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

© 1996-9

1999-05-26