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Variants of nim have been played since ancient times. [1] The game is said to have originated in China—it closely resembles the Chinese game of jiǎn-shízi (捡石子), or "picking stones" [2] —but the origin is uncertain; the earliest European references to nim are from the beginning of the 16th century.
A game is a nim game, if: it has a genus 0 1, 1 0, 2 2, 3 3... it has moves only to single nim heaps, i.e. move to a position *1, or *2, but not e.g. *x+*y (but see next point) it may also have moves to games which are not nim, provided they are not required to determine the genus, and those games each have at least one option to a nim game of ...
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The octal games are a class of two-player heap 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, Kayles, and similar games. [1] [2] Octal games are impartial meaning that every move available to one player is also available to the ...
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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; players alternate moves, removing one or more tokens in a single row or column until the last one is removed. At the time of its founding, TacTix was ...
The goal of the game is to be the player who removes the last object. The nimber of a heap is simply the number of objects in that heap. Using nim addition, one can calculate the nimber of the game as a whole. The winning strategy is to force the nimber of the game to 0 for the opponent's turn. [2]
In Nim, players take turns removing at least one object from a set of objects, with the goal of being the player who removes the last object; gameplay options can be modeled mathematically. In the version of the game Condon proposed using, there are multiple sets of objects, and on each turn the player can only remove objects from a single set. [2]
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