Mathematical puzzles make up an integral part of
recreational mathematicsRecreational mathematics is an umbrella term, referring to mathematical puzzles and mathematical games.Not all problems in this field require a knowledge of advanced mathematics, and thus, recreational mathematics often piques the curiosity of non-mathematicians, and inspires their further study of...
. They have specific rules as do
multiplayer gameA multiplayer video game is one which more than one person can play in the same game environment at the same time. Unlike most other games, computer and video games are often single-player activities that pit the player against preprogrammed challenges and/or AI-controlled opponents, which often...
s, but they do not usually involve competition between two or more players. Instead, to solve such a
puzzleA puzzle is a problem or enigma that tests the ingenuity of the solver. In a basic puzzle, one is intended to piece together objects in a logical way in order to come up with the desired shape, picture or solution...
, the solver must find a solution that satisfies the given conditions.
Mathematical puzzles require mathematics to solve them.
Logic puzzleA logic puzzle is a puzzle deriving from the mathematics field of deduction.-History:This branch was produced by Charles Lutwidge Dodgson, who is better known under his pseudonym Lewis Carroll, the author of Alice's Adventures in Wonderland...
s are a common type of mathematical puzzle.
Conway's Game of LifeThe Game of Life, also known simply as Life, is a cellular automaton devised by the British mathematician John Horton Conway in 1970. It is the best-known example of a cellular automaton....
and fractals, 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.
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Mathematical puzzles make up an integral part of
recreational mathematicsRecreational mathematics is an umbrella term, referring to mathematical puzzles and mathematical games.Not all problems in this field require a knowledge of advanced mathematics, and thus, recreational mathematics often piques the curiosity of non-mathematicians, and inspires their further study of...
. They have specific rules as do
multiplayer gameA multiplayer video game is one which more than one person can play in the same game environment at the same time. Unlike most other games, computer and video games are often single-player activities that pit the player against preprogrammed challenges and/or AI-controlled opponents, which often...
s, but they do not usually involve competition between two or more players. Instead, to solve such a
puzzleA puzzle is a problem or enigma that tests the ingenuity of the solver. In a basic puzzle, one is intended to piece together objects in a logical way in order to come up with the desired shape, picture or solution...
, the solver must find a solution that satisfies the given conditions.
Mathematical puzzles require mathematics to solve them.
Logic puzzleA logic puzzle is a puzzle deriving from the mathematics field of deduction.-History:This branch was produced by Charles Lutwidge Dodgson, who is better known under his pseudonym Lewis Carroll, the author of Alice's Adventures in Wonderland...
s are a common type of mathematical puzzle.
Conway's Game of LifeThe Game of Life, also known simply as Life, is a cellular automaton devised by the British mathematician John Horton Conway in 1970. It is the best-known example of a cellular automaton....
and fractals, 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.
List of mathematical puzzles
The following categories are not disjoint; some puzzles fall into more than one category.
Numbers, arithmetic, and algebra
- Cross-figure
A cross-figure is a puzzle similar to a crossword in structure, but with entries which consist of numbers rather than words, with individual digits being entered in the blank cells...
s or Crossnumber Puzzle
- Dyson numbers
- Four fours
Four fours is a mathematical puzzle. The goal of four fours is to find the simplest mathematical expression for every whole number from 0 to some maximum, using only common mathematical symbols and the digit four...
- Feynman Long Division Puzzles
Physicist Richard Feynman sent the following puzzle for his father attached to a letter to his mother in 1939.Each digit of a long division has been replaced by a dot or the letter A . None of the dots are the same as the A digit. The goal is to reconstruct the original figures...
- Pirate loot problem
- Verbal arithmetic
Verbal arithmetic, also known as alphametics, cryptarithmetic, crypt-arithmetic, or cryptarithm, is a type of mathematical game consisting of a mathematical equation among unknown numbers, whose digits are represented by letters. The goal is to identify the value of each letter...
s
Combinatorial
- Cryptograms
- Fifteen Puzzle
The n-puzzle is known in various versions, including the 8 puzzle, the 15 puzzle, and with various names . It is a sliding puzzle that consists of a frame of numbered square tiles in random order with one tile missing...
- Rubik's Cube
The Rubik's Cube is a 3-D mechanical puzzle 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 Ideal Toys in 1980 and won the German Game of the Year special award for Best Puzzle that year...
and other sequential movement puzzles
- Sudoku
is a logic-based, combinatorial number-placement puzzle. The objective is to fill a 9×9 grid so that each column, each row, and each of the nine 3×3 boxes contains the digits from 1 to 9 only one time each. The puzzle setter provides a partially completed grid...
- Think-a-Dot
The Think-a-Dot was a mathematical toy made by E.S.R., Inc. during the 1960s that demonstrated group theory. It had eight coloured disks on its front, and three holes on its top - left, right, and center - through which a ball bearing could be dropped. Each disk would display either a yellow or...
- Tower of Hanoi
The Tower of Hanoi or Towers of Hanoi is a mathematical game or puzzle. It consists of three rods, and a number of disks of different sizes which can slide onto any rod...
Tiling, packing, and dissection
- Mutilated chessboard problem
The mutilated chessboard problem is a tiling puzzle introduced by and discussed by Martin Gardner in his Scientific American column "Mathematical Games." The problem is as follows:...
- the generic Packing problem
Packing problems are one area where mathematics meets puzzles . Many of these problems stem from real-life problems with packing items.In a packing problem, you are given:...
- tiling Pentomino
A pentomino is a polyomino composed of five congruent squares, connected along their edges ....
es
- Tangram
The tangram is a dissection puzzle consisting of seven flat shapes, called tans, which are put together to form shapes. The objective of the puzzle is to form a specific shape using all seven pieces, which may not overlap.-History:The Tangram may have roots in the yanjitu furniture set of the...
- 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 ....
- Conway puzzle
Conway's puzzle 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 × 1 × 3 blocks into a 5 × 5 × 5 box....
- Bedlam cube
The Bedlam cube is a solid dissection puzzle invented by 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 x 4 x 4 cube...
- Soma cube
The Soma cube is a solid dissection puzzle invented by Piet Hein during a lecture on quantum mechanics conducted by Werner Heisenberg. Seven pieces made out of unit cubes must be assembled into a 3x3x3 cube...
- T puzzle
The T puzzle is a puzzle the object of which is to assemble four shapes into the form of a letter T.-External links:* at MathWorld*...
Involves a board
- 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 the best-known example of a cellular automaton....
- Sudoku
is a logic-based, combinatorial number-placement puzzle. The objective is to fill a 9×9 grid so that each column, each row, and each of the nine 3×3 boxes contains the digits from 1 to 9 only one time each. The puzzle setter provides a partially completed grid...
- Mutilated chessboard problem
The mutilated chessboard problem is a tiling puzzle introduced by and discussed by Martin Gardner in his Scientific American column "Mathematical Games." The problem is as follows:...
- Peg solitaire
Peg 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 simply as Solitaire in the United Kingdom where the card games are called Patience...
Chessboard tasks
- Eight queens puzzle
The eight queens puzzle is the problem of putting eight chess queens on an 8×8 chessboard such that none of them are able to capture any other using the standard chess queen's moves. The queens must be placed in such a way that no two queens would be able to attack each other. Thus, a solution...
- Knight's Tour
The Knight's Tour is a mathematical problem involving a knight on a chessboard. The knight is placed on the empty board and, moving according to the rules of chess, must visit each square exactly once...
- No-three-in-line problem
In mathematics, in the area of discrete geometry, the no-three-in-line-problem, introduced by Henry Dudeney in 1917, asks for the maximum number of points that can be placed in the n × n grid so that no three points are collinear...
Topology, knots, graph theory
The fields of
knot theoryIn mathematics, knot theory is the area of topology that studies mathematical knots. While inspired by knots which appear in daily life in shoelaces and rope, a mathematician's knot differs in that the ends are joined together to prevent it from becoming undone. In precise mathematical language, a...
and
topologyTopology is a major area of mathematics concerned with spatial properties that are preserved under continuous deformations of objects, for example deformations that involve stretching, but no tearing or gluing...
, especially their non-intuitive conclusions, are often seen as a part of recreational mathematics.
- Disentanglement puzzle
A disentanglement puzzle is a type of mechanical puzzle that involves disentangling one piece or set of pieces from another piece or set of pieces. The reverse problem of reassembling the puzzle can be as hard as—or even harder than—disentanglement...
s
- Seven Bridges of Königsberg
The Seven Bridges of Königsberg is a famous historical problem in mathematics. Its negative resolution by Leonhard Euler in 1735 laid the foundations of graph theory and presaged the idea of topology.-Description:...
- Water, gas, and electricity
Mechanical
- Main article: Mechanical puzzle
A mechanical puzzle is a puzzle presented as a set of mechanically interlinked pieces.- History :The oldest known mechanical puzzle comes from Greece and appeared in the 3rd century BC....
- Rubik's Cube
The Rubik's Cube is a 3-D mechanical puzzle 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 Ideal Toys in 1980 and won the German Game of the Year special award for Best Puzzle that year...
- Think-a-Dot
The Think-a-Dot was a mathematical toy made by E.S.R., Inc. during the 1960s that demonstrated group theory. It had eight coloured disks on its front, and three holes on its top - left, right, and center - through which a ball bearing could be dropped. Each disk would display either a yellow or...
- Many others
External links