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Blocking Wythoff Nim

Urban Larsson (Institutionen för matematiska vetenskaper, matematik)
The Electronic Journal of Combinatorics (1077-8926). Vol. 18 (2011), 1, p. 18.
[Artikel, refereegranskad vetenskaplig]

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 ≥ 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 ≤ k ≤ 20. Certain comply variations of impartial games are also discussed.

Nyckelord: Beatty sequence, Blocking maneuver, Exact $k$-cover, Impartial game, Muller Twist, Wythoff Nim



Denna post skapades 2011-05-30. Senast ändrad 2016-08-22.
CPL Pubid: 141238

 

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Institutioner (Chalmers)

Institutionen för matematiska vetenskaper, matematik (2005-2016)

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Diskret matematik

Chalmers infrastruktur

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