Dynamic Single-Pile Nim Using Multiple Bases
نویسندگان
چکیده
منابع مشابه
Dynamic Single-Pile Nim Using Multiple Bases
In the game G0 two players alternate removing positive numbers of counters from a single pile and the winner is the player who removes the last counter. On the first move of the game, the player moving first can remove a maximum of k counters, k being specified in advance. On each subsequent move, a player can remove a maximum of f(n, t) counters where t was the number of counters removed by hi...
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Several authors have written papers dealing with a class of combinatorial games consisting of one-pile and two-pile counter pickup games for which the maximum number of counters that can be removed on each move changes during the play of the game. See Holshouser [8],[7], and Flanigan [4]. The maximum number of counters that can be removed can depend upon a number of factors including the number...
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1 Introduction The purpose of this paper is to solve a class of combinatorial games consisting of one-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 game. Two players alternate removing a positive number of counters from the pile. An ordered pair (N, x) of positive integers is called a position. The n...
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The purpose of this paper is to solve a class of combinatorial games consisting of one-pile counter pickup games for which the number of counters that can be removed on each successive turn changes during the play of the game. Both the minimum and the maximum number of counters that can be removed is dependent upon the move number. Also, on each move, the opposing player can block some of the m...
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1 Introduction. In this paper, two players alternate removing a positive number of counters from one of n piles of counters, and the choice of which pile he removes from can change on each move. On his initial move, the player moving first can remove from one pile of his choice at most t counters. On each subsequent move, a player can remove from one pile of his choice at most f (x) counters, w...
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ژورنال
عنوان ژورنال: The Electronic Journal of Combinatorics
سال: 2006
ISSN: 1077-8926
DOI: 10.37236/1145