Thomas Jenrich

  1. Guaranteed successful strategies for a square achievement game on an n by n grid.

    Authors: Thomas Jenrich
    Subjects: Discrete Mathematics
    Abstract

    At some places (see the references) Martin Erickson describes a certain game:

    "Two players alternately write O's (first player) and X's (second player) in
    the unoccupied cells of an n x n grid. The first player (if any) to occupy four
    cells at the vertices of a square with horizontal and vertical sides is the
    winner."

    Then he asks "What is the outcome of the game given optimal play?" or

    "What is the smallest n such that the first player has a winning strategy?"

    For n lower than 3 a win is obviously impossible.

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