author: | Holshouser, Arthur and Reiter, Harold |
---|---|

title: | Two Pile Move-Size Dynamic Nim |

keywords: | Nim, dynamic, combinatorial games |

abstract: | The purpose of this paper is to solve a special class of combinational games consisting of two-pile counter pickup games for
which the maximum number of counters that can be removed on each
successive move changes during the play of the games. Two players
alternate moving. Each player in his turn first chooses one of the
piles, and his choice of piles can change from move to move. He then
removes counters from this chosen pile. A function
f:
is given which determines the maximum size of the next move in terms
of the current move size. The game ends as soon as one of the two
piles is empty, and the winner is the last player to move in the
game. The games for which ^{+}^{+}f(k)=k, f(k)=2k, and
f(k)=3k use the same formula for computing the smallest
winning move size. Here we find all the functions f for
which this formula works, and we also give the winning strategy for
each function. See Holshouser, A, James Rudzinski and Harold
Reiter: Dynamic One-Pile Nim for a discussion of the single pile game.
If your browser does not display the abstract correctly (because of the different mathematical symbols) you can look it up in the PostScript or PDF files. |

reference: | Holshouser, Arthur and Reiter, Harold (2005),
Two Pile Move-Size Dynamic Nim,
Discrete Mathematics and Theoretical Computer Science 7, pp. 1-10 |

bibtex: | For a corresponding BibTeX entry, please consider our BibTeX-file. |

ps.gz-source: | dm070101.ps.gz (41 K) |

ps-source: | dm070101.ps (131 K) |

pdf-source: | dm070101.pdf (94 K) |

The first *source* gives you the `gzipped' PostScript, the second the plain
PostScript and the third the format for the Adobe accrobat
reader. Depending on the installation of your web browser, at least
one of these should (after some amount of time) pop up a window for
you that shows the full article. If this is not the case, you should
contact your system administrator to install your browser correctly.

Due to limitations of your local software, the two formats may show up differently on your screen. If eg you use xpdf to visualize pdf, some of the graphics in the file may not come across. On the other hand, pdf has a capacity of giving links to sections, bibliography and external references that will not appear with PostScript.

Automatically produced on Fri Jan 21 21:57:44 CET 2005 by falk