A Hex Handicap Strategy
نویسندگان
چکیده
We give an ⌈ 6 ⌉-cell handicap strategy for the game of Hex on an n×n board: the first player is guaranteed victory if she is allowed to colour ⌈ 6 ⌉ cells on her first move. Our strategy exploits a new kind of inferior Hex cell.
منابع مشابه
Random-Turn Hex and Other Selection Games
Overview. The game of Hex , invented independently by Piet Hein in 1942 and John Nash in 1948 [9], has two players who take turns placing stones of their respective colors on the hexagons of a rhombus-shaped hexagonal grid (see Figure 1). A player wins by completing a path connecting the two opposite sides of his or her color. Although it is easy to show that player I has a winning strategy, it...
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Gale [D. Gale, The game of HEX and the Brouwer fixed-point theorem, American Mathematical Monthly 86 (1979) 818–827] has shown that the so called HEX game theorem that any HEX game has one winner is equivalent to the Brouwer fixed point theorem. In this paper we will show that under some assumptions about marking rules of HEX games, the HEX game theorem for a 6 · 6 HEX game is equivalent to the...
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تاریخ انتشار 2010