### 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 language | English |
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Title of host publication | Progress in Applied Mathematics in Science and Engineering Proceedings, PIAMSE 2015 |

Editors | Hamzah Asyrani Sulaiman, Mohd Azlishah Othman, Mohamad Zoinol Abidin Abd. Aziz, Mohd Shakir Md Saat, Mai Mariam Mohamed Aminuddin, Abd Majid Darsono, Mohamad Harris Misran |

Publisher | American Institute of Physics Inc. |

ISBN (Electronic) | 9780735413528 |

DOIs | |

Publication status | Published - 2016 Feb 1 |

Event | 1st Progress in Applied Mathematics in Science and Engineering, PIAMSE 2015 - Bali, Indonesia Duration: 2015 Sep 29 → 2015 Oct 1 |

### Publication series

Name | AIP Conference Proceedings |
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Volume | 1705 |

ISSN (Print) | 0094-243X |

ISSN (Electronic) | 1551-7616 |

### Other

Other | 1st Progress in Applied Mathematics in Science and Engineering, PIAMSE 2015 |
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Country | Indonesia |

City | Bali |

Period | 15/9/29 → 15/10/1 |

### ASJC Scopus subject areas

- Physics and Astronomy(all)

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## Cite this

*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