Mathematical games

Nim is a mathematical combinatorial game 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 remove any number of objects provided they all come from the same heap or pile. Depending on the version being played, the goal of the game is either to avoid taking the last object or to take the last object.

thumb|right|upright=1.7|The 12 pentominoes can form 18 different shapes, with 6 of them (the chiral pentominoes) being mirrored.

abstract strategy game

thumb|200px|The five free tetrominoes. thumb|A snapshot from a typical game of Tetris. 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 polyomino. The corresponding polycube, called a tetracube, is a geometric shape composed of four cubes connected orthogonally.

abstract two-player strategy game

Paper and pencil game

mathmatical puzzle to find expressions for various whole numbers using only common mathematical symbols and the digit four

game defined by mathematical parameters

game whose outcome can be correctly predicted

thumb|A move in the game of Chomp, removing two blocks: a player has chosen a block to "eat", and must also eat the block below it. The top-left block is "poisoned" and whoever eats it loses the game. 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 block and "eat it" (remove from the board), together with those that are below it and to its right. The top left block is "poisoned" and the player who eats this loses.

abstract strategy game

thumb|1554 illustration of a Rithmomachy board and pieces by Claude de Boissière Rithmomachia (also known as rithmomachy, arithmomachia, rythmomachy, rhythmomachy, the '''philosophers' game''', and other variants) is an early European mathematical board game. Its earliest known description dates from the eleventh century. The name comes loosely from Greek and means "The Battle of the Numbers." The game is somewhat like chess except that most methods of capture depend on the numbers inscribed on each piece.

an algorithmthat produces a solution to a combinatorial puzzle with the fewest possible moves

Method of random selection

twist to the original game tic-tac-toe

thumb|A game of phutball after five men have been placed (the ball has yet to move)

public domain arithmetical card game

group word game to teach mathematical division

paper-and-pencil game

card game

abstract strategy game

paper-and-pencil game

argument in combinatorial game theory

thumb|A starting setup for the game of Hackenbush Hackenbush is a two-player game invented by mathematician John Horton Conway. It may be played on any configuration of line segments connected to one another by their endpoints and to a "ground" line. Other versions of the game use differently colored lines.

game

two-player mathematical subtraction game

mathematical puzzle by John Conway

coin game

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 n×m, each player begins with m pawns, one for each square in the row closest to them. The goal of each player is to either advance a pawn to the opposite end of the board or leave the other player with no legal moves (akin to stalemate), including by capturing all of their pawns.

Mathematical game

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 rectangle, a polyomino, or a combination of any number of such components. Two players have a collection of dominoes which they place on the grid in turn, covering up squares. One player places tiles vertically, while the other places them horizontally. (Traditionally, these players are called "Left" and "Right", respectively, or "V" and "H". Both conventions are used in this article.) As in most game

pencil game

mathematical game

right|thumb|Starting position for 3×3 Dodgem Dodgem is a simple abstract strategy game invented by Colin Vout 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 n-1 cars for each player—two cars each on a 3×3 board is enough for an interesting game, but larger sizes are also possible.