Dynamic One-Pile Blocking Nim
نویسندگان
چکیده
منابع مشابه
Dynamic One-Pile Blocking Nim
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...
متن کاملDynamic One-pile Nim
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...
متن کاملPilesize Dynamic One-pile Nim and Beatty’s Theorem
In [4] we proved a generalization of Beatty’s Theorem which we stated came from the Nim value analysis of a game. In this paper we give the Nim value analysis of this game and show its relationship with Beatty’s Theorem. The game is a one-pile counter pickup game for which the maximum number of counters that can be removed on each successive move changes during the play of the game. The move si...
متن کاملDynamic One and Two Pile Nim Games Using Generalized Bases
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...
متن کاملDynamic 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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ژورنال
عنوان ژورنال: The Electronic Journal of Combinatorics
سال: 2003
ISSN: 1077-8926
DOI: 10.37236/1744