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Games to Play on a Tic-Tac-Toe Board

First played by the Romans, tic tac toe (called "Naughts and Crosses" in the UK), continues to capture the imagination of people all over the world, from excited children, to distracted adults, to some of the world's brightest mathematicians (albeit in an expanded form). The game evokes some entrancing nostalgia for a world more easily understood, more definite in its rules and more finite in its possibilities. However, for more adventurous types, the board is, often literally, a clean slate.
  1. Traditional Tic Tac Toe

    • This childhood game of Xs and Os attains a certain beauty in its symmetry and repetitive nature. Most adults will cease to be surprised by any outcome on the 3 x 3 board, and can usually predict the final pattern from the first move. A game of complete information and minimal skill, it usually requires self-sabotage to wind up with anything but a draw. However, being the first to get 3-in-a-row and drawing the line across the winning marks is among many people's most satisfying childhood memories.

    Expanded Tic Tac Toe (2 dimensions)

    • The first way that tic tac toe can be made into an adult game is to make the board larger. On a single plane, this simply means adding more parallel lines. Even a 4 x 4 board makes the game much more complicated, but not necessarily more satisfying. However, the game gets much more interesting if the object is not to be the first with a string, but to have the most strings. Make a 5 x 5 board, and alternate filling in Xs and Os until every spot is taken. Then, score the sets as follows: 1 point for 3-in-a-row, 3 points for 4-in-a-row, and 5 points for 5-in-a-row.

    Expanded Tic Tac Toe (3 dimensions)

    • This tic tac toe tests the players' spatial awareness. Draw three tic tac toe boards on the paper, one at the top, one in the middle and one at the bottom. If you can, draw them at such an angle that both players can easily imagine the three boards as existing in parallel planes. Players still try to be the first to get three in a row, but because they are working in a cube, not a square, the possibilities become much more intriguing. If someone wins, trying to draw a line across the planes can be part of the fun.

    Moveable Pieces (3 Men's Morris)

    • In the original Roman game, Xs and Os were not stagnant marks. Each player had only three pieces (stones or coins work well), and after placing them, could move them one at a time, on alternating turns, to try to block the other player and make a row. Since the pieces keep moving, there is never a permanent block on a particular row, and the game becomes much more dynamic. A version of this game, "3 Men's Morris," removes the possibility of making diagonal sets, and can be a good introduction to the medieval strategic pastime "9 Men's Morris."

    Magic Squares

    • The simple 3 x 3 tic tac toe board is also a great vehicle for mathematical experimentation. The players work together to place the digits 1 through 9 in each space, so that the sum of any horizontal, diagonal or vertical set equals 15. This can also be played as a solitary game. When the first magic square is finished, players can expand to 4 x 4, and the total of each row will equal 16.


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