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# Nim

A game which is played by the following rules. Given one or more piles (nim-heaps), players alternate by taking all or some of the counters in a single heap. The player taking the last counter or stack of counters is the winner. Nim-like games are also called take-away games and disjunctive games. If optimal strategies are used, the winner can be determined from any intermediate position by its associated nim-value. The nim-heap illustrated above corresponds to the game of Marienbad.

## See also

Marienbad, Misère-Form Game, Nim-Value, Wythoff's Game

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## References

Ball, W. W. R. and Coxeter, H. S. M. Mathematical Recreations and Essays, 13th ed. New York: Dover, pp. 36-38, 1987.Bewersdorff, J. "Nim: The Easy Winner!" Ch. 21 in Luck, Logic, & White Lies: The Mathematics of Games. Wellesley, MA: A K Peters, pp. 169-173, 2005.Bogomolny, A. "The Game of Nim." http://www.cut-the-knot.org/nim_st.shtml.Bouton, C. L. "Nim, A Game with a Complete Mathematical Theory." Ann. Math. Princeton 3, 35-39, 1901-1902.Gardner, M. "Mathematical Games: Concerning the Game of Nim and Its Mathematical Analysis." Sci. Amer. 198, 104-111, Feb. 1958.Gardner, M. "Nim and Hackenbush." Ch. 14 in Wheels, Life, and other Mathematical Amusements. New York: W. H. Freeman, pp. 142-151, 1983.Hardy, G. H. and Wright, E. M. An Introduction to the Theory of Numbers, 5th ed. Oxford, England: Oxford University Press, pp. 117-120, 1990.Kraitchik, M. "Nim." §3.12.2 in Mathematical Recreations. New York: W. W. Norton, pp. 86-88, 1942.

Nim

## Cite this as:

Weisstein, Eric W. "Nim." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/Nim.html