Modular Nim
نویسندگان
چکیده
منابع مشابه
Building Nim
The game of nim, with its simple rules, its elegant solution and its historical importance is the quintessence of a combinatorial game, which is why it led to so many generalizations and modifications. We present a modification with a new spin: building nim. With given finite numbers of tokens and stacks, this two-player game is played in two stages (thus belonging to the same family of games a...
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A circular Nim game is a two player impartial combinatorial game consisting of n stacks of tokens placed in a circle. A move consists of choosing k consecutive stacks, and taking at least one token from one or more of the k stacks. The last player able to make a move wins. We prove results on the structure of the losing positions for small n and k and pose some open questions for further invest...
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In the standard Nim with n heaps, a player by one move can reduce (by a positive amount) exactly one heap of his choice. In this paper we consider the game of complementary Nim (Co-Nim), in which a player by one move can reduce at least one and at most n − 1 heaps, of his choice. An explicit formula for the Sprague-Grundy (SG) function of Co-Nim was obtained by Jenkyns and Mayberry in 1980. We ...
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We present a new family of Nim games where the rules depend on a given ‘coloring’ of the tokens, each token being either black or white. The rules are as in Nim with the restriction that a white token on top of each heap is not allowed. We resolve the winning strategies of two disjoint game families played on two heaps. The heap-sizes with black tokens correspond to the numbers ⌊βn⌋, where β > ...
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...
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ژورنال
عنوان ژورنال: Theoretical Computer Science
سال: 1995
ISSN: 0304-3975
DOI: 10.1016/0304-3975(94)00260-p