Tic-Tac-Toe

The usual game of tic-tac-toe (also called Ticktacktoe) is 3-in-a-row on a board. However, ageneralized n-in-a-Row on an board can also be considered. For and 2 the first player can alwayswin. If the board is at least , the first player can win for .

However, for Tic-Tac-Toe which uses a board, a draw can always be obtained. If the board is at least, the first player can win for . For , a draw can always be obtained on a board, but thefirst player can win if the board is at least . The cases and 7 have not yet been fully analyzed for an board, although draws can always be forced for and 9. On an board, the first playercan win for , 2, 3, and 4, but a tie can always be forced for . For and , the first player can always win (Gardner 1979).

References

Ball, W. W. R. and Coxeter, H. S. M. Mathematical Recreations and Essays, 13th ed. New York: Dover, pp. 103-104, 1987.

de Fouquières, B. Ch. 18 in Les Jeux des Anciens, 2nd ed.. Paris, 1873.

Gardner, M. ``Mathematical Games: The Diverse Pleasures of Circles that Are Tangent to One Another.'' Sci. Amer. 240, 18-28, Jan. 1979a.

Gardner, M. ``Ticktacktoe Games.'' Ch. 9 in Wheels, Life, and Other Mathematical Amusements. New York: W. H. Freeman, 1983.

Stewart, I. ``A Shepherd Takes A Sheep Shot.'' Sci. Amer. 269, 154-156, 1993.

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