منابع مشابه
Slow k-Nim
Given n piles of tokens and a positive integer k ≤ n, we study the following two impartial combinatorial games Nimn,≤k and Nim 1 n,=k. In the first (resp. second) game, a player, by one move, chooses at least 1 and at most (resp. exactly) k non-empty piles and removes one token from each of these piles. For the normal and misère version of each game we compute the Sprague-Grundy function for th...
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In the game of End-Nim two players take turns in removing one or more boxes from a string of non-empty stacks. At each move boxes may only be taken from the two stacks which form the ends of the string (unless only one stack remains!). We give a solution for both impartial and partizan versions of the game and explain the significance of the mystic hieroglyphs:
متن کاملThe game of n-times nim
The following game is considered. The 0rst player can take any number of stones, but not all the stones, from a single pile of stones. After that, each player can take at most n-times as many as the previous one. The player 0rst unable to move loses and his opponent wins. Let f1; f2; : : : be an initial sequence of stones in increasing order, such that the second player has a winning strategy w...
متن کاملA Nim game played on graphs
We propose a new impartial game played by two players, which can be compared to the well-known Nim game [1, 3, 4] played on graphs. In this paper, we consider this game and investigate its winning strategies. In the proof, Menger’s theorem [2] noted in graph theory plays a crucial role.
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: Advances in Applied Mathematics
سال: 2017
ISSN: 2324-7991,2324-8009
DOI: 10.12677/aam.2017.63027