Map-coloring games
Several map-coloring games are studied in combinatorial game theory. The general idea is that we are given a map with regions drawn in but with not all the regions colored. Two players, Left and Right
Clumsy Thief
Clumsy Thief is a dedicated deck card game published by the company Melon Rind. The game was created by Jeanie Mehran in an effort to help her son with his addition skills. Clumsy Thief won several ga
Dots (game)
Dots (Czech: Židi, Polish: Kropki, Russian: Точки) is an abstract strategy game, played by two or more people on a sheet of squared paper. The game is somewhat similar to Go, in that the goal is to "c
Poset game
In combinatorial game theory, poset games are mathematical games of strategy, generalizing many well-known games such as Nim and Chomp. In such games, two players start with a poset (a partially order
Nim
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
Ghost Leg
Ghost Leg (Chinese: 畫鬼腳), known in Japan as Amidakuji (阿弥陀籤, "Amida lottery", so named because the paper was folded into a fan shape resembling Amida's halo) or in Korea as Sadaritagi (사다리타기, literall
Four fours
Four fours is a mathematical puzzle, the goal of which is to find the simplest mathematical expression for every whole number from 0 to some maximum, using only common mathematical symbols and the dig
Racetrack (game)
Racetrack is a paper and pencil game that simulates a car race, played by two or more players. The game is played on a squared sheet of paper, with a pencil line tracking each car's movement. The rule
Tennis (paper game)
Tennis is an (abstract) strategic pencil and paper game for two players. The game field consists of 4 fields and a centre line. These are called (-2,-1,0,1,2), with negative numbers belonging to playe
Seega (game)
Seega is an abstract strategy game that originated in Egypt. It can be played on boards with cells in a 5×5, 7×7 or 9×9 disposition. Other names include Seejeh, Siga and Sidjah. The board starts out e
TacTix
TacTix is a two-player strategy game invented by Piet Hein, a poet well known for dabbling in math and science, best known for his game Hex. TacTix is essentially a two-dimension version of Nim; playe
Black Path Game
The Black Path Game (also known by various other names, such as Brick) is a two-player board game described and analysed in Winning Ways for your Mathematical Plays. It was invented by Larry Black in
Tetromino
A tetromino is a geometric shape composed of four squares, connected orthogonally (i.e. at the edges and not the corners). Tetrominoes, like dominoes and pentominoes, are a particular type of polyomin
Buchholz hydra
In mathematical logic, the Buchholz hydra game is a hydra game, which is a single-player game based on the idea of chopping pieces off a mathematical tree. The hydra game can be used to generate a rap
Dodgem
Dodgem is a simple abstract strategy game invented by in 1972 while he was a mathematics student at the University of Cambridge as described in the book Winning Ways. It is played on an n×n board with
Hexapawn
Hexapawn is a deterministic two-player game invented by Martin Gardner. It is played on a rectangular board of variable size, for example on a 3×3 board or on a regular chessboard. On a board of size
Phutball
Phutball (short for Philosopher's Football) is a two-player abstract strategy board game described in Elwyn Berlekamp, John Horton Conway, and Richard K. Guy's Winning Ways for your Mathematical Plays
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
Wythoff's game
Wythoff's game is a two-player mathematical subtraction game, played with two piles of counters. Players take turns removing counters from one or both piles; when removing counters from both piles, th
Cram (game)
Cram is a mathematical game played on a sheet of graph paper. It is the impartial version of Domineering and the only difference in the rules is that each player may place their dominoes in either ori
Penney's game
Penney's game, named after its inventor Walter Penney, is a binary (head/tail) sequence generating game between two players. Player A selects a sequence of heads and tails (of length 3 or larger), and
Kayles
Kayles is a simple impartial game in combinatorial game theory, invented by Henry Dudeney in 1908. Given a row of imagined bowling pins, players take turns to knock out either one pin, or two adjacent
Integration Bee
The Integration Bee is an annual integral calculus competition pioneered in 1981 by Andy Bernoff, an applied mathematics student at the Massachusetts Institute of Technology (MIT). Similar contests ar
Octal game
The octal games are a class of two-player games that involve removing tokens (game pieces or stones) from heaps of tokens.They have been studied in combinatorial game theory as a generalization of Nim
Toads and Frogs
The combinatorial game Toads and Frogs is a partisan game invented by Richard Guy. This mathematical game was used as an introductory game in the book Winning Ways for your Mathematical Plays. Known f
Spoof (game)
Spoof is a strategy game, typically played as a gambling game, often in bars and pubs where the loser buys the other participants a round of drinks. The exact origin of the game is unknown, but one sc
13th root
Extracting the 13th root of a number is a famous category for the mental calculation world records. The challenge consists of being given a large number (possibly over 100 digits) and asked to return
Chomp
Chomp is a two-player strategy game played on a rectangular grid made up of smaller square cells, which can be thought of as the blocks of a chocolate bar. The players take it in turns to choose one b
Polyomino
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
Finite promise games and greedy clique sequences
The finite promise games are a collection of mathematical games developed by American mathematician Harvey Friedman in 2009 which are used to develop a family of fast-growing functions , and . The gre
Mixmath
mi×ma+h (or Mixmath) is a Canadian board game developed by Wrebbit and published in 1987. It resembles a variant of Scrabble in that tiles are placed on a crossword-style grid, with special premiums s
Planarity
Planarity is a puzzle computer game by John Tantalo, based on a concept by Mary Radcliffe at Western Michigan University.The name comes from the concept of planar graphs in graph theory; these are gra
Domineering
Domineering (also called Stop-Gate or Crosscram) is a mathematical game that can be played on any collection of squares on a sheet of graph paper. For example, it can be played on a 6×6 square, a rect
24 (puzzle)
The 24 puzzle is an arithmetical puzzle in which the objective is to find a way to manipulate four integers so that the end result is 24. For example, for the numbers 4, 7, 8, 8, a possible solution i
Dots and Boxes
Dots and Boxes is a pencil-and-paper game for two players (sometimes more). It was first published in the 19th century by French mathematician Édouard Lucas, who called it la pipopipette. It has gone
Ultimate tic-tac-toe
Ultimate tic-tac-toe (also known as ten-tac-toe, super tic-tac-toe,strategic tic-tac-toe, meta tic-tac-toe, tic-tac-tic-tac-toe-toe, or (tic-tac-toe)²) is a board game composed of nine tic-tac-toe boa
Tangloids
Tangloids is a mathematical game for two players created by Piet Hein to model the calculus of spinors. A description of the game appeared in the book "Martin Gardner's New Mathematical Diversions fro
Rithmomachia
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
Berlekamp switching game
The Berlekamp switching game is a mathematical game proposed by American mathematician Elwyn Berlekamp. It has also been called the Gale–Berlekamp switching game, after David Gale, who discovered the
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
Mathematical game
A mathematical game is a game whose rules, strategies, and outcomes are defined by clear mathematical parameters. Often, such games have simple rules and match procedures, such as Tic-tac-toe and Dots
Ulam's game
Ulam's game, or the Rényi–Ulam game, is a mathematical game similar to the popular game of twenty questions. In Ulam's game, a player attempts to guess an unnamed object or number by asking yes–no que
SESI Mathematics
SESI Mathematics is a project developed by FIRJAN System with the aim of improving the teaching of math for high school students. The program consists of a series of initiatives, from the organization
Strategy-stealing argument
In combinatorial game theory, the strategy-stealing argument is a general argument that shows, for many two-player games, that the second player cannot have a guaranteed winning strategy. The strategy
L game
The L game is a simple abstract strategy board game invented by Edward de Bono. It was introduced in his book The Five-Day Course in Thinking (1967).
Cayley's mousetrap
Mousetrap is the name of a game introduced by the English mathematician Arthur Cayley. In the game, cards numbered through ("say thirteen" in Cayley's original article) are shuffled to place them in s
Ponte del Diavolo
Ponte del Diavolo (Italian for "Devil's bridge") by Martin Ebel is a territorial game (with connective elements similar to Go), in which two players create islands and then add bridges to connect them
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
Hackenbush
Hackenbush is a two-player game invented by mathematician John Horton Conway. It may be played on any configuration of colored line segments connected to one another by their endpoints and to a "groun
Conway's Soldiers
Conway's Soldiers or the checker-jumping problem is a one-person mathematical game or puzzle devised and analyzed by mathematician John Horton Conway in 1961. A variant of peg solitaire, it takes plac
First-player and second-player win
In combinatorial game theory, a two-player deterministic perfect information turn-based game is a first-player-win if with perfect play the first player to move can always force a win. Similarly, a ga
Order and Chaos
Order and Chaos is a variant of the game tic-tac-toe on a 6×6 gameboard. It was invented by Stephen Sniderman and introduced by him in Games magazine in 1981. The player Order strives to create a five
SOS (game)
SOS is paper and pencil game for two or more players. It is similar to tic-tac-toe and dots and boxes, but has greater complexity. SOS is a combinatorial game when played with two players. In terms of
Icosian game
The icosian game is a mathematical game invented in 1857 by William Rowan Hamilton. The game's object is finding a Hamiltonian cycle along the edges of a dodecahedron such that every vertex is visited
Notakto
Notakto is a tic-tac-toe variant, also known as neutral or impartial tic-tac-toe. The game is a combination of the games tic-tac-toe and Nim, played across one or several boards with both of the playe
Fizz buzz
Fizz buzz is a group word game for children to teach them about division. Players take turns to count incrementally, replacing any number divisible by three with the word "fizz", and any number divisi
Solved game
A solved game is a game whose outcome (win, lose or draw) can be correctly predicted from any position, assuming that both players play perfectly.This concept is usually applied to abstract strategy g
Sprouts (game)
Sprouts is a paper-and-pencil game which can be analyzed for its mathematical properties. It was invented by mathematicians John Horton Conway and Michael S. Paterson at Cambridge University in the ea
Krypto (game)
Krypto is a card game designed by in 1963 and published by Parker Brothers and MPH Games Co. It is a mathematical game that promotes proficiency with basic arithmetic operations. More detailed analysi
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 rotati
God's algorithm
God's algorithm is a notion originating in discussions of ways to solve the Rubik's Cube puzzle, but which can also be applied to other combinatorial puzzles and mathematical games. It refers to any a
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