. It is a polyf
Bellman's lost in a forest problem
Bellman's lost-in-a-forest problem is an unsolved minimization problem in geometry, originating in 1955 by the American applied mathematician Richard E. Bellman. The problem is often stated as follows
Popular mathematics
Popular mathematics is mathematical presentation aimed at a general audience.Sometimes this is in the form of books which require no mathematical background and in other cases it is in the form of exp
Mathematical fiction
Mathematical fiction is a genre of creative fictional work in which mathematics and mathematicians play important roles. The form and the medium of the works are not important. The genre may include p
Six nines in pi
A sequence of six consecutive nines occurs in the decimal representation of the number pi (π), starting at the 762nd decimal place. It has become famous because of the mathematical coincidence and bec
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
Carpenter's rule problem
The carpenter's rule problem is a discrete geometry problem, which can be stated in the following manner: Can a simple planar polygon be moved continuously to a position where all its vertices are in
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 al
Coin problem
The coin problem (also referred to as the Frobenius coin problem or Frobenius problem, after the mathematician Ferdinand Frobenius) is a mathematical problem that asks for the largest monetary amount
Homicidal chauffeur problem
In game theory, the homicidal chauffeur problem is a mathematical pursuit problem which pits a hypothetical runner, who can only move slowly, but is highly maneuverable, against the driver of a motor
Mathematical coincidence
A mathematical coincidence is said to occur when two expressions with no direct relationship show a near-equality which has no apparent theoretical explanation. For example, there is a near-equality c
Sylver coinage
Sylver coinage is a mathematical game for two players, invented by John H. Conway. It is discussed in chapter 18 ofWinning Ways for Your Mathematical Plays. This article summarizes that chapter. The t
Turing tarpit
A Turing tarpit (or Turing tar-pit) is any programming language or computer interface that allows for flexibility in function but is difficult to learn and use because it offers little or no support f
Magic hyperbeam
No description available.
List of recreational number theory topics
This is a list of recreational number theory topics (see number theory, recreational mathematics). Listing here is not pejorative: many famous topics in number theory have origins in challenging probl
Mice problem
In mathematics, the mice problem is a continuous pursuit–evasion problem in which a number of mice (or insects, dogs, missiles, etc.) are considered to be placed at the corners of a regular polygon. I
Problem Solving Through Recreational Mathematics
Problem Solving Through Recreational Mathematics is a textbook in mathematics on problem solving techniques and their application to problems in recreational mathematics, intended as a textbook for ge
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
Hooper's paradox
Hooper's paradox is a falsidical paradox based on an optical illusion. A geometric shape with an area of 32 units is dissected into four parts, which afterwards get assembled into a rectangle with an
Harary's generalized tic-tac-toe
Harary's generalized tic-tac-toe or animal tic-tac-toe is a generalization of the game tic-tac-toe, defining the game as a race to complete a particular polyomino on a square grid of varying size, rat
The Lady's and Gentleman's Diary
The Lady's and Gentleman's Diary was a recreational mathematics magazine formed as a successor of The Ladies' Diary and Gentleman's Diary in 1841. It was published annually between 1841 and 1871 by th
Moser's worm problem
Moser's worm problem (also known as mother worm's blanket problem) is an unsolved problem in geometry formulated by the Austrian-Canadian mathematician Leo Moser in 1966. The problem asks for the regi
Journal of Recreational Mathematics
The Journal of Recreational Mathematics was an American journal dedicated to recreational mathematics, started in 1968. It had generally been published quarterly by the Baywood Publishing Company, unt
Home prime
In number theory, the home prime HP(n) of an integer n greater than 1 is the prime number obtained by repeatedly factoring the increasing concatenation of prime factors including repetitions. The mth
Möbius strip
In mathematics, a Möbius strip, Möbius band, or Möbius loop is a surface that can be formed by attaching the ends of a strip of paper together with a half-twist. As a mathematical object, it was disco
Sangaku or San Gaku (Japanese: 算額, lit. 'calculation tablet') are Japanese geometrical problems or theorems on wooden tablets which were placed as offerings at Shinto shrines or Buddhist temples durin
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
List of Martin Gardner Mathematical Games columns
Over a period of 24 years (January 1957 – December 1980), Martin Gardner wrote 288 consecutive monthly "Mathematical Games" columns for Scientific American magazine. During the next 7+1⁄2 years, throu
In recreational mathematics, a repdigit or sometimes monodigit is a natural number composed of repeated instances of the same digit in a positional number system (often implicitly decimal). The word i
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
Missing dollar riddle
The missing dollar riddle is a famous riddle that involves an informal fallacy. It dates to at least the 1930s, although similar puzzles are much older.
Missing square puzzle
The missing square puzzle is an optical illusion used in mathematics classes to help students reason about geometrical figures; or rather to teach them not to reason using figures, but to use only tex
Hinged dissection
In geometry, a hinged dissection, also known as a swing-hinged dissection or Dudeney dissection, is a kind of geometric dissection in which all of the pieces are connected into a chain by "hinged" poi
Napkin ring problem
In geometry, the napkin-ring problem involves finding the volume of a "band" of specified height around a sphere, i.e. the part that remains after a hole in the shape of a circular cylinder is drilled
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
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 ref
Str8ts is a logic-based number-placement puzzle, invented by Jeff Widderich in 2008. It is distinct from, but shares some properties and rules with Sudoku. The name is derived from the poker straight.
Necklace problem
The necklace problem is a problem in recreational mathematics concerning the reconstruction of necklaces (cyclic arrangements of binary values) from partial information.
Polyhedron model
A polyhedron model is a physical construction of a polyhedron, constructed from cardboard, plastic board, wood board or other panel material, or, less commonly, solid material. Since there are 75 unif
The tangram (Chinese: 七巧板; pinyin: qīqiǎobǎn; lit. 'seven boards of skill') is a dissection puzzle consisting of seven flat polygons, called tans, which are put together to form shapes. The objective
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, co
Bedlam cube
The Bedlam cube is a solid dissection puzzle invented by British puzzle expert Bruce Bedlam.
Eleusis (card game)
Eleusis is a shedding-type card game where one player chooses a secret rule to determine which cards can be played on top of others, and the other players attempt to determine the rule using inductive
The spider and the fly problem
The spider and the fly problem is a recreational geodesics problem with an unintuitive solution.
A cross-figure (also variously called cross number puzzle or figure logic) is a puzzle similar to a crossword in structure, but with entries that consist of numbers rather than words, where individual
Change-making problem
The change-making problem addresses the question of finding the minimum number of coins (of certain denominations) that add up to a given amount of money. It is a special case of the integer knapsack
The Man Who Counted
The Man Who Counted (original Portuguese title: O Homem que Calculava) is a book on recreational mathematics and curious word problems by Brazilian writer Júlio César de Mello e Souza, published under