The Magnus-Derek game

Z. Nedev, S. Muthukrishnan

Research output: Contribution to journalArticlepeer-review

12 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)124-132
Number of pages9
JournalTheoretical Computer Science
Issue number1-3
StatePublished - Mar 20 2008

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Computer Science(all)


  • Algorithmic strategies
  • Combinatorial number theory
  • Discrete mathematics
  • Mobile agent
  • Network with inconsistent global sense of direction
  • Two-person games

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