The skeletion of an impartial game and the Nim-function of Moore's Nimk

1980 ◽  
Vol 9 (1) ◽  
pp. 51-63 ◽  
Author(s):  
T. A. Jenkyns ◽  
J. P. Mayberry
Keyword(s):  
Impartial Game

scholarly journals Impartial achievement games for generating nilpotent groups

2019 ◽  
Vol 22 (3) ◽  
pp. 515-527
Author(s):  
Bret J. Benesh ◽  
Dana C. Ernst ◽  
Nándor Sieben
Keyword(s):  
Finite Group ◽  
Finite Groups ◽  
Abelian Groups ◽  
Nilpotent Groups ◽  
Generating Set ◽  
Odd Order ◽  
Impartial Game ◽  
A Finite Group

AbstractWe study an impartial game introduced by Anderson and Harary. The game is played by two players who alternately choose previously-unselected elements of a finite group. The first player who builds a generating set from the jointly-selected elements wins. We determine the nim-numbers of this game for finite groups of the form{T\times H}, whereTis a 2-group andHis a group of odd order. This includes all nilpotent and hence abelian groups.

scholarly journals Multivision: An Intractable Impartial Game with a Linear Winning Strategy

1998 ◽  
Vol 105 (10) ◽  
pp. 923
Author(s):  
Aviezri S. Fraenkel
Keyword(s):  
Winning Strategy ◽  
Impartial Game

scholarly journals One-pile misère Nim for three or more players

2006 ◽  
Vol 2006 ◽  
pp. 1-8 ◽  
Author(s):  
Annela R. Kelly
Keyword(s):  
Game Theory ◽  
Binary Representation ◽  
Impartial Game ◽  
Classical Game

The analysis of the classical game of Nim relies on binary representation of numbers as shown in the books of Berlekamp and Gardener. There is considerable interest in generalizations and modifications of the game. We will consider one-pile misère Nim for more than two players. In the case of three or more players, the impartial game theory results rarely apply. In this note, we analyze the game in a variety of cases where alliances are formed among the players.

scholarly journals Multivision: An Intractable Impartial Game With a Linear Winning Strategy

1998 ◽  
Vol 105 (10) ◽  
pp. 923-928
Author(s):  
Aviezri S. Fraenkel
Keyword(s):  
Winning Strategy ◽  
Impartial Game

scholarly journals Developing an Impartial Game by Mathematical Approach

2020 ◽  
Vol 864 ◽  
pp. 012092
Author(s):  
Azlan Mohd Zain ◽  
Afiq Abdul Rahman ◽  
Nurhafiyah Hawani Haris Fadzillah ◽  
Aimi Rusdi ◽  
Ainur Najwa Anuar Rosdi ◽  
...  
Keyword(s):  
Mathematical Approach ◽  
Impartial Game

scholarly journals Blocking Wythoff Nim

10.37236/607 ◽  
2011 ◽  
Vol 18 (1) ◽  
Author(s):  
Urban Larsson
Keyword(s):  
Computer Simulations ◽  
Winning Strategy ◽  
Impartial Games ◽  
Impartial Game ◽  
Predetermined Number

The 2-player impartial game of Wythoff Nim is played on two piles of tokens. A move consists in removing any number of tokens from precisely one of the piles or the same number of tokens from both piles. The winner is the player who removes the last token. We study this game with a blocking maneuver, that is, for each move, before the next player moves the previous player may declare at most a predetermined number, $k - 1 \ge 0$, of the options as forbidden. When the next player has moved, any blocking maneuver is forgotten and does not have any further impact on the game. We resolve the winning strategy of this game for $k = 2$ and $k = 3$ and, supported by computer simulations, state conjectures of 'sets of aggregation points' for the $P$-positions whenever $4 \le k \le 20$. Certain comply variations of impartial games are also discussed.

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