Skip to content
DraconiticResearch
Search Sources API
194,164 studies31 sourcesUpdated 42 min ago
PreprintarXiv licencearXiv

Forbidden-Total-Size Nim

  • Hiromi Oginuma
  • Masato Shinoda
Open at sourcePDFDOICite

Abstract

We consider a variant of Nim in which, for a fixed set S of nonnegative integers, a move is forbidden if the total number of remaining stones belongs to S. This game coincides with normal-play Nim when S=∅, and with misère Nim when S={0}. In this paper, we focus in particular on the case where S is the set of multiples of d, and show that simple criteria for determining the outcome can be obtained for d=2,3,4.

Related

  1. Linear dependencies, polynomial factors in the Duke–Erdős forbidden sunflower problem – CORRIGENDUM
    Andrey Kupavskii, Fedor Noskov
    Forum of Mathematics, SigmaPeer-reviewedCC BY 4.0General mathematicsCrossref
  2. Analytic Combinatorics of Lattice Paths with Forbidden Patterns: Asymptotics Aspects and Borges's Theorem
    Andrei Asinowski, Axel Bacher, Cyril Banderier +1
    Leibniz International Proceedings in InformaticsPeer-reviewedCC BY 4.0Full textAnalysis & PDEsCombinatorics & discrete mathematicsHAL
  3. An Improved Bound for Smith's Longest Cycles Conjecture via a Forbidden Subdivision
    Douglas M. Chen
    arXivPreprintCC BY 4.0Full textCombinatorics & discrete mathematicsarXiv
  4. Generating Forbidden Words and Measures of Maximal Entropy for Subshifts
    Xinxing Wu, Xu Zhang
    arXivPreprintCC BY-NC-ND 4.0Full textDynamical systemsarXiv
  5. Maxima of the Q-index: Forbidden an odd wheel
    Hongyu Wang, Yue Ma
    arXivPreprintCC BY 4.0Full textCombinatorics & discrete mathematicsarXiv

Cite

BibTeXRIS
BibTeX
@misc{oginuma2026forbiddentotalsize,
  title = {{Forbidden-Total-Size Nim}},
  author = {Hiromi Oginuma and Masato Shinoda},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2608.11665},
  eprint = {2608.11665},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2608.11665},
}
RIS
TY  - UNPB
TI  - Forbidden-Total-Size Nim
AU  - Hiromi Oginuma
AU  - Masato Shinoda
PY  - 2026
DA  - 2026/09/27
PB  - arXiv
DO  - 10.48550/arxiv.2608.11665
UR  - https://arxiv.org/abs/2608.11665
AB  - We consider a variant of Nim in which, for a fixed set S of nonnegative integers, a move is forbidden if the total number of remaining stones belongs to S. This game coincides with normal-play Nim when S=∅, and with misère Nim when S={0}. In this paper, we focus in particular on the case where S is the set of multiples of d, and show that simple criteria for determining the outcome can be obtained for d=2,3,4.
ER  -