The Japanese game go-moku is played by two players, X and

Chapter , Problem 8.10

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The Japanese game go-moku is played by two players, X and O, on a 19 19 grid. Players take turns placing markers, and the rst player to achieve ve of her markers consecutively in a row, column, or diagonal is the winner. Consider this game generalized to an n n board. LetGM = {hBi| B is a position in generalized go-moku, where player X has a winning strategy}.By a position we mean a board with markers placed on it, such as may occur in the middle of a play of the game, together with an indication of which player moves next. Show that GM PSPACE.

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