Winning Strategies for Hexagonal Polyomino Achievement
نویسندگان
چکیده
In polyomino achievement games, two players alternately mark the cells of a tessellation and try to achieve a given polyomino. In [2], Bode and Harborth investigated polyomino achievement games for the hexagonal tessellation and determined all but five polyominoes with at most five cells whether they are achieved by the first player. In this paper, we show winning strategies for three hexagonal polyominoes with five cells called Y, Z, and C, which were left unsolved in [2]. Key–Words: Polyomino, Achievement game, Hexagonal tessellation, Winning strategy, Winner, Loser
منابع مشابه
Rectangular polyomino set weak (1, 2)-achievement games
In a polyomino set (1,2)-achievement game the maker and the breaker alternately mark one and two previously unmarked cells respectively. The maker's goal is to mark a set of cells congruent to one of a given set of polyominoes. The breaker tries to prevent the maker from achieving his goal. The teams of polyominoes for which the maker has a winning strategy is determined up to size 4. In set ac...
متن کاملPolyominoes with minimum site-perimeter and full set achievement games
The site-perimeter of a polyomino is the number of empty cells connected to the polyomino by an edge. A formula for the minimum site-perimeter with a given cell size is found. This formula is used to show the effectiveness of a simple random strategy in polyomino set achievement games.
متن کاملAnalysis of Translation Strategies Employed in Awards-winning Subtitled Dramas
The increasing impact of audiovisual media and film industry in particular has led researchers to think of audiovisual translation strategies. Huge investments in film industry need global markets. Hence, there is a need for qualified translations and systematic studies dedicated to this area are in great demand. This study aims to investigate translation strategies adopted in the translation o...
متن کاملA parallelogram tile fills the plane by translation in at most two distinct ways
We consider the tilings by translation of a single polyomino or tile on the square grid Z. It is well-known that there are two regular tilings of the plane, namely, parallelogram and hexagonal tilings. Although there exist tiles admitting an arbitrary number of distinct hexagon tilings, it has been conjectured that no polyomino admits more than two distinct parallogram tilings. In this paper, w...
متن کاملQBF Encoding of Generalized Tic-Tac-Toe
Harary’s generalized Tic-Tac-Toe is an achievement game for polyominoes, where two players alternately put a stone on a grid board, and the player who first achieves a given polyomino wins the game. It is known whether the first player has a winning strategy in the generalized Tic-Tac-Toe for almost all polyominoes except the one called Snaky. GTTT(p, q) is an extension of the generalized Tic-T...
متن کامل