### Abstract

A parallel algorithm for solving the 'Hip' games based on an artificial neural network model is presented in this paper. The game of 'Hip' is named because of the hipster's reputed disdain for 'squares'. The rule of the game is to place the counters on a checkerboard so that four of them do not mark the corners of a square. The square may be of any size and be tipped at any angle. Normally this game is played by two players, where the game on a six-by-six checkerboard is the maximum size for the solution. The solution means that every player can place all the counters on the checkerboard without violations. In other words, the goal of our algorithm is to find the pattern of a draw game between players where they should not mark the corners of a square. In order to enlarge the size of the checkerboard where a solution exists, we modified the game as n/2 players play on an n-by-n checkerboard where n is an even number. The proposed parallel algorithm requires m × n^{2} processing elements for the m-player-n-by-n-checkerboard game to find the solution of the 'Hip' games. The algorithm is verified by solving six games where the size of the checkerboard is varied from 4 to 12.

Original language | English |
---|---|

Pages (from-to) | 97-106 |

Number of pages | 10 |

Journal | Neurocomputing |

Volume | 3 |

Issue number | 2 |

DOIs | |

Publication status | Published - 1991 |

Externally published | Yes |

### Fingerprint

### Keywords

- artificial neural network
- draw game pattern
- Hip game
- modified McCulloch-Pitts neuron model
- Parallel algorithm

### ASJC Scopus subject areas

- Artificial Intelligence
- Cellular and Molecular Neuroscience

### Cite this

*Neurocomputing*,

*3*(2), 97-106. https://doi.org/10.1016/0925-2312(91)90052-D

**A parallel algorithm for solving the 'Hip' games.** / Funabiki, Nobuo; Takefuji, Yoshiyasu.

Research output: Contribution to journal › Article

*Neurocomputing*, vol. 3, no. 2, pp. 97-106. https://doi.org/10.1016/0925-2312(91)90052-D

}

TY - JOUR

T1 - A parallel algorithm for solving the 'Hip' games

AU - Funabiki, Nobuo

AU - Takefuji, Yoshiyasu

PY - 1991

Y1 - 1991

N2 - A parallel algorithm for solving the 'Hip' games based on an artificial neural network model is presented in this paper. The game of 'Hip' is named because of the hipster's reputed disdain for 'squares'. The rule of the game is to place the counters on a checkerboard so that four of them do not mark the corners of a square. The square may be of any size and be tipped at any angle. Normally this game is played by two players, where the game on a six-by-six checkerboard is the maximum size for the solution. The solution means that every player can place all the counters on the checkerboard without violations. In other words, the goal of our algorithm is to find the pattern of a draw game between players where they should not mark the corners of a square. In order to enlarge the size of the checkerboard where a solution exists, we modified the game as n/2 players play on an n-by-n checkerboard where n is an even number. The proposed parallel algorithm requires m × n2 processing elements for the m-player-n-by-n-checkerboard game to find the solution of the 'Hip' games. The algorithm is verified by solving six games where the size of the checkerboard is varied from 4 to 12.

AB - A parallel algorithm for solving the 'Hip' games based on an artificial neural network model is presented in this paper. The game of 'Hip' is named because of the hipster's reputed disdain for 'squares'. The rule of the game is to place the counters on a checkerboard so that four of them do not mark the corners of a square. The square may be of any size and be tipped at any angle. Normally this game is played by two players, where the game on a six-by-six checkerboard is the maximum size for the solution. The solution means that every player can place all the counters on the checkerboard without violations. In other words, the goal of our algorithm is to find the pattern of a draw game between players where they should not mark the corners of a square. In order to enlarge the size of the checkerboard where a solution exists, we modified the game as n/2 players play on an n-by-n checkerboard where n is an even number. The proposed parallel algorithm requires m × n2 processing elements for the m-player-n-by-n-checkerboard game to find the solution of the 'Hip' games. The algorithm is verified by solving six games where the size of the checkerboard is varied from 4 to 12.

KW - artificial neural network

KW - draw game pattern

KW - Hip game

KW - modified McCulloch-Pitts neuron model

KW - Parallel algorithm

UR - http://www.scopus.com/inward/record.url?scp=0026220309&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0026220309&partnerID=8YFLogxK

U2 - 10.1016/0925-2312(91)90052-D

DO - 10.1016/0925-2312(91)90052-D

M3 - Article

AN - SCOPUS:0026220309

VL - 3

SP - 97

EP - 106

JO - Neurocomputing

JF - Neurocomputing

SN - 0925-2312

IS - 2

ER -