منابع مشابه
Circular Nim Games
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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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 کاملEvolving Winning Strategies for Nim-like Games
An evolutionary approach for computing the winning strategy for Nim-like games is proposed in this paper. The winning strategy is computed by using the Multi Expression Programming (MEP) technique a fast and efficient variant of the Genetic Programming (GP). Each play strategy is represented by a mathematical expression that contains mathematical operators (such as +, -, *, mod, div, and , or, ...
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 کاملA nim-type game and continued fractions
In the two-person nim-type game called Euclid a position consists of a pair (a, b) of positive integers. Players alternate moves, a move consisting of decreasing the larger number in the current position by any positive multiple of the smaller number, as long as the result remains positive. The first player unable to make a move loses. In the restricted version a set of natural numbers Λ is giv...
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ژورنال
عنوان ژورنال: Journal of the Mathematical Society of Japan
سال: 1980
ISSN: 0025-5645
DOI: 10.2969/jmsj/03230461