TY - JOUR
T1 - Cannibal Animal Games
T2 - A new variant of Tic-Tac-Toe
AU - Cardinal, Jean
AU - Collette, Sébastien
AU - Ito, Hiro
AU - Korman, Matias
AU - Langerman, Stefan
AU - Sakaidani, Hikaru
AU - Taslakian, Perouz
N1 - Publisher Copyright:
© 2015 Information Processing Society of Japan.
Copyright:
Copyright 2015 Elsevier B.V., All rights reserved.
PY - 2015
Y1 - 2015
N2 - This paper presents a new partial two-player game, called the cannibal animal game, which is a variant of Tic-Tac-Toe. The game is played on the infinite grid, where in each round a player chooses and occupies free cells. The first player Alice can occupy a cell in each turn and wins if she occupies a set of cells, the union of a subset of which is a translated, reflected and/or rotated copy of a previously agreed upon polyomino P (called an animal). The objective of the second player Bob is to prevent Alice from creating her animal by occupying in each round a translated, reflected and/or rotated copy of P. An animal is a cannibal if Bob has a winning strategy, and a non-cannibal otherwise. This paper presents some new tools, such as the bounding strategy and the punching lemma, to classify animals into cannibals or non-cannibals. We also show that the pairing strategy works for this problem.
AB - This paper presents a new partial two-player game, called the cannibal animal game, which is a variant of Tic-Tac-Toe. The game is played on the infinite grid, where in each round a player chooses and occupies free cells. The first player Alice can occupy a cell in each turn and wins if she occupies a set of cells, the union of a subset of which is a translated, reflected and/or rotated copy of a previously agreed upon polyomino P (called an animal). The objective of the second player Bob is to prevent Alice from creating her animal by occupying in each round a translated, reflected and/or rotated copy of P. An animal is a cannibal if Bob has a winning strategy, and a non-cannibal otherwise. This paper presents some new tools, such as the bounding strategy and the punching lemma, to classify animals into cannibals or non-cannibals. We also show that the pairing strategy works for this problem.
KW - Bounding strategy
KW - Cannibal animal
KW - Harary’s generalized Tic-Tac-Toe
KW - Pairing strategy
KW - Partial game
KW - Polyomino
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U2 - 10.2197/ipsjjip.23.265
DO - 10.2197/ipsjjip.23.265
M3 - Article
AN - SCOPUS:84929409385
VL - 23
SP - 265
EP - 271
JO - Journal of Information Processing
JF - Journal of Information Processing
SN - 0387-5806
IS - 3
ER -