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- W2065444014 abstract "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 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." @default.
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- W2065444014 date "2008-03-01" @default.
- W2065444014 modified "2023-09-26" @default.
- W2065444014 title "The Magnus–Derek game" @default.
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- W2065444014 doi "https://doi.org/10.1016/j.tcs.2007.11.016" @default.
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