A game, also called Tactix, 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.

**References**

Ball, W. W. R. and Coxeter, H. S. M. *Mathematical Recreations and Essays, 13th ed.* New York: Dover, pp. 36-38,
1987.

Bogomolny, A. ``The Game of Nim.'' http://www.cut-the-knot.com/bottom_nim.html.

Bouton, C. L. ``Nim, A Game with a Complete Mathematical Theory.'' *Ann. Math. Princeton* **3**, 35-39, 1901-1902.

Gardner, M. ``Nim and Hackenbush.'' Ch. 14 in *Wheels, Life, and other Mathematical Amusements.*
New York: W. H. Freeman, 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.

© 1996-9

1999-05-25