Androids Armed With Poisoned Chocolate Squares: Ideal Nim and Its Relatives
Document Type
Article
Publication Date
10-1-2016
Abstract
We describe two new combinatorial games. The first, Ideal Nim, both generalizes the well-known game Nim and its relative Chomp, and provides a recreational perspective on some important ideas of commutative algebra; for instance, the fact that the game is guaranteed to end is equivalent to Dickson's lemma, a well-known fact of commutative algebra. This relationship leads to a game-based proof of Dickson's lemma. The second game, Gröbner Nim, is really a variant of Ideal Nim that illustrates Buchberger's algorithm to compute a Gröbner basis. We conclude by describing the relationship between Gröbner Nim and polynomial rings.
Publication Title
Mathematics Magazine
Volume
89
Issue
4
First Page
235
Last Page
250
Recommended Citation
Dozier, H.,
Perry, J.
(2016). Androids Armed With Poisoned Chocolate Squares: Ideal Nim and Its Relatives. Mathematics Magazine, 89(4), 235-250.
Available at: https://aquila.usm.edu/fac_pubs/19515