Drawing strategies for generalized tic-Tac-Toe (p, q)

Diptarama, Kazuyuki Narisawa, Ayumi Shinohara

Research output: Chapter in Book/Report/Conference proceedingConference contribution

1 Citation (Scopus)

Abstract

GTTT(p, q) is an achievement game for polyominoes, which is an extension of Harary's generalized tic-Tac-Toe. Two players alternately put p stones over a board with the exception that the first player Black puts q stones for the first move. The player who first achieves a given polyomino wins the game. Unlike the generalized tic-Tac-Toe, we define winner for polyomino that Black can achieve, loser that White can achieve, and draw that both players cannot achieve in each GTTT(p, q). In this paper we define three classes of polyominoes for GTTT(p, q) and show that any polyomino that satisfies some conditions for each classes is a draw.

Original languageEnglish
Title of host publicationProgress in Applied Mathematics in Science and Engineering Proceedings, PIAMSE 2015
EditorsHamzah Asyrani Sulaiman, Mohd Azlishah Othman, Mohamad Zoinol Abidin Abd. Aziz, Mohd Shakir Md Saat, Mai Mariam Mohamed Aminuddin, Abd Majid Darsono, Mohamad Harris Misran
PublisherAmerican Institute of Physics Inc.
ISBN (Electronic)9780735413528
DOIs
Publication statusPublished - 2016 Feb 1
Event1st Progress in Applied Mathematics in Science and Engineering, PIAMSE 2015 - Bali, Indonesia
Duration: 2015 Sep 292015 Oct 1

Publication series

NameAIP Conference Proceedings
Volume1705
ISSN (Print)0094-243X
ISSN (Electronic)1551-7616

Other

Other1st Progress in Applied Mathematics in Science and Engineering, PIAMSE 2015
CountryIndonesia
CityBali
Period15/9/2915/10/1

ASJC Scopus subject areas

  • Physics and Astronomy(all)

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  • Cite this

    Diptarama, Narisawa, K., & Shinohara, A. (2016). Drawing strategies for generalized tic-Tac-Toe (p, q). In H. A. Sulaiman, M. A. Othman, M. Z. A. A. Aziz, M. S. M. Saat, M. M. M. Aminuddin, A. M. Darsono, & M. H. Misran (Eds.), Progress in Applied Mathematics in Science and Engineering Proceedings, PIAMSE 2015 [4940269] (AIP Conference Proceedings; Vol. 1705). American Institute of Physics Inc.. https://doi.org/10.1063/1.4940269