The Magnus-Derek game

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The Magnus-Derek game
We introduce a new combinatorial game between two players: Magnus and Derek. Initially, a token is placed at position 0 on a round table with n positions. In each round of the game Magnus chooses the number of positions for the token to move, and Derek decides in which direction, + (clockwise) or (counterclockwise), the token will be moved. Magnus aims to maximize the total number of positions visited during the course of the game, while Derek aims to minimize this quantity. We define f (n) to be the eventual size of of the set of visited positions when both players play optimally. We prove a closed form expression for f (n) in terms of the prime factorization of n, and provide algorithmic strategies for Magnus and Derek to meet this bound. We note the relevance of the game for a mobile agent exploring a ring network with faulty sense of direction, and we pose variants of the game for future study.
Zhivko Prodanov Nedev, S. Muthukrishnan
Added 15 Dec 2010
Updated 15 Dec 2010
Type Journal
Year 2008
Where TCS
Authors Zhivko Prodanov Nedev, S. Muthukrishnan
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