Nim-Game

Nim is a mathematical game of strategy in which two players take turns removing objects from distinct heaps. 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. 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 "Tsyan-shizi", or "picking stones"[2]—but the origin is uncertain; the earliest European references to Nim are from the beginning of the 16th century. Its current name was coined by Charles L. Bouton of Harvard University, who also developed the complete theory of the game in 1901,[3] but the origins of the name were never fully explained. The name is probably derived from German nimm meaning "take [imperative]", or the obsolete English verb nim of the same meaning.[4] Nim can be played as a misère game, in which the player to take the last object loses. Nim can also be played as a normal play game, which means that the person who makes the last move (i.e., who takes the last object) wins. This is called normal play because most games follow this convention, even though Nim usually does not.