Mathematical puzzle
Encyclopedia
Mathematical puzzles make up an integral part of recreational mathematics
. They have specific rules as do multiplayer game
s, but they do not usually involve competition between two or more players. Instead, to solve such a puzzle
, the solver must find a solution that satisfies the given conditions. Mathematical puzzles require mathematics to solve them. Logic puzzle
s are a common type of mathematical puzzle.
Conway's Game of Life
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. Many of the puzzles are well known because they were discussed by Martin Gardner
in his "Mathematical Games" column in Scientific American.
and topology
, especially their non-intuitive conclusions, are often seen as a part of recreational mathematics.
Recreational mathematics
Recreational 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 attracts the curiosity of non-mathematicians, and inspires their further study...
. They have specific rules as do multiplayer game
Multiplayer game
A 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 put 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 puzzle
Puzzle
A puzzle is a problem or enigma that tests the ingenuity of the solver. In a basic puzzle, one is intended to put together pieces in a logical way in order to come up with the desired solution...
, the solver must find a solution that satisfies the given conditions. Mathematical puzzles require mathematics to solve them. Logic puzzle
Logic puzzle
A logic puzzle is a puzzle deriving from the mathematics 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 Wonderland...
s are a common type of mathematical puzzle.
Conway's Game of Life
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....
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. Many of the puzzles are well known because they were discussed by Martin Gardner
Martin Gardner
Martin Gardner was an American mathematics and science writer specializing in recreational mathematics, but with interests encompassing micromagic, stage magic, literature , philosophy, scientific skepticism, and religion...
in his "Mathematical Games" column in Scientific American.
List of mathematical puzzles
The following categories are not disjoint; some puzzles fall into more than one category.Numbers, arithmetic, and algebra
- Cross-figureCross-figureA 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 Cross number Puzzle - Dyson numbers
- Four foursFour foursFour 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 PuzzlesFeynman Long Division PuzzlesPhysicist 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 arithmeticVerbal arithmeticVerbal arithmetic, also known as alphametics, cryptarithmetic, crypt-arithmetic, cryptarithm or word addition, 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 PuzzleN-puzzleThe 15-puzzle is a sliding puzzle that consists of a frame of numbered square tiles in random order with one tile missing. The puzzle also exists in other sizes, particularly the smaller 8-puzzle...
- Kakuro
- Rubik's CubeRubik's CubeRubik'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 Toy Corp. in 1980 and won the German Game of the Year special award for Best Puzzle that...
and other sequential movement puzzles - Str8tsStr8tsStr8ts 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. The puzzle is published in a number of newspapers internationally, in 2 book collections, and in...
a number puzzle based on sequences - SudokuSudokuis a logic-based, combinatorial number-placement puzzle. The objective is to fill a 9×9 grid with digits so that each column, each row, and each of the nine 3×3 sub-grids that compose the grid contains all of the digits from 1 to 9...
- Think-a-DotThink-a-DotThe 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 HanoiTower of HanoiThe Tower of Hanoi or Towers of Hanoi, also called the Tower of Brahma or Towers of Brahma, 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
- Bedlam cubeBedlam cubeThe 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 x 4 x 4 cube...
- Conway puzzleConway puzzleConway'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....
- Mutilated chessboard problemMutilated chessboard problemThe 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:...
- Packing problemPacking problemPacking problems are a class of optimization problems in mathematics which involve attempting to pack objects together , as densely as possible. Many of these problems can be related to real life packaging, storage and transportation issues...
- PentominoPentominoA pentomino is a polyomino composed of five congruent squares, connected along their edges ....
es tiling - Slothouber–Graatsma puzzleSlothouber–Graatsma puzzleThe 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 ....
- Soma cubeSoma cubeThe Soma cube is a solid dissection puzzle invented by 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 3x3x3 cube...
- T puzzleT puzzleThe 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*...
- TangramTangramThe 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...
Involves a board
- Conway's Game of LifeConway'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....
- Mutilated chessboard problemMutilated chessboard problemThe 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 solitairePeg solitairePeg 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...
- SudokuSudokuis a logic-based, combinatorial number-placement puzzle. The objective is to fill a 9×9 grid with digits so that each column, each row, and each of the nine 3×3 sub-grids that compose the grid contains all of the digits from 1 to 9...
Chessboard tasks
- Eight queens puzzleEight queens puzzleThe eight queens puzzle is the problem of placing eight chess queens on an 8×8 chessboard so that no two queens attack each other. Thus, a solution requires that no two queens share the same row, column, or diagonal...
- Knight's TourKnight's tourThe 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. A knight's tour is called a closed tour if the knight ends on a square attacking the square from...
- No-three-in-line problemNo-three-in-line problemIn 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 theoryKnot theory
In topology, knot theory is the study of 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 so that it cannot be undone. In precise mathematical language, a knot is an embedding of a...
and topology
Topology
Topology is a major area of mathematics concerned with properties that are preserved under continuous deformations of objects, such as deformations that involve stretching, but no tearing or gluing...
, especially their non-intuitive conclusions, are often seen as a part of recreational mathematics.
- Disentanglement puzzleDisentanglement puzzleA 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 KönigsbergSeven Bridges of KönigsbergThe Seven Bridges of Königsberg is a historically notable problem in mathematics. Its negative resolution by Leonhard Euler in 1735 laid the foundations of graph theory and prefigured the idea of topology....
- Water, gas, and electricity
External links
- Historical Math Problems/Puzzles at Mathematical Association of AmericaMathematical Association of AmericaThe Mathematical Association of America is a professional society that focuses on mathematics accessible at the undergraduate level. Members include university, college, and high school teachers; graduate and undergraduate students; pure and applied mathematicians; computer scientists;...
Convergence