Journal of Combinatorial Optimization

, Volume 35, Issue 4, pp 1241–1249 | Cite as

Greedy Nim\(_\mathrm{{k}}\) Game

Article
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Abstract

This paper introduces a new variant of Nim game, the Greedy Nim\(_\mathrm{{k}}\) Game. We present a complete solution for this game.

Keywords

Nim game Greedy Nim game Greedy Nim\(_\mathrm{k}\) game 

Notes

Acknowledgements

Funding was provided by The National Natural Science Fund (Grant Nos. KYZKJY11186 and NSF11571319).

References

  1. Albert MH, Nowakowski RJ (2001) The game of end-nim. Electron J Combin 8(2):1MathSciNetMATHGoogle Scholar
  2. Albert MH, Nowakowski RJ (2004) Nim restrictions. Integers Electron J Comb Number Theory 4:G01MathSciNetMATHGoogle Scholar
  3. Bouton CL (1902) Nim, a game with a complete mathematical theory. Ann Math 3(2):35–39MathSciNetMATHGoogle Scholar
  4. Cole AJ, Davie AJ (1969) A game based on the Euclidean algorithm and a winning strategy for it. Math Gaz 53:354–357MathSciNetCrossRefMATHGoogle Scholar
  5. Fukuyama M (2003) A Nim game played on graphs. Theor Comput Sci 304:387–399MathSciNetCrossRefMATHGoogle Scholar
  6. Li S-YR (1978) N-person Nim and N-person Moore’s games. Int J Game Theory 7:31–36MathSciNetCrossRefMATHGoogle Scholar
  7. Lim C-W (2005) Partial Nim. Integers Electron J Comb Number Theory 5:G02MathSciNetMATHGoogle Scholar
  8. Low RM, Chan WH (2015) An Atlas of N- and P-positions in ‘nim with a pass’. Integers 15:G2MathSciNetMATHGoogle Scholar
  9. Moore EH (1910) A generalization of a game called nim. Ann Math 11:93–94MathSciNetCrossRefMATHGoogle Scholar
  10. Schwartz BL (1971) Some extensions of nim. Math Mag 44(5):252–257MathSciNetCrossRefMATHGoogle Scholar
  11. Wythoff W (1907) A modification of the game of Nim. Nieuw Arch Wisk 7:199–202MATHGoogle Scholar
  12. Xu R, Zhu X (2018) Bounded greedy nim game. Theor Comput Sci (to appear) Google Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of MathematicsZhejiang Normal UniversityJinhuaChina

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